TSTP Solution File: ITP282^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP282^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 03:31:15 EDT 2023
% Result : Timeout 300.13s 298.54s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.55/2.72 % Problem : ITP282^1 : TPTP v8.1.2. Released v8.1.0.
% 2.55/2.73 % Command : do_cvc5 %s %d
% 5.17/2.94 % Computer : n025.cluster.edu
% 5.17/2.94 % Model : x86_64 x86_64
% 5.17/2.94 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 5.17/2.94 % Memory : 8042.1875MB
% 5.17/2.94 % OS : Linux 3.10.0-693.el7.x86_64
% 5.17/2.94 % CPULimit : 300
% 5.17/2.94 % WCLimit : 300
% 5.17/2.94 % DateTime : Sun Aug 27 11:28:11 EDT 2023
% 5.17/2.94 % CPUTime :
% 7.75/5.63 %----Proving TH0
% 7.75/5.64 %------------------------------------------------------------------------------
% 7.75/5.64 % File : ITP282^1 : TPTP v8.1.2. Released v8.1.0.
% 7.75/5.64 % Domain : Interactive Theorem Proving
% 7.75/5.64 % Problem : Sledgehammer problem VEBT_BuildupMemImp 00337_015688
% 7.75/5.64 % Version : [Des22] axioms.
% 7.75/5.64 % English :
% 7.75/5.64
% 7.75/5.64 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 7.75/5.64 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 7.75/5.64 % Source : [Des22]
% 7.75/5.64 % Names : 0093_VEBT_BuildupMemImp_00337_015688 [Des22]
% 7.75/5.64
% 7.75/5.64 % Status : Theorem
% 7.75/5.64 % Rating : 1.00 v8.1.0
% 7.75/5.64 % Syntax : Number of formulae : 11211 (5999 unt; 958 typ; 0 def)
% 7.75/5.64 % Number of atoms : 28381 (13532 equ; 0 cnn)
% 7.75/5.64 % Maximal formula atoms : 71 ( 2 avg)
% 7.75/5.64 % Number of connectives : 125413 (2841 ~; 502 |;1873 &;109928 @)
% 7.75/5.64 % ( 0 <=>;10269 =>; 0 <=; 0 <~>)
% 7.75/5.64 % Maximal formula depth : 39 ( 6 avg)
% 7.75/5.64 % Number of types : 85 ( 84 usr)
% 7.75/5.64 % Number of type conns : 3364 (3364 >; 0 *; 0 +; 0 <<)
% 7.75/5.64 % Number of symbols : 877 ( 874 usr; 62 con; 0-8 aty)
% 7.75/5.64 % Number of variables : 25381 (1332 ^;23182 !; 867 ?;25381 :)
% 7.75/5.64 % SPC : TH0_THM_EQU_NAR
% 7.75/5.64
% 7.75/5.64 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 7.75/5.64 % from the van Emde Boas Trees session in the Archive of Formal
% 7.75/5.64 % proofs -
% 7.75/5.64 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 7.75/5.64 % 2022-02-18 18:08:53.009
% 7.75/5.64 %------------------------------------------------------------------------------
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% 7.75/5.64 thf(sy_c_Least__significant__bit_Olsb__class_Olsb_001t__Int__Oint,type,
% 7.75/5.64 least_4859182151741483524sb_int: int > $o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 7.75/5.64 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oappend_001_Eo,type,
% 7.75/5.64 append_o: list_o > list_o > list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 7.75/5.64 append_int: list_int > list_int > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 7.75/5.64 append_nat: list_nat > list_nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 7.75/5.64 distinct_int: list_int > $o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 7.75/5.64 distinct_nat: list_nat > $o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
% 7.75/5.64 filter_nat2: ( nat > $o ) > list_nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Ofoldr_001_Eo_001t__Nat__Onat,type,
% 7.75/5.64 foldr_o_nat: ( $o > nat > nat ) > list_o > nat > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Ofoldr_001t__Int__Oint_001t__Nat__Onat,type,
% 7.75/5.64 foldr_int_nat: ( int > nat > nat ) > list_int > nat > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Ofoldr_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.75/5.64 foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Nat__Onat,type,
% 7.75/5.64 foldr_real_nat: ( real > nat > nat ) > list_real > nat > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Real__Oreal,type,
% 7.75/5.64 foldr_real_real: ( real > real > real ) > list_real > real > real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 7.75/5.64 linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.75/5.64 linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 7.75/5.64 linord2614967742042102400et_nat: set_nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 7.75/5.64 cons_o: $o > list_o > list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 7.75/5.64 cons_int: int > list_int > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 7.75/5.64 cons_nat: nat > list_nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_ONil_001_Eo,type,
% 7.75/5.64 nil_o: list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 7.75/5.64 nil_int: list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 7.75/5.64 nil_nat: list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 7.75/5.64 hd_nat: list_nat > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001_Eo_001_Eo,type,
% 7.75/5.64 map_o_o: ( $o > $o ) > list_o > list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001_Eo_001t__Nat__Onat,type,
% 7.75/5.64 map_o_nat: ( $o > nat ) > list_o > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001_Eo_001t__Real__Oreal,type,
% 7.75/5.64 map_o_real: ( $o > real ) > list_o > list_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 map_o_VEBT_VEBT: ( $o > vEBT_VEBT ) > list_o > list_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 7.75/5.64 map_complex_complex: ( complex > complex ) > list_complex > list_complex ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 7.75/5.64 map_complex_real: ( complex > real ) > list_complex > list_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001_Eo,type,
% 7.75/5.64 map_int_o: ( int > $o ) > list_int > list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Int__Oint,type,
% 7.75/5.64 map_int_int: ( int > int ) > list_int > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Nat__Onat,type,
% 7.75/5.64 map_int_nat: ( int > nat ) > list_int > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Real__Oreal,type,
% 7.75/5.64 map_int_real: ( int > real ) > list_int > list_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 map_int_VEBT_VEBT: ( int > vEBT_VEBT ) > list_int > list_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001_Eo,type,
% 7.75/5.64 map_nat_o: ( nat > $o ) > list_nat > list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 7.75/5.64 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Real__Oreal,type,
% 7.75/5.64 map_nat_real: ( nat > real ) > list_nat > list_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 map_nat_VEBT_VEBT: ( nat > vEBT_VEBT ) > list_nat > list_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001_Eo,type,
% 7.75/5.64 map_real_o: ( real > $o ) > list_real > list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001t__Nat__Onat,type,
% 7.75/5.64 map_real_nat: ( real > nat ) > list_real > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001t__Real__Oreal,type,
% 7.75/5.64 map_real_real: ( real > real ) > list_real > list_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 map_real_VEBT_VEBT: ( real > vEBT_VEBT ) > list_real > list_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__VEBT____BuildupMemImp__OVEBTi_001t__Int__Oint,type,
% 7.75/5.64 map_VEBT_VEBTi_int: ( vEBT_VEBTi > int ) > list_VEBT_VEBTi > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__VEBT____BuildupMemImp__OVEBTi_001t__Nat__Onat,type,
% 7.75/5.64 map_VEBT_VEBTi_nat: ( vEBT_VEBTi > nat ) > list_VEBT_VEBTi > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.64 map_VE483055756984248624_VEBTi: ( vEBT_VEBTi > vEBT_VEBTi ) > list_VEBT_VEBTi > list_VEBT_VEBTi ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 map_VE7998069337340375161T_VEBT: ( vEBT_VEBTi > vEBT_VEBT ) > list_VEBT_VEBTi > list_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 7.75/5.64 map_VEBT_VEBT_int: ( vEBT_VEBT > int ) > list_VEBT_VEBT > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 7.75/5.64 map_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 7.75/5.64 map_VEBT_VEBT_real: ( vEBT_VEBT > real ) > list_VEBT_VEBT > list_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.64 map_VE7029150624388687525_VEBTi: ( vEBT_VEBT > vEBT_VEBTi ) > list_VEBT_VEBT > list_VEBT_VEBTi ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 7.75/5.64 set_o2: list_o > set_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Oset_001t__Code____Numeral__Ointeger,type,
% 7.75/5.64 set_Code_integer2: list_Code_integer > set_Code_integer ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 7.75/5.64 set_complex2: list_complex > set_complex ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 7.75/5.64 set_int2: list_int > set_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 7.75/5.64 set_nat2: list_nat > set_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 7.75/5.64 set_real2: list_real > set_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Oset_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.64 set_VEBT_VEBTi2: list_VEBT_VEBTi > set_VEBT_VEBTi ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 7.75/5.64 tl_nat: list_nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist__update_001_Eo,type,
% 7.75/5.64 list_update_o: list_o > nat > $o > list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 7.75/5.64 list_update_complex: list_complex > nat > complex > list_complex ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 7.75/5.64 list_update_int: list_int > nat > int > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 7.75/5.64 list_update_nat: list_nat > nat > nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 7.75/5.64 list_update_real: list_real > nat > real > list_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist__update_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.64 list_u6098035379799741383_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi > list_VEBT_VEBTi ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Onth_001_Eo,type,
% 7.75/5.64 nth_o: list_o > nat > $o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 7.75/5.64 nth_complex: list_complex > nat > complex ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 7.75/5.64 nth_int: list_int > nat > int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 7.75/5.64 nth_nat: list_nat > nat > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 7.75/5.64 nth_real: list_real > nat > real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Onth_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.64 nth_VEBT_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oreplicate_001_Eo,type,
% 7.75/5.64 replicate_o: nat > $o > list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 7.75/5.64 replicate_complex: nat > complex > list_complex ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 7.75/5.64 replicate_int: nat > int > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 7.75/5.64 replicate_nat: nat > nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 7.75/5.64 replicate_real: nat > real > list_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oreplicate_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.64 replicate_VEBT_VEBTi: nat > vEBT_VEBTi > list_VEBT_VEBTi ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oupt,type,
% 7.75/5.64 upt: nat > nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oupto,type,
% 7.75/5.64 upto: int > int > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oupto__aux,type,
% 7.75/5.64 upto_aux: int > int > list_int > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_List_Oupto__rel,type,
% 7.75/5.64 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Misc_Oslice_001_Eo,type,
% 7.75/5.64 slice_o: nat > nat > list_o > list_o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Misc_Oslice_001t__Int__Oint,type,
% 7.75/5.64 slice_int: nat > nat > list_int > list_int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Misc_Oslice_001t__Nat__Onat,type,
% 7.75/5.64 slice_nat: nat > nat > list_nat > list_nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Misc_Oslice_001t__Real__Oreal,type,
% 7.75/5.64 slice_real: nat > nat > list_real > list_real ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Misc_Oslice_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.64 slice_VEBT_VEBTi: nat > nat > list_VEBT_VEBTi > list_VEBT_VEBTi ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Misc_Oslice_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.64 slice_VEBT_VEBT: nat > nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_OSuc,type,
% 7.75/5.64 suc: nat > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 7.75/5.64 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 7.75/5.64 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 7.75/5.64 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 7.75/5.64 semiri4939895301339042750nteger: nat > code_integer ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 7.75/5.64 semiri8010041392384452111omplex: nat > complex ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 7.75/5.64 semiri4216267220026989637d_enat: nat > extended_enat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 7.75/5.64 semiri1314217659103216013at_int: nat > int ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 7.75/5.64 semiri1316708129612266289at_nat: nat > nat ).
% 7.75/5.64
% 7.75/5.64 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 7.75/5.64 semiri681578069525770553at_rat: nat > rat ).
% 7.75/5.64
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% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Real__Oreal,type,
% 7.75/5.65 set_or66887138388493659n_real: real > real > set_real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 7.75/5.65 set_or3540276404033026485et_nat: set_nat > set_nat > set_set_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 7.75/5.65 set_ord_atMost_nat: nat > set_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Code____Numeral__Ointeger,type,
% 7.75/5.65 set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 7.75/5.65 set_or6656581121297822940st_int: int > int > set_int ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 7.75/5.65 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Code____Numeral__Ointeger,type,
% 7.75/5.65 set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 7.75/5.65 set_or5832277885323065728an_int: int > int > set_int ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 7.75/5.65 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 7.75/5.65 set_or1633881224788618240n_real: real > real > set_real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 7.75/5.65 set_or1210151606488870762an_nat: nat > set_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 7.75/5.65 set_or5849166863359141190n_real: real > set_real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 7.75/5.65 set_ord_lessThan_nat: nat > set_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 7.75/5.65 set_or5984915006950818249n_real: real > set_real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Signed__Division_Osigned__division__class_Osigned__divide_001t__Int__Oint,type,
% 7.75/5.65 signed6714573509424544716de_int: int > int > int ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Signed__Division_Osigned__division__class_Osigned__modulo_001t__Int__Oint,type,
% 7.75/5.65 signed6292675348222524329lo_int: int > int > int ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_String_Oascii__of,type,
% 7.75/5.65 ascii_of: char > char ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_String_Ochar_OChar,type,
% 7.75/5.65 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_String_Ochar_Osize__char,type,
% 7.75/5.65 size_char: char > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 7.75/5.65 comm_s629917340098488124ar_nat: char > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_String_Ointeger__of__char,type,
% 7.75/5.65 integer_of_char: char > code_integer ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 7.75/5.65 unique3096191561947761185of_nat: nat > char ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Syntax__Match_Osyntax__fo__nomatch_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 7.75/5.65 syntax7398250324933576852n_assn: assn > assn > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Time__Reasoning_Ohtt_001t__Nat__Onat,type,
% 7.75/5.65 time_htt_nat: assn > heap_Time_Heap_nat > ( nat > assn ) > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Time__Reasoning_Otime_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.65 time_time_VEBT_VEBTi: heap_T8145700208782473153_VEBTi > heap_e7401611519738050253t_unit > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 7.75/5.65 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 7.75/5.65 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 7.75/5.65 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 7.75/5.65 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 7.75/5.65 topolo2815343760600316023s_real: real > filter_real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 7.75/5.65 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Oarccos,type,
% 7.75/5.65 arccos: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 7.75/5.65 arcosh_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Oarcsin,type,
% 7.75/5.65 arcsin: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Oarctan,type,
% 7.75/5.65 arctan: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 7.75/5.65 arsinh_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 7.75/5.65 artanh_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 7.75/5.65 cos_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Ocos__coeff,type,
% 7.75/5.65 cos_coeff: nat > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 7.75/5.65 cosh_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 7.75/5.65 cot_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 7.75/5.65 exp_complex: complex > complex ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 7.75/5.65 exp_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 7.75/5.65 ln_ln_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Olog,type,
% 7.75/5.65 log: real > real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Opi,type,
% 7.75/5.65 pi: real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 7.75/5.65 powr_real: real > real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 7.75/5.65 sin_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Osin__coeff,type,
% 7.75/5.65 sin_coeff: nat > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 7.75/5.65 sinh_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 7.75/5.65 tan_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 7.75/5.65 tanh_complex: complex > complex ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 7.75/5.65 tanh_real: real > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Type__Length_Olen0__class_Olen__of_001t__Enum__Ofinite____1,type,
% 7.75/5.65 type_l31302759751748491nite_1: itself_finite_1 > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Type__Length_Olen0__class_Olen__of_001t__Enum__Ofinite____2,type,
% 7.75/5.65 type_l31302759751748492nite_2: itself_finite_2 > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Type__Length_Olen0__class_Olen__of_001t__Enum__Ofinite____3,type,
% 7.75/5.65 type_l31302759751748493nite_3: itself_finite_3 > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Type__Length_Olen0__class_Olen__of_001t__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Onum1_J_J_J_J_J,type,
% 7.75/5.65 type_l796852477590012082l_num1: itself8794530163899892676l_num1 > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Type__Length_Olen0__class_Olen__of_001t__Numeral____Type__Onum0,type,
% 7.75/5.65 type_l4264026598287037464l_num0: itself_Numeral_num0 > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Type__Length_Olen0__class_Olen__of_001t__Numeral____Type__Onum1,type,
% 7.75/5.65 type_l4264026598287037465l_num1: itself_Numeral_num1 > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Uint32_OUint32,type,
% 7.75/5.65 uint322: code_integer > uint32 ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Uint32_OUint32__signed,type,
% 7.75/5.65 uint32_signed: code_integer > uint32 ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 7.75/5.65 vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t__rel,type,
% 7.75/5.65 vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 7.75/5.65
% 7.75/5.65 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,
% 7.75/5.65 vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 7.75/5.65 vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 7.75/5.65 vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d,type,
% 7.75/5.65 vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H,type,
% 7.75/5.65 vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H__rel,type,
% 7.75/5.65 vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d__rel,type,
% 7.75/5.65 vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c,type,
% 7.75/5.65 vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H,type,
% 7.75/5.65 vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H__rel,type,
% 7.75/5.65 vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c__rel,type,
% 7.75/5.65 vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi,type,
% 7.75/5.65 vEBT_V441764108873111860ildupi: nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi__rel,type,
% 7.75/5.65 vEBT_V2957053500504383685pi_rel: nat > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ohighi,type,
% 7.75/5.65 vEBT_VEBT_highi: nat > nat > heap_Time_Heap_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Olowi,type,
% 7.75/5.65 vEBT_VEBT_lowi: nat > nat > heap_Time_Heap_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__buildupi_H,type,
% 7.75/5.65 vEBT_V739175172307565963ildupi: nat > heap_T8145700208782473153_VEBTi ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_OLeafi,type,
% 7.75/5.65 vEBT_Leafi: $o > $o > vEBT_VEBTi ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_ONodei,type,
% 7.75/5.65 vEBT_Nodei: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > vEBT_VEBTi ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_Osize__VEBTi,type,
% 7.75/5.65 vEBT_size_VEBTi: vEBT_VEBTi > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_Ovebt__assn__raw,type,
% 7.75/5.65 vEBT_vebt_assn_raw: vEBT_VEBT > vEBT_VEBTi > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__BuildupMemImp_Ovebt__assn__raw__rel,type,
% 7.75/5.65 vEBT_v8524038756793281170aw_rel: produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 7.75/5.65 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 7.75/5.65 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 7.75/5.65 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 7.75/5.65 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 7.75/5.65 vEBT_VEBT_high: nat > nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 7.75/5.65 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 7.75/5.65 vEBT_VEBT_low: nat > nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 7.75/5.65 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 7.75/5.65 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 7.75/5.65 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 7.75/5.65 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 7.75/5.65 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 7.75/5.65 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 7.75/5.65 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 7.75/5.65 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 7.75/5.65 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 7.75/5.65 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e,type,
% 7.75/5.65 vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e__rel,type,
% 7.75/5.65 vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__DeleteBounds_OVEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H,type,
% 7.75/5.65 vEBT_V1232361888498592333_e_t_e: vEBT_VEBT > nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__DeleteBounds_OVEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H__rel,type,
% 7.75/5.65 vEBT_V6368547301243506412_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 7.75/5.65 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 7.75/5.65 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 7.75/5.65 vEBT_VEBT_height: vEBT_VEBT > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 7.75/5.65 vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 7.75/5.65 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 7.75/5.65 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.65 vEBT_L1528199826722428489_VEBTi: set_nat > ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001_Eo_001_Eo,type,
% 7.75/5.65 vEBT_L7363604446928714179sn_o_o: ( $o > $o > assn ) > list_o > list_o > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001_Eo_001t__Nat__Onat,type,
% 7.75/5.65 vEBT_L4785011123346445925_o_nat: ( $o > nat > assn ) > list_o > list_nat > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001_Eo_001t__Real__Oreal,type,
% 7.75/5.65 vEBT_L4725278957065240257o_real: ( $o > real > assn ) > list_o > list_real > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 7.75/5.65 vEBT_L4260503343685368993omplex: ( complex > complex > assn ) > list_complex > list_complex > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 7.75/5.65 vEBT_L134985006839036959ex_int: ( complex > int > assn ) > list_complex > list_int > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Complex__Ocomplex_001t__Nat__Onat,type,
% 7.75/5.65 vEBT_L137475477348087235ex_nat: ( complex > nat > assn ) > list_complex > list_nat > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 7.75/5.65 vEBT_L2479436891206192927x_real: ( complex > real > assn ) > list_complex > list_real > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Complex__Ocomplex_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.65 vEBT_L8524933119956041985T_VEBT: ( complex > vEBT_VEBT > assn ) > list_complex > list_VEBT_VEBT > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001_Eo,type,
% 7.75/5.65 vEBT_L6066640139021943271_int_o: ( int > $o > assn ) > list_int > list_o > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__Real__Oreal,type,
% 7.75/5.65 vEBT_L8288995350762215837t_real: ( int > real > assn ) > list_int > list_real > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Nat__Onat_001_Eo,type,
% 7.75/5.65 vEBT_L7887682484454631235_nat_o: ( nat > $o > assn ) > list_nat > list_o > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Nat__Onat_001t__Real__Oreal,type,
% 7.75/5.65 vEBT_L6102073776069194049t_real: ( nat > real > assn ) > list_nat > list_real > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001_Eo,type,
% 7.75/5.65 vEBT_L6234343332106409831real_o: ( real > $o > assn ) > list_real > list_o > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__Nat__Onat,type,
% 7.75/5.65 vEBT_L1446010312343316929al_nat: ( real > nat > assn ) > list_real > list_nat > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__Real__Oreal,type,
% 7.75/5.65 vEBT_L1930518968523514909l_real: ( real > real > assn ) > list_real > list_real > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Complex__Ocomplex,type,
% 7.75/5.65 vEBT_L2162147798726695391omplex: ( vEBT_VEBT > complex > assn ) > list_VEBT_VEBT > list_complex > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 7.75/5.65 vEBT_L8294436054247626077BT_int: ( vEBT_VEBT > int > assn ) > list_VEBT_VEBT > list_int > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 7.75/5.65 vEBT_L8296926524756676353BT_nat: ( vEBT_VEBT > nat > assn ) > list_VEBT_VEBT > list_nat > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 7.75/5.65 vEBT_L5781919052683127133T_real: ( vEBT_VEBT > real > assn ) > list_VEBT_VEBT > list_real > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.65 vEBT_L6296928887356842470_VEBTi: ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.65 vEBT_L1279224858307276611T_VEBT: ( vEBT_VEBT > vEBT_VEBT > assn ) > list_VEBT_VEBT > list_VEBT_VEBT > assn ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 7.75/5.65 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 7.75/5.65 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 7.75/5.65 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 7.75/5.65 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 7.75/5.65 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 7.75/5.65 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 7.75/5.65 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 7.75/5.65 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 7.75/5.65 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 7.75/5.65 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 7.75/5.65 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 7.75/5.65 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 7.75/5.65 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 7.75/5.65 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 7.75/5.65 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 7.75/5.65 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 7.75/5.65 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 7.75/5.65 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 7.75/5.65 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 7.75/5.65 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 7.75/5.65 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 7.75/5.65 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 7.75/5.65 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 7.75/5.65 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d,type,
% 7.75/5.65 vEBT_V8646137997579335489_i_l_d: nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p,type,
% 7.75/5.65 vEBT_V8346862874174094_d_u_p: nat > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p__rel,type,
% 7.75/5.65 vEBT_V1247956027447740395_p_rel: nat > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d__rel,type,
% 7.75/5.65 vEBT_V5144397997797733112_d_rel: nat > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt,type,
% 7.75/5.65 vEBT_VEBT_cnt: vEBT_VEBT > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt_H,type,
% 7.75/5.65 vEBT_VEBT_cnt2: vEBT_VEBT > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt_H__rel,type,
% 7.75/5.65 vEBT_VEBT_cnt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt__rel,type,
% 7.75/5.65 vEBT_VEBT_cnt_rel2: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace,type,
% 7.75/5.65 vEBT_VEBT_space: vEBT_VEBT > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace_H,type,
% 7.75/5.65 vEBT_VEBT_space2: vEBT_VEBT > nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace_H__rel,type,
% 7.75/5.65 vEBT_VEBT_space_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace__rel,type,
% 7.75/5.65 vEBT_VEBT_space_rel2: vEBT_VEBT > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 7.75/5.65 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 7.75/5.65 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 7.75/5.65 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 7.75/5.65 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 7.75/5.65 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 7.75/5.65 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____BuildupMemImp__OVEBTi_J,type,
% 7.75/5.65 accp_P7675410724331315407_VEBTi: ( produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o ) > produc3625547720036274456_VEBTi > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.65 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 7.75/5.65 fChoice_real: ( real > $o ) > real ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001_Eo,type,
% 7.75/5.65 member_o: $o > set_o > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 7.75/5.65 member_Code_integer: code_integer > set_Code_integer > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 7.75/5.65 member_complex: complex > set_complex > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__Int__Oint,type,
% 7.75/5.65 member_int: int > set_int > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 7.75/5.65 member_list_o: list_o > set_list_o > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 7.75/5.65 member_list_int: list_int > set_list_int > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 7.75/5.65 member_list_nat: list_nat > set_list_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__List__Olist_It__Real__Oreal_J,type,
% 7.75/5.65 member_list_real: list_real > set_list_real > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__Nat__Onat,type,
% 7.75/5.65 member_nat: nat > set_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__Num__Onum,type,
% 7.75/5.65 member_num: num > set_num > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__Rat__Orat,type,
% 7.75/5.65 member_rat: rat > set_rat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__Real__Oreal,type,
% 7.75/5.65 member_real: real > set_real > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 7.75/5.65 member_set_nat: set_nat > set_set_nat > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 7.75/5.65 member_VEBT_VEBTi: vEBT_VEBTi > set_VEBT_VEBTi > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 7.75/5.65 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 7.75/5.65
% 7.75/5.65 thf(sy_v_na____,type,
% 7.75/5.65 na: nat ).
% 7.75/5.65
% 7.75/5.65 thf(sy_v_x____,type,
% 7.75/5.65 x: list_VEBT_VEBTi ).
% 7.75/5.65
% 7.75/5.65 thf(sy_v_xa____,type,
% 7.75/5.65 xa: array_VEBT_VEBTi ).
% 7.75/5.65
% 7.75/5.65 thf(sy_v_xb____,type,
% 7.75/5.65 xb: vEBT_VEBTi ).
% 7.75/5.65
% 7.75/5.65 thf(sy_v_xc____,type,
% 7.75/5.65 xc: vEBT_VEBTi ).
% 7.75/5.65
% 7.75/5.65 % Relevant facts (10206)
% 7.75/5.65 thf(fact_0_VEBTi_Oinject_I1_J,axiom,
% 7.75/5.65 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi,Y11: option4927543243414619207at_nat,Y12: nat,Y13: array_VEBT_VEBTi,Y14: vEBT_VEBTi] :
% 7.75/5.65 ( ( ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 )
% 7.75/5.65 = ( vEBT_Nodei @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 7.75/5.65 = ( ( X11 = Y11 )
% 7.75/5.65 & ( X12 = Y12 )
% 7.75/5.65 & ( X13 = Y13 )
% 7.75/5.65 & ( X14 = Y14 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % VEBTi.inject(1)
% 7.75/5.65 thf(fact_1_assnle,axiom,
% 7.75/5.65 ! [TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] : ( entails @ ( times_times_assn @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % assnle
% 7.75/5.65 thf(fact_2_False,axiom,
% 7.75/5.65 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ na ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % False
% 7.75/5.65 thf(fact_3_div2__Suc__Suc,axiom,
% 7.75/5.65 ! [M: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div2_Suc_Suc
% 7.75/5.65 thf(fact_4_ent__pure__pre__iff,axiom,
% 7.75/5.65 ! [P: assn,B: $o,Q: assn] :
% 7.75/5.65 ( ( entails @ ( times_times_assn @ P @ ( pure_assn @ B ) ) @ Q )
% 7.75/5.65 = ( B
% 7.75/5.65 => ( entails @ P @ Q ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ent_pure_pre_iff
% 7.75/5.65 thf(fact_5_power__odd__eq,axiom,
% 7.75/5.65 ! [A: complex,N: nat] :
% 7.75/5.65 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.65 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_odd_eq
% 7.75/5.65 thf(fact_6_power__odd__eq,axiom,
% 7.75/5.65 ! [A: code_integer,N: nat] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.65 = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_odd_eq
% 7.75/5.65 thf(fact_7_power__odd__eq,axiom,
% 7.75/5.65 ! [A: assn,N: nat] :
% 7.75/5.65 ( ( power_power_assn @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.65 = ( times_times_assn @ A @ ( power_power_assn @ ( power_power_assn @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_odd_eq
% 7.75/5.65 thf(fact_8_power__odd__eq,axiom,
% 7.75/5.65 ! [A: real,N: nat] :
% 7.75/5.65 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.65 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_odd_eq
% 7.75/5.65 thf(fact_9_power__odd__eq,axiom,
% 7.75/5.65 ! [A: nat,N: nat] :
% 7.75/5.65 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.65 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_odd_eq
% 7.75/5.65 thf(fact_10_power__odd__eq,axiom,
% 7.75/5.65 ! [A: int,N: nat] :
% 7.75/5.65 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.65 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_odd_eq
% 7.75/5.65 thf(fact_11_merge__pure__star,axiom,
% 7.75/5.65 ! [A: $o,B: $o] :
% 7.75/5.65 ( ( times_times_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 7.75/5.65 = ( pure_assn
% 7.75/5.65 @ ( A
% 7.75/5.65 & B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % merge_pure_star
% 7.75/5.65 thf(fact_12_power__even__eq,axiom,
% 7.75/5.65 ! [A: assn,N: nat] :
% 7.75/5.65 ( ( power_power_assn @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 = ( power_power_assn @ ( power_power_assn @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_even_eq
% 7.75/5.65 thf(fact_13_power__even__eq,axiom,
% 7.75/5.65 ! [A: nat,N: nat] :
% 7.75/5.65 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_even_eq
% 7.75/5.65 thf(fact_14_power__even__eq,axiom,
% 7.75/5.65 ! [A: real,N: nat] :
% 7.75/5.65 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_even_eq
% 7.75/5.65 thf(fact_15_power__even__eq,axiom,
% 7.75/5.65 ! [A: int,N: nat] :
% 7.75/5.65 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_even_eq
% 7.75/5.65 thf(fact_16_power__even__eq,axiom,
% 7.75/5.65 ! [A: complex,N: nat] :
% 7.75/5.65 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_even_eq
% 7.75/5.65 thf(fact_17_power__even__eq,axiom,
% 7.75/5.65 ! [A: code_integer,N: nat] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 = ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_even_eq
% 7.75/5.65 thf(fact_18_Suc__double__not__eq__double,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.65 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % Suc_double_not_eq_double
% 7.75/5.65 thf(fact_19_double__not__eq__Suc__double,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 7.75/5.65 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % double_not_eq_Suc_double
% 7.75/5.65 thf(fact_20_times__divide__eq__left,axiom,
% 7.75/5.65 ! [B: complex,C: complex,A: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 7.75/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % times_divide_eq_left
% 7.75/5.65 thf(fact_21_times__divide__eq__left,axiom,
% 7.75/5.65 ! [B: real,C: real,A: real] :
% 7.75/5.65 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 7.75/5.65 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % times_divide_eq_left
% 7.75/5.65 thf(fact_22_times__divide__eq__left,axiom,
% 7.75/5.65 ! [B: rat,C: rat,A: rat] :
% 7.75/5.65 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 7.75/5.65 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % times_divide_eq_left
% 7.75/5.65 thf(fact_23_divide__divide__eq__left,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 7.75/5.65 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_eq_left
% 7.75/5.65 thf(fact_24_divide__divide__eq__left,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 7.75/5.65 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_eq_left
% 7.75/5.65 thf(fact_25_divide__divide__eq__left,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 7.75/5.65 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_eq_left
% 7.75/5.65 thf(fact_26_divide__divide__eq__right,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_eq_right
% 7.75/5.65 thf(fact_27_divide__divide__eq__right,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 7.75/5.65 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_eq_right
% 7.75/5.65 thf(fact_28_divide__divide__eq__right,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.65 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_eq_right
% 7.75/5.65 thf(fact_29_times__divide__eq__right,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % times_divide_eq_right
% 7.75/5.65 thf(fact_30_times__divide__eq__right,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 7.75/5.65 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % times_divide_eq_right
% 7.75/5.65 thf(fact_31_times__divide__eq__right,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.65 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % times_divide_eq_right
% 7.75/5.65 thf(fact_32_power4__eq__xxxx,axiom,
% 7.75/5.65 ! [X: assn] :
% 7.75/5.65 ( ( power_power_assn @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ X @ X ) @ X ) @ X ) ) ).
% 7.75/5.65
% 7.75/5.65 % power4_eq_xxxx
% 7.75/5.65 thf(fact_33_power4__eq__xxxx,axiom,
% 7.75/5.65 ! [X: real] :
% 7.75/5.65 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 7.75/5.65
% 7.75/5.65 % power4_eq_xxxx
% 7.75/5.65 thf(fact_34_power4__eq__xxxx,axiom,
% 7.75/5.65 ! [X: nat] :
% 7.75/5.65 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 7.75/5.65
% 7.75/5.65 % power4_eq_xxxx
% 7.75/5.65 thf(fact_35_power4__eq__xxxx,axiom,
% 7.75/5.65 ! [X: int] :
% 7.75/5.65 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 7.75/5.65
% 7.75/5.65 % power4_eq_xxxx
% 7.75/5.65 thf(fact_36_power4__eq__xxxx,axiom,
% 7.75/5.65 ! [X: code_integer] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ X @ X ) @ X ) @ X ) ) ).
% 7.75/5.65
% 7.75/5.65 % power4_eq_xxxx
% 7.75/5.65 thf(fact_37_power4__eq__xxxx,axiom,
% 7.75/5.65 ! [X: complex] :
% 7.75/5.65 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 7.75/5.65
% 7.75/5.65 % power4_eq_xxxx
% 7.75/5.65 thf(fact_38_pure__assn__eq__conv,axiom,
% 7.75/5.65 ! [P: $o,Q: $o] :
% 7.75/5.65 ( ( ( pure_assn @ P )
% 7.75/5.65 = ( pure_assn @ Q ) )
% 7.75/5.65 = ( P = Q ) ) ).
% 7.75/5.65
% 7.75/5.65 % pure_assn_eq_conv
% 7.75/5.65 thf(fact_39_power__mult__numeral,axiom,
% 7.75/5.65 ! [A: nat,M: num,N: num] :
% 7.75/5.65 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_numeral
% 7.75/5.65 thf(fact_40_power__mult__numeral,axiom,
% 7.75/5.65 ! [A: real,M: num,N: num] :
% 7.75/5.65 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_numeral
% 7.75/5.65 thf(fact_41_power__mult__numeral,axiom,
% 7.75/5.65 ! [A: int,M: num,N: num] :
% 7.75/5.65 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_numeral
% 7.75/5.65 thf(fact_42_power__mult__numeral,axiom,
% 7.75/5.65 ! [A: complex,M: num,N: num] :
% 7.75/5.65 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_numeral
% 7.75/5.65 thf(fact_43_power__mult__numeral,axiom,
% 7.75/5.65 ! [A: code_integer,M: num,N: num] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_numeral
% 7.75/5.65 thf(fact_44_power__mult__numeral,axiom,
% 7.75/5.65 ! [A: assn,M: num,N: num] :
% 7.75/5.65 ( ( power_power_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( power_power_assn @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_numeral
% 7.75/5.65 thf(fact_45_even__mult__iff,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 7.75/5.65 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_mult_iff
% 7.75/5.65 thf(fact_46_even__mult__iff,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 7.75/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_mult_iff
% 7.75/5.65 thf(fact_47_even__mult__iff,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 7.75/5.65 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_mult_iff
% 7.75/5.65 thf(fact_48_even__Suc__Suc__iff,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 7.75/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_Suc_Suc_iff
% 7.75/5.65 thf(fact_49_even__Suc,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 7.75/5.65 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_Suc
% 7.75/5.65 thf(fact_50_even__Suc__div__two,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.65 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_Suc_div_two
% 7.75/5.65 thf(fact_51_odd__Suc__div__two,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.65 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % odd_Suc_div_two
% 7.75/5.65 thf(fact_52_dvd__power__same,axiom,
% 7.75/5.65 ! [X: nat,Y: nat,N: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ X @ Y )
% 7.75/5.65 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_power_same
% 7.75/5.65 thf(fact_53_dvd__power__same,axiom,
% 7.75/5.65 ! [X: real,Y: real,N: nat] :
% 7.75/5.65 ( ( dvd_dvd_real @ X @ Y )
% 7.75/5.65 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_power_same
% 7.75/5.65 thf(fact_54_dvd__power__same,axiom,
% 7.75/5.65 ! [X: int,Y: int,N: nat] :
% 7.75/5.65 ( ( dvd_dvd_int @ X @ Y )
% 7.75/5.65 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_power_same
% 7.75/5.65 thf(fact_55_dvd__power__same,axiom,
% 7.75/5.65 ! [X: complex,Y: complex,N: nat] :
% 7.75/5.65 ( ( dvd_dvd_complex @ X @ Y )
% 7.75/5.65 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_power_same
% 7.75/5.65 thf(fact_56_dvd__power__same,axiom,
% 7.75/5.65 ! [X: code_integer,Y: code_integer,N: nat] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ X @ Y )
% 7.75/5.65 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_power_same
% 7.75/5.65 thf(fact_57_div__power,axiom,
% 7.75/5.65 ! [B: code_integer,A: code_integer,N: nat] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ B @ A )
% 7.75/5.65 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 7.75/5.65 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_power
% 7.75/5.65 thf(fact_58_div__power,axiom,
% 7.75/5.65 ! [B: nat,A: nat,N: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.65 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 7.75/5.65 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_power
% 7.75/5.65 thf(fact_59_div__power,axiom,
% 7.75/5.65 ! [B: int,A: int,N: nat] :
% 7.75/5.65 ( ( dvd_dvd_int @ B @ A )
% 7.75/5.65 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 7.75/5.65 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_power
% 7.75/5.65 thf(fact_60_div__mult2__numeral__eq,axiom,
% 7.75/5.65 ! [A: nat,K: num,L: num] :
% 7.75/5.65 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 7.75/5.65 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_mult2_numeral_eq
% 7.75/5.65 thf(fact_61_div__mult2__numeral__eq,axiom,
% 7.75/5.65 ! [A: int,K: num,L: num] :
% 7.75/5.65 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 7.75/5.65 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_mult2_numeral_eq
% 7.75/5.65 thf(fact_62_even__numeral,axiom,
% 7.75/5.65 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_numeral
% 7.75/5.65 thf(fact_63_even__numeral,axiom,
% 7.75/5.65 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_numeral
% 7.75/5.65 thf(fact_64_evenE,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ~ ! [B2: code_integer] :
% 7.75/5.65 ( A
% 7.75/5.65 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % evenE
% 7.75/5.65 thf(fact_65_evenE,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ~ ! [B2: nat] :
% 7.75/5.65 ( A
% 7.75/5.65 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % evenE
% 7.75/5.65 thf(fact_66_evenE,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ~ ! [B2: int] :
% 7.75/5.65 ( A
% 7.75/5.65 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % evenE
% 7.75/5.65 thf(fact_67_even__two__times__div__two,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = A ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_two_times_div_two
% 7.75/5.65 thf(fact_68_even__two__times__div__two,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = A ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_two_times_div_two
% 7.75/5.65 thf(fact_69_even__two__times__div__two,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = A ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_two_times_div_two
% 7.75/5.65 thf(fact_70_assn__times__assoc,axiom,
% 7.75/5.65 ! [P: assn,Q: assn,R: assn] :
% 7.75/5.65 ( ( times_times_assn @ ( times_times_assn @ P @ Q ) @ R )
% 7.75/5.65 = ( times_times_assn @ P @ ( times_times_assn @ Q @ R ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % assn_times_assoc
% 7.75/5.65 thf(fact_71_assn__times__comm,axiom,
% 7.75/5.65 ( times_times_assn
% 7.75/5.65 = ( ^ [P2: assn,Q2: assn] : ( times_times_assn @ Q2 @ P2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % assn_times_comm
% 7.75/5.65 thf(fact_72_ent__trans,axiom,
% 7.75/5.65 ! [P: assn,Q: assn,R: assn] :
% 7.75/5.65 ( ( entails @ P @ Q )
% 7.75/5.65 => ( ( entails @ Q @ R )
% 7.75/5.65 => ( entails @ P @ R ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ent_trans
% 7.75/5.65 thf(fact_73_ent__refl,axiom,
% 7.75/5.65 ! [P: assn] : ( entails @ P @ P ) ).
% 7.75/5.65
% 7.75/5.65 % ent_refl
% 7.75/5.65 thf(fact_74_ent__iffI,axiom,
% 7.75/5.65 ! [A2: assn,B3: assn] :
% 7.75/5.65 ( ( entails @ A2 @ B3 )
% 7.75/5.65 => ( ( entails @ B3 @ A2 )
% 7.75/5.65 => ( A2 = B3 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ent_iffI
% 7.75/5.65 thf(fact_75_divide__divide__eq__left_H,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 7.75/5.65 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_eq_left'
% 7.75/5.65 thf(fact_76_divide__divide__eq__left_H,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 7.75/5.65 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_eq_left'
% 7.75/5.65 thf(fact_77_divide__divide__eq__left_H,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 7.75/5.65 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_eq_left'
% 7.75/5.65 thf(fact_78_divide__divide__times__eq,axiom,
% 7.75/5.65 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 7.75/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_times_eq
% 7.75/5.65 thf(fact_79_divide__divide__times__eq,axiom,
% 7.75/5.65 ! [X: real,Y: real,Z: real,W: real] :
% 7.75/5.65 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 7.75/5.65 = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_times_eq
% 7.75/5.65 thf(fact_80_divide__divide__times__eq,axiom,
% 7.75/5.65 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 7.75/5.65 = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_divide_times_eq
% 7.75/5.65 thf(fact_81_times__divide__times__eq,axiom,
% 7.75/5.65 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 7.75/5.65 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % times_divide_times_eq
% 7.75/5.65 thf(fact_82_times__divide__times__eq,axiom,
% 7.75/5.65 ! [X: real,Y: real,Z: real,W: real] :
% 7.75/5.65 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 7.75/5.65 = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % times_divide_times_eq
% 7.75/5.65 thf(fact_83_times__divide__times__eq,axiom,
% 7.75/5.65 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 7.75/5.65 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 7.75/5.65 = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % times_divide_times_eq
% 7.75/5.65 thf(fact_84_power__commuting__commutes,axiom,
% 7.75/5.65 ! [X: assn,Y: assn,N: nat] :
% 7.75/5.65 ( ( ( times_times_assn @ X @ Y )
% 7.75/5.65 = ( times_times_assn @ Y @ X ) )
% 7.75/5.65 => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ Y )
% 7.75/5.65 = ( times_times_assn @ Y @ ( power_power_assn @ X @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commuting_commutes
% 7.75/5.65 thf(fact_85_power__commuting__commutes,axiom,
% 7.75/5.65 ! [X: real,Y: real,N: nat] :
% 7.75/5.65 ( ( ( times_times_real @ X @ Y )
% 7.75/5.65 = ( times_times_real @ Y @ X ) )
% 7.75/5.65 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y )
% 7.75/5.65 = ( times_times_real @ Y @ ( power_power_real @ X @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commuting_commutes
% 7.75/5.65 thf(fact_86_power__commuting__commutes,axiom,
% 7.75/5.65 ! [X: nat,Y: nat,N: nat] :
% 7.75/5.65 ( ( ( times_times_nat @ X @ Y )
% 7.75/5.65 = ( times_times_nat @ Y @ X ) )
% 7.75/5.65 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 7.75/5.65 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commuting_commutes
% 7.75/5.65 thf(fact_87_power__commuting__commutes,axiom,
% 7.75/5.65 ! [X: int,Y: int,N: nat] :
% 7.75/5.65 ( ( ( times_times_int @ X @ Y )
% 7.75/5.65 = ( times_times_int @ Y @ X ) )
% 7.75/5.65 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 7.75/5.65 = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commuting_commutes
% 7.75/5.65 thf(fact_88_power__commuting__commutes,axiom,
% 7.75/5.65 ! [X: code_integer,Y: code_integer,N: nat] :
% 7.75/5.65 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 7.75/5.65 = ( times_3573771949741848930nteger @ Y @ X ) )
% 7.75/5.65 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ Y )
% 7.75/5.65 = ( times_3573771949741848930nteger @ Y @ ( power_8256067586552552935nteger @ X @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commuting_commutes
% 7.75/5.65 thf(fact_89_power__commuting__commutes,axiom,
% 7.75/5.65 ! [X: complex,Y: complex,N: nat] :
% 7.75/5.65 ( ( ( times_times_complex @ X @ Y )
% 7.75/5.65 = ( times_times_complex @ Y @ X ) )
% 7.75/5.65 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y )
% 7.75/5.65 = ( times_times_complex @ Y @ ( power_power_complex @ X @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commuting_commutes
% 7.75/5.65 thf(fact_90_power__mult__distrib,axiom,
% 7.75/5.65 ! [A: assn,B: assn,N: nat] :
% 7.75/5.65 ( ( power_power_assn @ ( times_times_assn @ A @ B ) @ N )
% 7.75/5.65 = ( times_times_assn @ ( power_power_assn @ A @ N ) @ ( power_power_assn @ B @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_distrib
% 7.75/5.65 thf(fact_91_power__mult__distrib,axiom,
% 7.75/5.65 ! [A: real,B: real,N: nat] :
% 7.75/5.65 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 7.75/5.65 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_distrib
% 7.75/5.65 thf(fact_92_power__mult__distrib,axiom,
% 7.75/5.65 ! [A: nat,B: nat,N: nat] :
% 7.75/5.65 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 7.75/5.65 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_distrib
% 7.75/5.65 thf(fact_93_power__mult__distrib,axiom,
% 7.75/5.65 ! [A: int,B: int,N: nat] :
% 7.75/5.65 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 7.75/5.65 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_distrib
% 7.75/5.65 thf(fact_94_power__mult__distrib,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,N: nat] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ ( times_3573771949741848930nteger @ A @ B ) @ N )
% 7.75/5.65 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_distrib
% 7.75/5.65 thf(fact_95_power__mult__distrib,axiom,
% 7.75/5.65 ! [A: complex,B: complex,N: nat] :
% 7.75/5.65 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 7.75/5.65 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult_distrib
% 7.75/5.65 thf(fact_96_power__commutes,axiom,
% 7.75/5.65 ! [A: assn,N: nat] :
% 7.75/5.65 ( ( times_times_assn @ ( power_power_assn @ A @ N ) @ A )
% 7.75/5.65 = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commutes
% 7.75/5.65 thf(fact_97_power__commutes,axiom,
% 7.75/5.65 ! [A: real,N: nat] :
% 7.75/5.65 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 7.75/5.65 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commutes
% 7.75/5.65 thf(fact_98_power__commutes,axiom,
% 7.75/5.65 ! [A: nat,N: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 7.75/5.65 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commutes
% 7.75/5.65 thf(fact_99_power__commutes,axiom,
% 7.75/5.65 ! [A: int,N: nat] :
% 7.75/5.65 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 7.75/5.65 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commutes
% 7.75/5.65 thf(fact_100_power__commutes,axiom,
% 7.75/5.65 ! [A: code_integer,N: nat] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ A )
% 7.75/5.65 = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commutes
% 7.75/5.65 thf(fact_101_power__commutes,axiom,
% 7.75/5.65 ! [A: complex,N: nat] :
% 7.75/5.65 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 7.75/5.65 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_commutes
% 7.75/5.65 thf(fact_102_power__divide,axiom,
% 7.75/5.65 ! [A: complex,B: complex,N: nat] :
% 7.75/5.65 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 7.75/5.65 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_divide
% 7.75/5.65 thf(fact_103_power__divide,axiom,
% 7.75/5.65 ! [A: real,B: real,N: nat] :
% 7.75/5.65 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 7.75/5.65 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_divide
% 7.75/5.65 thf(fact_104_power__divide,axiom,
% 7.75/5.65 ! [A: rat,B: rat,N: nat] :
% 7.75/5.65 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 7.75/5.65 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_divide
% 7.75/5.65 thf(fact_105_power__mult,axiom,
% 7.75/5.65 ! [A: nat,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 7.75/5.65 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult
% 7.75/5.65 thf(fact_106_power__mult,axiom,
% 7.75/5.65 ! [A: real,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 7.75/5.65 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult
% 7.75/5.65 thf(fact_107_power__mult,axiom,
% 7.75/5.65 ! [A: int,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 7.75/5.65 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult
% 7.75/5.65 thf(fact_108_power__mult,axiom,
% 7.75/5.65 ! [A: complex,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 7.75/5.65 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult
% 7.75/5.65 thf(fact_109_power__mult,axiom,
% 7.75/5.65 ! [A: code_integer,M: nat,N: nat] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ A @ ( times_times_nat @ M @ N ) )
% 7.75/5.65 = ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A @ M ) @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult
% 7.75/5.65 thf(fact_110_power__mult,axiom,
% 7.75/5.65 ! [A: assn,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_assn @ A @ ( times_times_nat @ M @ N ) )
% 7.75/5.65 = ( power_power_assn @ ( power_power_assn @ A @ M ) @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_mult
% 7.75/5.65 thf(fact_111_div__mult2__eq,axiom,
% 7.75/5.65 ! [M: nat,N: nat,Q3: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q3 ) )
% 7.75/5.65 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q3 ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_mult2_eq
% 7.75/5.65 thf(fact_112_ent__star__mono,axiom,
% 7.75/5.65 ! [P: assn,P3: assn,Q: assn,Q4: assn] :
% 7.75/5.65 ( ( entails @ P @ P3 )
% 7.75/5.65 => ( ( entails @ Q @ Q4 )
% 7.75/5.65 => ( entails @ ( times_times_assn @ P @ Q ) @ ( times_times_assn @ P3 @ Q4 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ent_star_mono
% 7.75/5.65 thf(fact_113_power__Suc2,axiom,
% 7.75/5.65 ! [A: assn,N: nat] :
% 7.75/5.65 ( ( power_power_assn @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_assn @ ( power_power_assn @ A @ N ) @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc2
% 7.75/5.65 thf(fact_114_power__Suc2,axiom,
% 7.75/5.65 ! [A: real,N: nat] :
% 7.75/5.65 ( ( power_power_real @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc2
% 7.75/5.65 thf(fact_115_power__Suc2,axiom,
% 7.75/5.65 ! [A: nat,N: nat] :
% 7.75/5.65 ( ( power_power_nat @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc2
% 7.75/5.65 thf(fact_116_power__Suc2,axiom,
% 7.75/5.65 ! [A: int,N: nat] :
% 7.75/5.65 ( ( power_power_int @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc2
% 7.75/5.65 thf(fact_117_power__Suc2,axiom,
% 7.75/5.65 ! [A: code_integer,N: nat] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc2
% 7.75/5.65 thf(fact_118_power__Suc2,axiom,
% 7.75/5.65 ! [A: complex,N: nat] :
% 7.75/5.65 ( ( power_power_complex @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc2
% 7.75/5.65 thf(fact_119_power__Suc,axiom,
% 7.75/5.65 ! [A: assn,N: nat] :
% 7.75/5.65 ( ( power_power_assn @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc
% 7.75/5.65 thf(fact_120_power__Suc,axiom,
% 7.75/5.65 ! [A: real,N: nat] :
% 7.75/5.65 ( ( power_power_real @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc
% 7.75/5.65 thf(fact_121_power__Suc,axiom,
% 7.75/5.65 ! [A: nat,N: nat] :
% 7.75/5.65 ( ( power_power_nat @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc
% 7.75/5.65 thf(fact_122_power__Suc,axiom,
% 7.75/5.65 ! [A: int,N: nat] :
% 7.75/5.65 ( ( power_power_int @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc
% 7.75/5.65 thf(fact_123_power__Suc,axiom,
% 7.75/5.65 ! [A: code_integer,N: nat] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc
% 7.75/5.65 thf(fact_124_power__Suc,axiom,
% 7.75/5.65 ! [A: complex,N: nat] :
% 7.75/5.65 ( ( power_power_complex @ A @ ( suc @ N ) )
% 7.75/5.65 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_Suc
% 7.75/5.65 thf(fact_125_mem__Collect__eq,axiom,
% 7.75/5.65 ! [A: real,P: real > $o] :
% 7.75/5.65 ( ( member_real @ A @ ( collect_real @ P ) )
% 7.75/5.65 = ( P @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % mem_Collect_eq
% 7.75/5.65 thf(fact_126_mem__Collect__eq,axiom,
% 7.75/5.65 ! [A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 7.75/5.65 ( ( member_VEBT_VEBT @ A @ ( collect_VEBT_VEBT @ P ) )
% 7.75/5.65 = ( P @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % mem_Collect_eq
% 7.75/5.65 thf(fact_127_mem__Collect__eq,axiom,
% 7.75/5.65 ! [A: nat,P: nat > $o] :
% 7.75/5.65 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 7.75/5.65 = ( P @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % mem_Collect_eq
% 7.75/5.65 thf(fact_128_mem__Collect__eq,axiom,
% 7.75/5.65 ! [A: int,P: int > $o] :
% 7.75/5.65 ( ( member_int @ A @ ( collect_int @ P ) )
% 7.75/5.65 = ( P @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % mem_Collect_eq
% 7.75/5.65 thf(fact_129_mem__Collect__eq,axiom,
% 7.75/5.65 ! [A: complex,P: complex > $o] :
% 7.75/5.65 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 7.75/5.65 = ( P @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % mem_Collect_eq
% 7.75/5.65 thf(fact_130_mem__Collect__eq,axiom,
% 7.75/5.65 ! [A: set_nat,P: set_nat > $o] :
% 7.75/5.65 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 7.75/5.65 = ( P @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % mem_Collect_eq
% 7.75/5.65 thf(fact_131_Collect__mem__eq,axiom,
% 7.75/5.65 ! [A2: set_real] :
% 7.75/5.65 ( ( collect_real
% 7.75/5.65 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 7.75/5.65 = A2 ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_mem_eq
% 7.75/5.65 thf(fact_132_Collect__mem__eq,axiom,
% 7.75/5.65 ! [A2: set_VEBT_VEBT] :
% 7.75/5.65 ( ( collect_VEBT_VEBT
% 7.75/5.65 @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A2 ) )
% 7.75/5.65 = A2 ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_mem_eq
% 7.75/5.65 thf(fact_133_Collect__mem__eq,axiom,
% 7.75/5.65 ! [A2: set_nat] :
% 7.75/5.65 ( ( collect_nat
% 7.75/5.65 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 7.75/5.65 = A2 ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_mem_eq
% 7.75/5.65 thf(fact_134_Collect__mem__eq,axiom,
% 7.75/5.65 ! [A2: set_int] :
% 7.75/5.65 ( ( collect_int
% 7.75/5.65 @ ^ [X2: int] : ( member_int @ X2 @ A2 ) )
% 7.75/5.65 = A2 ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_mem_eq
% 7.75/5.65 thf(fact_135_Collect__mem__eq,axiom,
% 7.75/5.65 ! [A2: set_complex] :
% 7.75/5.65 ( ( collect_complex
% 7.75/5.65 @ ^ [X2: complex] : ( member_complex @ X2 @ A2 ) )
% 7.75/5.65 = A2 ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_mem_eq
% 7.75/5.65 thf(fact_136_Collect__mem__eq,axiom,
% 7.75/5.65 ! [A2: set_set_nat] :
% 7.75/5.65 ( ( collect_set_nat
% 7.75/5.65 @ ^ [X2: set_nat] : ( member_set_nat @ X2 @ A2 ) )
% 7.75/5.65 = A2 ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_mem_eq
% 7.75/5.65 thf(fact_137_Collect__cong,axiom,
% 7.75/5.65 ! [P: nat > $o,Q: nat > $o] :
% 7.75/5.65 ( ! [X3: nat] :
% 7.75/5.65 ( ( P @ X3 )
% 7.75/5.65 = ( Q @ X3 ) )
% 7.75/5.65 => ( ( collect_nat @ P )
% 7.75/5.65 = ( collect_nat @ Q ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_cong
% 7.75/5.65 thf(fact_138_Collect__cong,axiom,
% 7.75/5.65 ! [P: int > $o,Q: int > $o] :
% 7.75/5.65 ( ! [X3: int] :
% 7.75/5.65 ( ( P @ X3 )
% 7.75/5.65 = ( Q @ X3 ) )
% 7.75/5.65 => ( ( collect_int @ P )
% 7.75/5.65 = ( collect_int @ Q ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_cong
% 7.75/5.65 thf(fact_139_Collect__cong,axiom,
% 7.75/5.65 ! [P: complex > $o,Q: complex > $o] :
% 7.75/5.65 ( ! [X3: complex] :
% 7.75/5.65 ( ( P @ X3 )
% 7.75/5.65 = ( Q @ X3 ) )
% 7.75/5.65 => ( ( collect_complex @ P )
% 7.75/5.65 = ( collect_complex @ Q ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_cong
% 7.75/5.65 thf(fact_140_Collect__cong,axiom,
% 7.75/5.65 ! [P: set_nat > $o,Q: set_nat > $o] :
% 7.75/5.65 ( ! [X3: set_nat] :
% 7.75/5.65 ( ( P @ X3 )
% 7.75/5.65 = ( Q @ X3 ) )
% 7.75/5.65 => ( ( collect_set_nat @ P )
% 7.75/5.65 = ( collect_set_nat @ Q ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % Collect_cong
% 7.75/5.65 thf(fact_141_numeral__Bit0__div__2,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( numeral_numeral_nat @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_Bit0_div_2
% 7.75/5.65 thf(fact_142_numeral__Bit0__div__2,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( numeral_numeral_int @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_Bit0_div_2
% 7.75/5.65 thf(fact_143_power2__eq__square,axiom,
% 7.75/5.65 ! [A: assn] :
% 7.75/5.65 ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( times_times_assn @ A @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_eq_square
% 7.75/5.65 thf(fact_144_power2__eq__square,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( times_times_real @ A @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_eq_square
% 7.75/5.65 thf(fact_145_power2__eq__square,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( times_times_nat @ A @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_eq_square
% 7.75/5.65 thf(fact_146_power2__eq__square,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( times_times_int @ A @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_eq_square
% 7.75/5.65 thf(fact_147_power2__eq__square,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_eq_square
% 7.75/5.65 thf(fact_148_power2__eq__square,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( times_times_complex @ A @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_eq_square
% 7.75/5.65 thf(fact_149_dvd__mult__div__cancel,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 7.75/5.65 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 7.75/5.65 = B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_div_cancel
% 7.75/5.65 thf(fact_150_dvd__mult__div__cancel,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 7.75/5.65 = B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_div_cancel
% 7.75/5.65 thf(fact_151_dvd__mult__div__cancel,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.65 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 7.75/5.65 = B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_div_cancel
% 7.75/5.65 thf(fact_152_dvd__div__mult__self,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 7.75/5.65 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 7.75/5.65 = B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_mult_self
% 7.75/5.65 thf(fact_153_dvd__div__mult__self,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 7.75/5.65 = B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_mult_self
% 7.75/5.65 thf(fact_154_dvd__div__mult__self,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.65 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 7.75/5.65 = B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_mult_self
% 7.75/5.65 thf(fact_155_div2__even__ext__nat,axiom,
% 7.75/5.65 ! [X: nat,Y: nat] :
% 7.75/5.65 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.65 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 7.75/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 7.75/5.65 => ( X = Y ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div2_even_ext_nat
% 7.75/5.65 thf(fact_156_div__dvd__div,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ A @ C )
% 7.75/5.65 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 7.75/5.65 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_dvd_div
% 7.75/5.65 thf(fact_157_div__dvd__div,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_int @ A @ C )
% 7.75/5.65 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 7.75/5.65 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_dvd_div
% 7.75/5.65 thf(fact_158_bit__eq__rec,axiom,
% 7.75/5.65 ( ( ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 ) )
% 7.75/5.65 = ( ^ [A3: nat,B4: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 7.75/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) )
% 7.75/5.65 & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( divide_divide_nat @ B4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % bit_eq_rec
% 7.75/5.65 thf(fact_159_bit__eq__rec,axiom,
% 7.75/5.65 ( ( ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
% 7.75/5.65 = ( ^ [A3: int,B4: int] :
% 7.75/5.65 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 7.75/5.65 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) )
% 7.75/5.65 & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( divide_divide_int @ B4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % bit_eq_rec
% 7.75/5.65 thf(fact_160_num__double,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 7.75/5.65 = ( bit0 @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % num_double
% 7.75/5.65 thf(fact_161_semiring__norm_I83_J,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( one
% 7.75/5.65 != ( bit0 @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % semiring_norm(83)
% 7.75/5.65 thf(fact_162_semiring__norm_I85_J,axiom,
% 7.75/5.65 ! [M: num] :
% 7.75/5.65 ( ( bit0 @ M )
% 7.75/5.65 != one ) ).
% 7.75/5.65
% 7.75/5.65 % semiring_norm(85)
% 7.75/5.65 thf(fact_163_mult__numeral__left__semiring__numeral,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Z ) )
% 7.75/5.65 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_left_semiring_numeral
% 7.75/5.65 thf(fact_164_mult__numeral__left__semiring__numeral,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 7.75/5.65 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_left_semiring_numeral
% 7.75/5.65 thf(fact_165_mult__numeral__left__semiring__numeral,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: real] :
% 7.75/5.65 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 7.75/5.65 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_left_semiring_numeral
% 7.75/5.65 thf(fact_166_mult__numeral__left__semiring__numeral,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: rat] :
% 7.75/5.65 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 7.75/5.65 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_left_semiring_numeral
% 7.75/5.65 thf(fact_167_mult__numeral__left__semiring__numeral,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 7.75/5.65 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_left_semiring_numeral
% 7.75/5.65 thf(fact_168_mult__numeral__left__semiring__numeral,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: int] :
% 7.75/5.65 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 7.75/5.65 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_left_semiring_numeral
% 7.75/5.65 thf(fact_169_numeral__times__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 7.75/5.65 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_times_numeral
% 7.75/5.65 thf(fact_170_numeral__times__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 7.75/5.65 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_times_numeral
% 7.75/5.65 thf(fact_171_numeral__times__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.65 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_times_numeral
% 7.75/5.65 thf(fact_172_numeral__times__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 7.75/5.65 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_times_numeral
% 7.75/5.65 thf(fact_173_numeral__times__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_times_numeral
% 7.75/5.65 thf(fact_174_numeral__times__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 7.75/5.65 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_times_numeral
% 7.75/5.65 thf(fact_175_pow__sum,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( 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 ) )
% 7.75/5.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % pow_sum
% 7.75/5.65 thf(fact_176_buildup__nothing__in__leaf,axiom,
% 7.75/5.65 ! [N: nat,X: nat] :
% 7.75/5.65 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 7.75/5.65
% 7.75/5.65 % buildup_nothing_in_leaf
% 7.75/5.65 thf(fact_177_even__odd__cases,axiom,
% 7.75/5.65 ! [X: nat] :
% 7.75/5.65 ( ! [N2: nat] :
% 7.75/5.65 ( X
% 7.75/5.65 != ( plus_plus_nat @ N2 @ N2 ) )
% 7.75/5.65 => ~ ! [N2: nat] :
% 7.75/5.65 ( X
% 7.75/5.65 != ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_odd_cases
% 7.75/5.65 thf(fact_178_numeral__eq__iff,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ( numera6690914467698888265omplex @ M )
% 7.75/5.65 = ( numera6690914467698888265omplex @ N ) )
% 7.75/5.65 = ( M = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_iff
% 7.75/5.65 thf(fact_179_numeral__eq__iff,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ( numeral_numeral_real @ M )
% 7.75/5.65 = ( numeral_numeral_real @ N ) )
% 7.75/5.65 = ( M = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_iff
% 7.75/5.65 thf(fact_180_numeral__eq__iff,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ( numeral_numeral_rat @ M )
% 7.75/5.65 = ( numeral_numeral_rat @ N ) )
% 7.75/5.65 = ( M = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_iff
% 7.75/5.65 thf(fact_181_numeral__eq__iff,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ( numeral_numeral_nat @ M )
% 7.75/5.65 = ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( M = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_iff
% 7.75/5.65 thf(fact_182_numeral__eq__iff,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ( numeral_numeral_int @ M )
% 7.75/5.65 = ( numeral_numeral_int @ N ) )
% 7.75/5.65 = ( M = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_iff
% 7.75/5.65 thf(fact_183_semiring__norm_I87_J,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ( bit0 @ M )
% 7.75/5.65 = ( bit0 @ N ) )
% 7.75/5.65 = ( M = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % semiring_norm(87)
% 7.75/5.65 thf(fact_184_add__numeral__left,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: complex] :
% 7.75/5.65 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 7.75/5.65 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_numeral_left
% 7.75/5.65 thf(fact_185_add__numeral__left,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: real] :
% 7.75/5.65 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 7.75/5.65 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_numeral_left
% 7.75/5.65 thf(fact_186_add__numeral__left,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: rat] :
% 7.75/5.65 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 7.75/5.65 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_numeral_left
% 7.75/5.65 thf(fact_187_add__numeral__left,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 7.75/5.65 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_numeral_left
% 7.75/5.65 thf(fact_188_add__numeral__left,axiom,
% 7.75/5.65 ! [V: num,W: num,Z: int] :
% 7.75/5.65 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 7.75/5.65 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_numeral_left
% 7.75/5.65 thf(fact_189_numeral__plus__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 7.75/5.65 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_plus_numeral
% 7.75/5.65 thf(fact_190_numeral__plus__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.65 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_plus_numeral
% 7.75/5.65 thf(fact_191_numeral__plus__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 7.75/5.65 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_plus_numeral
% 7.75/5.65 thf(fact_192_numeral__plus__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_plus_numeral
% 7.75/5.65 thf(fact_193_numeral__plus__numeral,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 7.75/5.65 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_plus_numeral
% 7.75/5.65 thf(fact_194_dvd__add__triv__right__iff,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 7.75/5.65 = ( dvd_dvd_real @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_triv_right_iff
% 7.75/5.65 thf(fact_195_dvd__add__triv__right__iff,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 7.75/5.65 = ( dvd_dvd_rat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_triv_right_iff
% 7.75/5.65 thf(fact_196_dvd__add__triv__right__iff,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 7.75/5.65 = ( dvd_dvd_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_triv_right_iff
% 7.75/5.65 thf(fact_197_dvd__add__triv__right__iff,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 7.75/5.65 = ( dvd_dvd_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_triv_right_iff
% 7.75/5.65 thf(fact_198_dvd__add__triv__left__iff,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 7.75/5.65 = ( dvd_dvd_real @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_triv_left_iff
% 7.75/5.65 thf(fact_199_dvd__add__triv__left__iff,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.65 = ( dvd_dvd_rat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_triv_left_iff
% 7.75/5.65 thf(fact_200_dvd__add__triv__left__iff,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 7.75/5.65 = ( dvd_dvd_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_triv_left_iff
% 7.75/5.65 thf(fact_201_dvd__add__triv__left__iff,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 7.75/5.65 = ( dvd_dvd_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_triv_left_iff
% 7.75/5.65 thf(fact_202_semiring__norm_I13_J,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 7.75/5.65 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % semiring_norm(13)
% 7.75/5.65 thf(fact_203_semiring__norm_I12_J,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( times_times_num @ one @ N )
% 7.75/5.65 = N ) ).
% 7.75/5.65
% 7.75/5.65 % semiring_norm(12)
% 7.75/5.65 thf(fact_204_semiring__norm_I11_J,axiom,
% 7.75/5.65 ! [M: num] :
% 7.75/5.65 ( ( times_times_num @ M @ one )
% 7.75/5.65 = M ) ).
% 7.75/5.65
% 7.75/5.65 % semiring_norm(11)
% 7.75/5.65 thf(fact_205_bit__concat__def,axiom,
% 7.75/5.65 ( vEBT_VEBT_bit_concat
% 7.75/5.65 = ( ^ [H: nat,L2: nat,D: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D ) ) @ L2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % bit_concat_def
% 7.75/5.65 thf(fact_206_distrib__left__numeral,axiom,
% 7.75/5.65 ! [V: num,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left_numeral
% 7.75/5.65 thf(fact_207_distrib__left__numeral,axiom,
% 7.75/5.65 ! [V: num,B: complex,C: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 7.75/5.65 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left_numeral
% 7.75/5.65 thf(fact_208_distrib__left__numeral,axiom,
% 7.75/5.65 ! [V: num,B: real,C: real] :
% 7.75/5.65 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 7.75/5.65 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left_numeral
% 7.75/5.65 thf(fact_209_distrib__left__numeral,axiom,
% 7.75/5.65 ! [V: num,B: rat,C: rat] :
% 7.75/5.65 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.65 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left_numeral
% 7.75/5.65 thf(fact_210_distrib__left__numeral,axiom,
% 7.75/5.65 ! [V: num,B: nat,C: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left_numeral
% 7.75/5.65 thf(fact_211_distrib__left__numeral,axiom,
% 7.75/5.65 ! [V: num,B: int,C: int] :
% 7.75/5.65 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 7.75/5.65 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left_numeral
% 7.75/5.65 thf(fact_212_distrib__right__numeral,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,V: num] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right_numeral
% 7.75/5.65 thf(fact_213_distrib__right__numeral,axiom,
% 7.75/5.65 ! [A: complex,B: complex,V: num] :
% 7.75/5.65 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 7.75/5.65 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right_numeral
% 7.75/5.65 thf(fact_214_distrib__right__numeral,axiom,
% 7.75/5.65 ! [A: real,B: real,V: num] :
% 7.75/5.65 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.65 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right_numeral
% 7.75/5.65 thf(fact_215_distrib__right__numeral,axiom,
% 7.75/5.65 ! [A: rat,B: rat,V: num] :
% 7.75/5.65 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.65 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right_numeral
% 7.75/5.65 thf(fact_216_distrib__right__numeral,axiom,
% 7.75/5.65 ! [A: nat,B: nat,V: num] :
% 7.75/5.65 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right_numeral
% 7.75/5.65 thf(fact_217_distrib__right__numeral,axiom,
% 7.75/5.65 ! [A: int,B: int,V: num] :
% 7.75/5.65 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.65 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right_numeral
% 7.75/5.65 thf(fact_218_dvd__add__times__triv__right__iff,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 7.75/5.65 = ( dvd_dvd_rat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_right_iff
% 7.75/5.65 thf(fact_219_dvd__add__times__triv__right__iff,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 7.75/5.65 = ( dvd_dvd_real @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_right_iff
% 7.75/5.65 thf(fact_220_dvd__add__times__triv__right__iff,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 7.75/5.65 = ( dvd_dvd_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_right_iff
% 7.75/5.65 thf(fact_221_dvd__add__times__triv__right__iff,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 7.75/5.65 = ( dvd_dvd_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_right_iff
% 7.75/5.65 thf(fact_222_dvd__add__times__triv__right__iff,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 7.75/5.65 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_right_iff
% 7.75/5.65 thf(fact_223_dvd__add__times__triv__right__iff,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 7.75/5.65 = ( dvd_dvd_complex @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_right_iff
% 7.75/5.65 thf(fact_224_dvd__add__times__triv__left__iff,axiom,
% 7.75/5.65 ! [A: rat,C: rat,B: rat] :
% 7.75/5.65 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 7.75/5.65 = ( dvd_dvd_rat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_left_iff
% 7.75/5.65 thf(fact_225_dvd__add__times__triv__left__iff,axiom,
% 7.75/5.65 ! [A: real,C: real,B: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 7.75/5.65 = ( dvd_dvd_real @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_left_iff
% 7.75/5.65 thf(fact_226_dvd__add__times__triv__left__iff,axiom,
% 7.75/5.65 ! [A: nat,C: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 7.75/5.65 = ( dvd_dvd_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_left_iff
% 7.75/5.65 thf(fact_227_dvd__add__times__triv__left__iff,axiom,
% 7.75/5.65 ! [A: int,C: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 7.75/5.65 = ( dvd_dvd_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_left_iff
% 7.75/5.65 thf(fact_228_dvd__add__times__triv__left__iff,axiom,
% 7.75/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 7.75/5.65 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_left_iff
% 7.75/5.65 thf(fact_229_dvd__add__times__triv__left__iff,axiom,
% 7.75/5.65 ! [A: complex,C: complex,B: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 7.75/5.65 = ( dvd_dvd_complex @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_times_triv_left_iff
% 7.75/5.65 thf(fact_230_div__add,axiom,
% 7.75/5.65 ! [C: nat,A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_add
% 7.75/5.65 thf(fact_231_div__add,axiom,
% 7.75/5.65 ! [C: int,A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_int @ C @ B )
% 7.75/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_add
% 7.75/5.65 thf(fact_232_odd__add,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 7.75/5.65 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 7.75/5.65 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % odd_add
% 7.75/5.65 thf(fact_233_odd__add,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 7.75/5.65 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 7.75/5.65 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % odd_add
% 7.75/5.65 thf(fact_234_even__add,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 7.75/5.65 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_add
% 7.75/5.65 thf(fact_235_even__add,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 7.75/5.65 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % even_add
% 7.75/5.65 thf(fact_236_add__2__eq__Suc,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.65 = ( suc @ ( suc @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_2_eq_Suc
% 7.75/5.65 thf(fact_237_add__2__eq__Suc_H,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( suc @ ( suc @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_2_eq_Suc'
% 7.75/5.65 thf(fact_238_add__self__div__2,axiom,
% 7.75/5.65 ! [M: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = M ) ).
% 7.75/5.65
% 7.75/5.65 % add_self_div_2
% 7.75/5.65 thf(fact_239_is__num__normalize_I1_J,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % is_num_normalize(1)
% 7.75/5.65 thf(fact_240_is__num__normalize_I1_J,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % is_num_normalize(1)
% 7.75/5.65 thf(fact_241_is__num__normalize_I1_J,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % is_num_normalize(1)
% 7.75/5.65 thf(fact_242_ring__class_Oring__distribs_I2_J,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(2)
% 7.75/5.65 thf(fact_243_ring__class_Oring__distribs_I2_J,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(2)
% 7.75/5.65 thf(fact_244_ring__class_Oring__distribs_I2_J,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(2)
% 7.75/5.65 thf(fact_245_ring__class_Oring__distribs_I2_J,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(2)
% 7.75/5.65 thf(fact_246_ring__class_Oring__distribs_I2_J,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(2)
% 7.75/5.65 thf(fact_247_ring__class_Oring__distribs_I1_J,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.65 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(1)
% 7.75/5.65 thf(fact_248_ring__class_Oring__distribs_I1_J,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 7.75/5.65 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(1)
% 7.75/5.65 thf(fact_249_ring__class_Oring__distribs_I1_J,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 7.75/5.65 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(1)
% 7.75/5.65 thf(fact_250_ring__class_Oring__distribs_I1_J,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(1)
% 7.75/5.65 thf(fact_251_ring__class_Oring__distribs_I1_J,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 7.75/5.65 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ring_class.ring_distribs(1)
% 7.75/5.65 thf(fact_252_comm__semiring__class_Odistrib,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % comm_semiring_class.distrib
% 7.75/5.65 thf(fact_253_comm__semiring__class_Odistrib,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % comm_semiring_class.distrib
% 7.75/5.65 thf(fact_254_comm__semiring__class_Odistrib,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % comm_semiring_class.distrib
% 7.75/5.65 thf(fact_255_comm__semiring__class_Odistrib,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % comm_semiring_class.distrib
% 7.75/5.65 thf(fact_256_comm__semiring__class_Odistrib,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % comm_semiring_class.distrib
% 7.75/5.65 thf(fact_257_comm__semiring__class_Odistrib,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % comm_semiring_class.distrib
% 7.75/5.65 thf(fact_258_distrib__left,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.65 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left
% 7.75/5.65 thf(fact_259_distrib__left,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 7.75/5.65 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left
% 7.75/5.65 thf(fact_260_distrib__left,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left
% 7.75/5.65 thf(fact_261_distrib__left,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 7.75/5.65 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left
% 7.75/5.65 thf(fact_262_distrib__left,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left
% 7.75/5.65 thf(fact_263_distrib__left,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 7.75/5.65 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_left
% 7.75/5.65 thf(fact_264_distrib__right,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right
% 7.75/5.65 thf(fact_265_distrib__right,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right
% 7.75/5.65 thf(fact_266_distrib__right,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right
% 7.75/5.65 thf(fact_267_distrib__right,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right
% 7.75/5.65 thf(fact_268_distrib__right,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right
% 7.75/5.65 thf(fact_269_distrib__right,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % distrib_right
% 7.75/5.65 thf(fact_270_combine__common__factor,axiom,
% 7.75/5.65 ! [A: rat,E: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 7.75/5.65 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % combine_common_factor
% 7.75/5.65 thf(fact_271_combine__common__factor,axiom,
% 7.75/5.65 ! [A: real,E: real,B: real,C: real] :
% 7.75/5.65 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 7.75/5.65 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % combine_common_factor
% 7.75/5.65 thf(fact_272_combine__common__factor,axiom,
% 7.75/5.65 ! [A: nat,E: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % combine_common_factor
% 7.75/5.65 thf(fact_273_combine__common__factor,axiom,
% 7.75/5.65 ! [A: int,E: int,B: int,C: int] :
% 7.75/5.65 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 7.75/5.65 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % combine_common_factor
% 7.75/5.65 thf(fact_274_combine__common__factor,axiom,
% 7.75/5.65 ! [A: code_integer,E: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ C ) )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ E ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % combine_common_factor
% 7.75/5.65 thf(fact_275_combine__common__factor,axiom,
% 7.75/5.65 ! [A: complex,E: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ C ) )
% 7.75/5.65 = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E ) @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % combine_common_factor
% 7.75/5.65 thf(fact_276_dvd__add__right__iff,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 7.75/5.65 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_right_iff
% 7.75/5.65 thf(fact_277_dvd__add__right__iff,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( dvd_dvd_rat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.65 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_right_iff
% 7.75/5.65 thf(fact_278_dvd__add__right__iff,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 7.75/5.65 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_right_iff
% 7.75/5.65 thf(fact_279_dvd__add__right__iff,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 7.75/5.65 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_right_iff
% 7.75/5.65 thf(fact_280_dvd__add__left__iff,axiom,
% 7.75/5.65 ! [A: real,C: real,B: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ C )
% 7.75/5.65 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 7.75/5.65 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_left_iff
% 7.75/5.65 thf(fact_281_dvd__add__left__iff,axiom,
% 7.75/5.65 ! [A: rat,C: rat,B: rat] :
% 7.75/5.65 ( ( dvd_dvd_rat @ A @ C )
% 7.75/5.65 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.65 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_left_iff
% 7.75/5.65 thf(fact_282_dvd__add__left__iff,axiom,
% 7.75/5.65 ! [A: nat,C: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ C )
% 7.75/5.65 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 7.75/5.65 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_left_iff
% 7.75/5.65 thf(fact_283_dvd__add__left__iff,axiom,
% 7.75/5.65 ! [A: int,C: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ C )
% 7.75/5.65 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 7.75/5.65 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add_left_iff
% 7.75/5.65 thf(fact_284_dvd__add,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_real @ A @ C )
% 7.75/5.65 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add
% 7.75/5.65 thf(fact_285_dvd__add,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( dvd_dvd_rat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_rat @ A @ C )
% 7.75/5.65 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add
% 7.75/5.65 thf(fact_286_dvd__add,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ A @ C )
% 7.75/5.65 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add
% 7.75/5.65 thf(fact_287_dvd__add,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_int @ A @ C )
% 7.75/5.65 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_add
% 7.75/5.65 thf(fact_288_left__add__mult__distrib,axiom,
% 7.75/5.65 ! [I: nat,U: nat,J: nat,K: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 7.75/5.65
% 7.75/5.65 % left_add_mult_distrib
% 7.75/5.65 thf(fact_289_add__divide__distrib,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_divide_distrib
% 7.75/5.65 thf(fact_290_add__divide__distrib,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_divide_distrib
% 7.75/5.65 thf(fact_291_add__divide__distrib,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_divide_distrib
% 7.75/5.65 thf(fact_292_numeral__Bit0,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 7.75/5.65 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_Bit0
% 7.75/5.65 thf(fact_293_numeral__Bit0,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 7.75/5.65 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_Bit0
% 7.75/5.65 thf(fact_294_numeral__Bit0,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 7.75/5.65 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_Bit0
% 7.75/5.65 thf(fact_295_numeral__Bit0,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 7.75/5.65 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_Bit0
% 7.75/5.65 thf(fact_296_numeral__Bit0,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 7.75/5.65 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_Bit0
% 7.75/5.65 thf(fact_297_div__plus__div__distrib__dvd__right,axiom,
% 7.75/5.65 ! [C: nat,B: nat,A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_plus_div_distrib_dvd_right
% 7.75/5.65 thf(fact_298_div__plus__div__distrib__dvd__right,axiom,
% 7.75/5.65 ! [C: int,B: int,A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ C @ B )
% 7.75/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_plus_div_distrib_dvd_right
% 7.75/5.65 thf(fact_299_div__plus__div__distrib__dvd__left,axiom,
% 7.75/5.65 ! [C: nat,A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ C @ A )
% 7.75/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_plus_div_distrib_dvd_left
% 7.75/5.65 thf(fact_300_div__plus__div__distrib__dvd__left,axiom,
% 7.75/5.65 ! [C: int,A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ C @ A )
% 7.75/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_plus_div_distrib_dvd_left
% 7.75/5.65 thf(fact_301_power__add,axiom,
% 7.75/5.65 ! [A: assn,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_assn @ A @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.65 = ( times_times_assn @ ( power_power_assn @ A @ M ) @ ( power_power_assn @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add
% 7.75/5.65 thf(fact_302_power__add,axiom,
% 7.75/5.65 ! [A: real,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.65 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add
% 7.75/5.65 thf(fact_303_power__add,axiom,
% 7.75/5.65 ! [A: nat,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.65 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add
% 7.75/5.65 thf(fact_304_power__add,axiom,
% 7.75/5.65 ! [A: int,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.65 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add
% 7.75/5.65 thf(fact_305_power__add,axiom,
% 7.75/5.65 ! [A: code_integer,M: nat,N: nat] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ A @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.65 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add
% 7.75/5.65 thf(fact_306_power__add,axiom,
% 7.75/5.65 ! [A: complex,M: nat,N: nat] :
% 7.75/5.65 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.65 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add
% 7.75/5.65 thf(fact_307_mult__2,axiom,
% 7.75/5.65 ! [Z: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2
% 7.75/5.65 thf(fact_308_mult__2,axiom,
% 7.75/5.65 ! [Z: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 7.75/5.65 = ( plus_plus_complex @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2
% 7.75/5.65 thf(fact_309_mult__2,axiom,
% 7.75/5.65 ! [Z: real] :
% 7.75/5.65 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 7.75/5.65 = ( plus_plus_real @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2
% 7.75/5.65 thf(fact_310_mult__2,axiom,
% 7.75/5.65 ! [Z: rat] :
% 7.75/5.65 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 7.75/5.65 = ( plus_plus_rat @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2
% 7.75/5.65 thf(fact_311_mult__2,axiom,
% 7.75/5.65 ! [Z: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 7.75/5.65 = ( plus_plus_nat @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2
% 7.75/5.65 thf(fact_312_mult__2,axiom,
% 7.75/5.65 ! [Z: int] :
% 7.75/5.65 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 7.75/5.65 = ( plus_plus_int @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2
% 7.75/5.65 thf(fact_313_mult__2__right,axiom,
% 7.75/5.65 ! [Z: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ Z @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2_right
% 7.75/5.65 thf(fact_314_mult__2__right,axiom,
% 7.75/5.65 ! [Z: complex] :
% 7.75/5.65 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( plus_plus_complex @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2_right
% 7.75/5.65 thf(fact_315_mult__2__right,axiom,
% 7.75/5.65 ! [Z: real] :
% 7.75/5.65 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( plus_plus_real @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2_right
% 7.75/5.65 thf(fact_316_mult__2__right,axiom,
% 7.75/5.65 ! [Z: rat] :
% 7.75/5.65 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( plus_plus_rat @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2_right
% 7.75/5.65 thf(fact_317_mult__2__right,axiom,
% 7.75/5.65 ! [Z: nat] :
% 7.75/5.65 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( plus_plus_nat @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2_right
% 7.75/5.65 thf(fact_318_mult__2__right,axiom,
% 7.75/5.65 ! [Z: int] :
% 7.75/5.65 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( plus_plus_int @ Z @ Z ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_2_right
% 7.75/5.65 thf(fact_319_left__add__twice,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer] :
% 7.75/5.65 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % left_add_twice
% 7.75/5.65 thf(fact_320_left__add__twice,axiom,
% 7.75/5.65 ! [A: complex,B: complex] :
% 7.75/5.65 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 7.75/5.65 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % left_add_twice
% 7.75/5.65 thf(fact_321_left__add__twice,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 7.75/5.65 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % left_add_twice
% 7.75/5.65 thf(fact_322_left__add__twice,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.65 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % left_add_twice
% 7.75/5.65 thf(fact_323_left__add__twice,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % left_add_twice
% 7.75/5.65 thf(fact_324_left__add__twice,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 7.75/5.65 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % left_add_twice
% 7.75/5.65 thf(fact_325_dvd__trans,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ B @ C )
% 7.75/5.65 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_trans
% 7.75/5.65 thf(fact_326_dvd__trans,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_int @ B @ C )
% 7.75/5.65 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_trans
% 7.75/5.65 thf(fact_327_dvd__refl,axiom,
% 7.75/5.65 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_refl
% 7.75/5.65 thf(fact_328_dvd__refl,axiom,
% 7.75/5.65 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_refl
% 7.75/5.65 thf(fact_329_div__exp__eq,axiom,
% 7.75/5.65 ! [A: code_integer,M: nat,N: nat] :
% 7.75/5.65 ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_exp_eq
% 7.75/5.65 thf(fact_330_div__exp__eq,axiom,
% 7.75/5.65 ! [A: nat,M: nat,N: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_exp_eq
% 7.75/5.65 thf(fact_331_div__exp__eq,axiom,
% 7.75/5.65 ! [A: int,M: nat,N: nat] :
% 7.75/5.65 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_exp_eq
% 7.75/5.65 thf(fact_332_odd__even__add,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 7.75/5.65 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % odd_even_add
% 7.75/5.65 thf(fact_333_odd__even__add,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 7.75/5.65 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % odd_even_add
% 7.75/5.65 thf(fact_334_power2__sum,axiom,
% 7.75/5.65 ! [X: code_integer,Y: code_integer] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_sum
% 7.75/5.65 thf(fact_335_power2__sum,axiom,
% 7.75/5.65 ! [X: complex,Y: complex] :
% 7.75/5.65 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( 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 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_sum
% 7.75/5.65 thf(fact_336_power2__sum,axiom,
% 7.75/5.65 ! [X: real,Y: real] :
% 7.75/5.65 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( 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 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_sum
% 7.75/5.65 thf(fact_337_power2__sum,axiom,
% 7.75/5.65 ! [X: rat,Y: rat] :
% 7.75/5.65 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( 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 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_sum
% 7.75/5.65 thf(fact_338_power2__sum,axiom,
% 7.75/5.65 ! [X: nat,Y: nat] :
% 7.75/5.65 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( 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 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_sum
% 7.75/5.65 thf(fact_339_power2__sum,axiom,
% 7.75/5.65 ! [X: int,Y: int] :
% 7.75/5.65 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.65 = ( 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 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power2_sum
% 7.75/5.65 thf(fact_340_dvdE,axiom,
% 7.75/5.65 ! [B: assn,A: assn] :
% 7.75/5.65 ( ( dvd_dvd_assn @ B @ A )
% 7.75/5.65 => ~ ! [K2: assn] :
% 7.75/5.65 ( A
% 7.75/5.65 != ( times_times_assn @ B @ K2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdE
% 7.75/5.65 thf(fact_341_dvdE,axiom,
% 7.75/5.65 ! [B: real,A: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ B @ A )
% 7.75/5.65 => ~ ! [K2: real] :
% 7.75/5.65 ( A
% 7.75/5.65 != ( times_times_real @ B @ K2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdE
% 7.75/5.65 thf(fact_342_dvdE,axiom,
% 7.75/5.65 ! [B: nat,A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.65 => ~ ! [K2: nat] :
% 7.75/5.65 ( A
% 7.75/5.65 != ( times_times_nat @ B @ K2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdE
% 7.75/5.65 thf(fact_343_dvdE,axiom,
% 7.75/5.65 ! [B: int,A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ B @ A )
% 7.75/5.65 => ~ ! [K2: int] :
% 7.75/5.65 ( A
% 7.75/5.65 != ( times_times_int @ B @ K2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdE
% 7.75/5.65 thf(fact_344_dvdE,axiom,
% 7.75/5.65 ! [B: code_integer,A: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ B @ A )
% 7.75/5.65 => ~ ! [K2: code_integer] :
% 7.75/5.65 ( A
% 7.75/5.65 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdE
% 7.75/5.65 thf(fact_345_dvdE,axiom,
% 7.75/5.65 ! [B: complex,A: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ B @ A )
% 7.75/5.65 => ~ ! [K2: complex] :
% 7.75/5.65 ( A
% 7.75/5.65 != ( times_times_complex @ B @ K2 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdE
% 7.75/5.65 thf(fact_346_dvdI,axiom,
% 7.75/5.65 ! [A: assn,B: assn,K: assn] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( times_times_assn @ B @ K ) )
% 7.75/5.65 => ( dvd_dvd_assn @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdI
% 7.75/5.65 thf(fact_347_dvdI,axiom,
% 7.75/5.65 ! [A: real,B: real,K: real] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( times_times_real @ B @ K ) )
% 7.75/5.65 => ( dvd_dvd_real @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdI
% 7.75/5.65 thf(fact_348_dvdI,axiom,
% 7.75/5.65 ! [A: nat,B: nat,K: nat] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( times_times_nat @ B @ K ) )
% 7.75/5.65 => ( dvd_dvd_nat @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdI
% 7.75/5.65 thf(fact_349_dvdI,axiom,
% 7.75/5.65 ! [A: int,B: int,K: int] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( times_times_int @ B @ K ) )
% 7.75/5.65 => ( dvd_dvd_int @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdI
% 7.75/5.65 thf(fact_350_dvdI,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,K: code_integer] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( times_3573771949741848930nteger @ B @ K ) )
% 7.75/5.65 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdI
% 7.75/5.65 thf(fact_351_dvdI,axiom,
% 7.75/5.65 ! [A: complex,B: complex,K: complex] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( times_times_complex @ B @ K ) )
% 7.75/5.65 => ( dvd_dvd_complex @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvdI
% 7.75/5.65 thf(fact_352_dvd__def,axiom,
% 7.75/5.65 ( dvd_dvd_assn
% 7.75/5.65 = ( ^ [B4: assn,A3: assn] :
% 7.75/5.65 ? [K3: assn] :
% 7.75/5.65 ( A3
% 7.75/5.65 = ( times_times_assn @ B4 @ K3 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_def
% 7.75/5.65 thf(fact_353_dvd__def,axiom,
% 7.75/5.65 ( dvd_dvd_real
% 7.75/5.65 = ( ^ [B4: real,A3: real] :
% 7.75/5.65 ? [K3: real] :
% 7.75/5.65 ( A3
% 7.75/5.65 = ( times_times_real @ B4 @ K3 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_def
% 7.75/5.65 thf(fact_354_dvd__def,axiom,
% 7.75/5.65 ( dvd_dvd_nat
% 7.75/5.65 = ( ^ [B4: nat,A3: nat] :
% 7.75/5.65 ? [K3: nat] :
% 7.75/5.65 ( A3
% 7.75/5.65 = ( times_times_nat @ B4 @ K3 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_def
% 7.75/5.65 thf(fact_355_dvd__def,axiom,
% 7.75/5.65 ( dvd_dvd_int
% 7.75/5.65 = ( ^ [B4: int,A3: int] :
% 7.75/5.65 ? [K3: int] :
% 7.75/5.65 ( A3
% 7.75/5.65 = ( times_times_int @ B4 @ K3 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_def
% 7.75/5.65 thf(fact_356_dvd__def,axiom,
% 7.75/5.65 ( dvd_dvd_Code_integer
% 7.75/5.65 = ( ^ [B4: code_integer,A3: code_integer] :
% 7.75/5.65 ? [K3: code_integer] :
% 7.75/5.65 ( A3
% 7.75/5.65 = ( times_3573771949741848930nteger @ B4 @ K3 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_def
% 7.75/5.65 thf(fact_357_dvd__def,axiom,
% 7.75/5.65 ( dvd_dvd_complex
% 7.75/5.65 = ( ^ [B4: complex,A3: complex] :
% 7.75/5.65 ? [K3: complex] :
% 7.75/5.65 ( A3
% 7.75/5.65 = ( times_times_complex @ B4 @ K3 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_def
% 7.75/5.65 thf(fact_358_dvd__mult,axiom,
% 7.75/5.65 ! [A: assn,C: assn,B: assn] :
% 7.75/5.65 ( ( dvd_dvd_assn @ A @ C )
% 7.75/5.65 => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult
% 7.75/5.65 thf(fact_359_dvd__mult,axiom,
% 7.75/5.65 ! [A: real,C: real,B: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ C )
% 7.75/5.65 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult
% 7.75/5.65 thf(fact_360_dvd__mult,axiom,
% 7.75/5.65 ! [A: nat,C: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ C )
% 7.75/5.65 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult
% 7.75/5.65 thf(fact_361_dvd__mult,axiom,
% 7.75/5.65 ! [A: int,C: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ C )
% 7.75/5.65 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult
% 7.75/5.65 thf(fact_362_dvd__mult,axiom,
% 7.75/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ A @ C )
% 7.75/5.65 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult
% 7.75/5.65 thf(fact_363_dvd__mult,axiom,
% 7.75/5.65 ! [A: complex,C: complex,B: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ A @ C )
% 7.75/5.65 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult
% 7.75/5.65 thf(fact_364_dvd__mult2,axiom,
% 7.75/5.65 ! [A: assn,B: assn,C: assn] :
% 7.75/5.65 ( ( dvd_dvd_assn @ A @ B )
% 7.75/5.65 => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult2
% 7.75/5.65 thf(fact_365_dvd__mult2,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ B )
% 7.75/5.65 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult2
% 7.75/5.65 thf(fact_366_dvd__mult2,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult2
% 7.75/5.65 thf(fact_367_dvd__mult2,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.65 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult2
% 7.75/5.65 thf(fact_368_dvd__mult2,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 7.75/5.65 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult2
% 7.75/5.65 thf(fact_369_dvd__mult2,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ A @ B )
% 7.75/5.65 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult2
% 7.75/5.65 thf(fact_370_dvd__mult__left,axiom,
% 7.75/5.65 ! [A: assn,B: assn,C: assn] :
% 7.75/5.65 ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_assn @ A @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_left
% 7.75/5.65 thf(fact_371_dvd__mult__left,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_real @ A @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_left
% 7.75/5.65 thf(fact_372_dvd__mult__left,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_nat @ A @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_left
% 7.75/5.65 thf(fact_373_dvd__mult__left,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_int @ A @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_left
% 7.75/5.65 thf(fact_374_dvd__mult__left,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_left
% 7.75/5.65 thf(fact_375_dvd__mult__left,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_complex @ A @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_left
% 7.75/5.65 thf(fact_376_dvd__triv__left,axiom,
% 7.75/5.65 ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_left
% 7.75/5.65 thf(fact_377_dvd__triv__left,axiom,
% 7.75/5.65 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_left
% 7.75/5.65 thf(fact_378_dvd__triv__left,axiom,
% 7.75/5.65 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_left
% 7.75/5.65 thf(fact_379_dvd__triv__left,axiom,
% 7.75/5.65 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_left
% 7.75/5.65 thf(fact_380_dvd__triv__left,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_left
% 7.75/5.65 thf(fact_381_dvd__triv__left,axiom,
% 7.75/5.65 ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_left
% 7.75/5.65 thf(fact_382_mult__dvd__mono,axiom,
% 7.75/5.65 ! [A: assn,B: assn,C: assn,D2: assn] :
% 7.75/5.65 ( ( dvd_dvd_assn @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_assn @ C @ D2 )
% 7.75/5.65 => ( dvd_dvd_assn @ ( times_times_assn @ A @ C ) @ ( times_times_assn @ B @ D2 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_dvd_mono
% 7.75/5.65 thf(fact_383_mult__dvd__mono,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_real @ C @ D2 )
% 7.75/5.65 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_dvd_mono
% 7.75/5.65 thf(fact_384_mult__dvd__mono,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ C @ D2 )
% 7.75/5.65 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_dvd_mono
% 7.75/5.65 thf(fact_385_mult__dvd__mono,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_int @ C @ D2 )
% 7.75/5.65 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_dvd_mono
% 7.75/5.65 thf(fact_386_mult__dvd__mono,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 7.75/5.65 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_dvd_mono
% 7.75/5.65 thf(fact_387_mult__dvd__mono,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex,D2: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_complex @ C @ D2 )
% 7.75/5.65 => ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D2 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_dvd_mono
% 7.75/5.65 thf(fact_388_dvd__mult__right,axiom,
% 7.75/5.65 ! [A: assn,B: assn,C: assn] :
% 7.75/5.65 ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_assn @ B @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_right
% 7.75/5.65 thf(fact_389_dvd__mult__right,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_real @ B @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_right
% 7.75/5.65 thf(fact_390_dvd__mult__right,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_nat @ B @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_right
% 7.75/5.65 thf(fact_391_dvd__mult__right,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_int @ B @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_right
% 7.75/5.65 thf(fact_392_dvd__mult__right,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_right
% 7.75/5.65 thf(fact_393_dvd__mult__right,axiom,
% 7.75/5.65 ! [A: complex,B: complex,C: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 7.75/5.65 => ( dvd_dvd_complex @ B @ C ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_right
% 7.75/5.65 thf(fact_394_dvd__triv__right,axiom,
% 7.75/5.65 ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_right
% 7.75/5.65 thf(fact_395_dvd__triv__right,axiom,
% 7.75/5.65 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_right
% 7.75/5.65 thf(fact_396_dvd__triv__right,axiom,
% 7.75/5.65 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_right
% 7.75/5.65 thf(fact_397_dvd__triv__right,axiom,
% 7.75/5.65 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_right
% 7.75/5.65 thf(fact_398_dvd__triv__right,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_right
% 7.75/5.65 thf(fact_399_dvd__triv__right,axiom,
% 7.75/5.65 ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_triv_right
% 7.75/5.65 thf(fact_400_dvd__div__eq__iff,axiom,
% 7.75/5.65 ! [C: complex,A: complex,B: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_complex @ C @ B )
% 7.75/5.65 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 7.75/5.65 = ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.65 = ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_iff
% 7.75/5.65 thf(fact_401_dvd__div__eq__iff,axiom,
% 7.75/5.65 ! [C: real,A: real,B: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_real @ C @ B )
% 7.75/5.65 => ( ( ( divide_divide_real @ A @ C )
% 7.75/5.65 = ( divide_divide_real @ B @ C ) )
% 7.75/5.65 = ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_iff
% 7.75/5.65 thf(fact_402_dvd__div__eq__iff,axiom,
% 7.75/5.65 ! [C: rat,A: rat,B: rat] :
% 7.75/5.65 ( ( dvd_dvd_rat @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_rat @ C @ B )
% 7.75/5.65 => ( ( ( divide_divide_rat @ A @ C )
% 7.75/5.65 = ( divide_divide_rat @ B @ C ) )
% 7.75/5.65 = ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_iff
% 7.75/5.65 thf(fact_403_dvd__div__eq__iff,axiom,
% 7.75/5.65 ! [C: nat,A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.65 => ( ( ( divide_divide_nat @ A @ C )
% 7.75/5.65 = ( divide_divide_nat @ B @ C ) )
% 7.75/5.65 = ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_iff
% 7.75/5.65 thf(fact_404_dvd__div__eq__iff,axiom,
% 7.75/5.65 ! [C: int,A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_int @ C @ B )
% 7.75/5.65 => ( ( ( divide_divide_int @ A @ C )
% 7.75/5.65 = ( divide_divide_int @ B @ C ) )
% 7.75/5.65 = ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_iff
% 7.75/5.65 thf(fact_405_dvd__div__eq__cancel,axiom,
% 7.75/5.65 ! [A: complex,C: complex,B: complex] :
% 7.75/5.65 ( ( ( divide1717551699836669952omplex @ A @ C )
% 7.75/5.65 = ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.65 => ( ( dvd_dvd_complex @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_complex @ C @ B )
% 7.75/5.65 => ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_cancel
% 7.75/5.65 thf(fact_406_dvd__div__eq__cancel,axiom,
% 7.75/5.65 ! [A: real,C: real,B: real] :
% 7.75/5.65 ( ( ( divide_divide_real @ A @ C )
% 7.75/5.65 = ( divide_divide_real @ B @ C ) )
% 7.75/5.65 => ( ( dvd_dvd_real @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_real @ C @ B )
% 7.75/5.65 => ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_cancel
% 7.75/5.65 thf(fact_407_dvd__div__eq__cancel,axiom,
% 7.75/5.65 ! [A: rat,C: rat,B: rat] :
% 7.75/5.65 ( ( ( divide_divide_rat @ A @ C )
% 7.75/5.65 = ( divide_divide_rat @ B @ C ) )
% 7.75/5.65 => ( ( dvd_dvd_rat @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_rat @ C @ B )
% 7.75/5.65 => ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_cancel
% 7.75/5.65 thf(fact_408_dvd__div__eq__cancel,axiom,
% 7.75/5.65 ! [A: nat,C: nat,B: nat] :
% 7.75/5.65 ( ( ( divide_divide_nat @ A @ C )
% 7.75/5.65 = ( divide_divide_nat @ B @ C ) )
% 7.75/5.65 => ( ( dvd_dvd_nat @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.65 => ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_cancel
% 7.75/5.65 thf(fact_409_dvd__div__eq__cancel,axiom,
% 7.75/5.65 ! [A: int,C: int,B: int] :
% 7.75/5.65 ( ( ( divide_divide_int @ A @ C )
% 7.75/5.65 = ( divide_divide_int @ B @ C ) )
% 7.75/5.65 => ( ( dvd_dvd_int @ C @ A )
% 7.75/5.65 => ( ( dvd_dvd_int @ C @ B )
% 7.75/5.65 => ( A = B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_eq_cancel
% 7.75/5.65 thf(fact_410_div__div__div__same,axiom,
% 7.75/5.65 ! [D2: nat,B: nat,A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ D2 @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.65 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D2 ) @ ( divide_divide_nat @ B @ D2 ) )
% 7.75/5.65 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_div_div_same
% 7.75/5.65 thf(fact_411_div__div__div__same,axiom,
% 7.75/5.65 ! [D2: int,B: int,A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ D2 @ B )
% 7.75/5.65 => ( ( dvd_dvd_int @ B @ A )
% 7.75/5.65 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D2 ) @ ( divide_divide_int @ B @ D2 ) )
% 7.75/5.65 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_div_div_same
% 7.75/5.65 thf(fact_412_mult__numeral__1,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ one ) @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1
% 7.75/5.65 thf(fact_413_mult__numeral__1,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1
% 7.75/5.65 thf(fact_414_mult__numeral__1,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1
% 7.75/5.65 thf(fact_415_mult__numeral__1,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1
% 7.75/5.65 thf(fact_416_mult__numeral__1,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1
% 7.75/5.65 thf(fact_417_mult__numeral__1,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1
% 7.75/5.65 thf(fact_418_mult__numeral__1__right,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ one ) )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1_right
% 7.75/5.65 thf(fact_419_mult__numeral__1__right,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1_right
% 7.75/5.65 thf(fact_420_mult__numeral__1__right,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1_right
% 7.75/5.65 thf(fact_421_mult__numeral__1__right,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1_right
% 7.75/5.65 thf(fact_422_mult__numeral__1__right,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1_right
% 7.75/5.65 thf(fact_423_mult__numeral__1__right,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_numeral_1_right
% 7.75/5.65 thf(fact_424_divide__numeral__1,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % divide_numeral_1
% 7.75/5.65 thf(fact_425_divide__numeral__1,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % divide_numeral_1
% 7.75/5.65 thf(fact_426_divide__numeral__1,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % divide_numeral_1
% 7.75/5.65 thf(fact_427_dvd__div__mult,axiom,
% 7.75/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ C @ B )
% 7.75/5.65 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 7.75/5.65 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_mult
% 7.75/5.65 thf(fact_428_dvd__div__mult,axiom,
% 7.75/5.65 ! [C: nat,B: nat,A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.65 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 7.75/5.65 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_mult
% 7.75/5.65 thf(fact_429_dvd__div__mult,axiom,
% 7.75/5.65 ! [C: int,B: int,A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ C @ B )
% 7.75/5.65 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 7.75/5.65 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_mult
% 7.75/5.65 thf(fact_430_div__mult__swap,axiom,
% 7.75/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ C @ B )
% 7.75/5.65 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 7.75/5.65 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_mult_swap
% 7.75/5.65 thf(fact_431_div__mult__swap,axiom,
% 7.75/5.65 ! [C: nat,B: nat,A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.65 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 7.75/5.65 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_mult_swap
% 7.75/5.65 thf(fact_432_div__mult__swap,axiom,
% 7.75/5.65 ! [C: int,B: int,A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ C @ B )
% 7.75/5.65 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 7.75/5.65 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_mult_swap
% 7.75/5.65 thf(fact_433_div__div__eq__right,axiom,
% 7.75/5.65 ! [C: code_integer,B: code_integer,A: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ C @ B )
% 7.75/5.65 => ( ( dvd_dvd_Code_integer @ B @ A )
% 7.75/5.65 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 7.75/5.65 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_div_eq_right
% 7.75/5.65 thf(fact_434_div__div__eq__right,axiom,
% 7.75/5.65 ! [C: nat,B: nat,A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.65 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 7.75/5.65 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_div_eq_right
% 7.75/5.65 thf(fact_435_div__div__eq__right,axiom,
% 7.75/5.65 ! [C: int,B: int,A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ C @ B )
% 7.75/5.65 => ( ( dvd_dvd_int @ B @ A )
% 7.75/5.65 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 7.75/5.65 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_div_eq_right
% 7.75/5.65 thf(fact_436_dvd__div__mult2__eq,axiom,
% 7.75/5.65 ! [B: code_integer,C: code_integer,A: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 7.75/5.65 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.65 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_mult2_eq
% 7.75/5.65 thf(fact_437_dvd__div__mult2__eq,axiom,
% 7.75/5.65 ! [B: nat,C: nat,A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 7.75/5.65 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 7.75/5.65 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_mult2_eq
% 7.75/5.65 thf(fact_438_dvd__div__mult2__eq,axiom,
% 7.75/5.65 ! [B: int,C: int,A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 7.75/5.65 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 7.75/5.65 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_div_mult2_eq
% 7.75/5.65 thf(fact_439_dvd__mult__imp__div,axiom,
% 7.75/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 7.75/5.65 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_imp_div
% 7.75/5.65 thf(fact_440_dvd__mult__imp__div,axiom,
% 7.75/5.65 ! [A: nat,C: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 7.75/5.65 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_imp_div
% 7.75/5.65 thf(fact_441_dvd__mult__imp__div,axiom,
% 7.75/5.65 ! [A: int,C: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 7.75/5.65 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_mult_imp_div
% 7.75/5.65 thf(fact_442_div__mult__div__if__dvd,axiom,
% 7.75/5.65 ! [B: code_integer,A: code_integer,D2: code_integer,C: code_integer] :
% 7.75/5.65 ( ( dvd_dvd_Code_integer @ B @ A )
% 7.75/5.65 => ( ( dvd_dvd_Code_integer @ D2 @ C )
% 7.75/5.65 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D2 ) )
% 7.75/5.65 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_mult_div_if_dvd
% 7.75/5.65 thf(fact_443_div__mult__div__if__dvd,axiom,
% 7.75/5.65 ! [B: nat,A: nat,D2: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.65 => ( ( dvd_dvd_nat @ D2 @ C )
% 7.75/5.65 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D2 ) )
% 7.75/5.65 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_mult_div_if_dvd
% 7.75/5.65 thf(fact_444_div__mult__div__if__dvd,axiom,
% 7.75/5.65 ! [B: int,A: int,D2: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ B @ A )
% 7.75/5.65 => ( ( dvd_dvd_int @ D2 @ C )
% 7.75/5.65 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D2 ) )
% 7.75/5.65 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_mult_div_if_dvd
% 7.75/5.65 thf(fact_445_mult__Suc__right,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( times_times_nat @ M @ ( suc @ N ) )
% 7.75/5.65 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_Suc_right
% 7.75/5.65 thf(fact_446_add__Suc__right,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 7.75/5.65 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_Suc_right
% 7.75/5.65 thf(fact_447_field__sum__of__halves,axiom,
% 7.75/5.65 ! [X: real] :
% 7.75/5.65 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = X ) ).
% 7.75/5.65
% 7.75/5.65 % field_sum_of_halves
% 7.75/5.65 thf(fact_448_field__sum__of__halves,axiom,
% 7.75/5.65 ! [X: rat] :
% 7.75/5.65 ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = X ) ).
% 7.75/5.65
% 7.75/5.65 % field_sum_of_halves
% 7.75/5.65 thf(fact_449_VEBT__internal_OT__vebt__buildupi_Osimps_I3_J,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.65 => ( ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ N ) ) )
% 7.75/5.65 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.65 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.65 => ( ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ N ) ) )
% 7.75/5.65 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % VEBT_internal.T_vebt_buildupi.simps(3)
% 7.75/5.65 thf(fact_450_triangle__def,axiom,
% 7.75/5.65 ( nat_triangle
% 7.75/5.65 = ( ^ [N3: nat] : ( divide_divide_nat @ ( times_times_nat @ N3 @ ( suc @ N3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % triangle_def
% 7.75/5.65 thf(fact_451_high__def,axiom,
% 7.75/5.65 ( vEBT_VEBT_high
% 7.75/5.65 = ( ^ [X2: nat,N3: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % high_def
% 7.75/5.65 thf(fact_452_bezout__lemma__nat,axiom,
% 7.75/5.65 ! [D2: nat,A: nat,B: nat,X: nat,Y: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ D2 @ A )
% 7.75/5.65 => ( ( dvd_dvd_nat @ D2 @ B )
% 7.75/5.65 => ( ( ( ( times_times_nat @ A @ X )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D2 ) )
% 7.75/5.65 | ( ( times_times_nat @ B @ X )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D2 ) ) )
% 7.75/5.65 => ? [X3: nat,Y3: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ D2 @ A )
% 7.75/5.65 & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A @ B ) )
% 7.75/5.65 & ( ( ( times_times_nat @ A @ X3 )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D2 ) )
% 7.75/5.65 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D2 ) ) ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % bezout_lemma_nat
% 7.75/5.65 thf(fact_453_bezout__add__nat,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ? [D3: nat,X3: nat,Y3: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ D3 @ A )
% 7.75/5.65 & ( dvd_dvd_nat @ D3 @ B )
% 7.75/5.65 & ( ( ( times_times_nat @ A @ X3 )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 7.75/5.65 | ( ( times_times_nat @ B @ X3 )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % bezout_add_nat
% 7.75/5.65 thf(fact_454_mult__Suc,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( suc @ M ) @ N )
% 7.75/5.65 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_Suc
% 7.75/5.65 thf(fact_455_highi__def,axiom,
% 7.75/5.65 ( vEBT_VEBT_highi
% 7.75/5.65 = ( ^ [X2: nat,N3: nat] : ( heap_Time_return_nat @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % highi_def
% 7.75/5.65 thf(fact_456_set__decode__Suc,axiom,
% 7.75/5.65 ! [N: nat,X: nat] :
% 7.75/5.65 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 7.75/5.65 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % set_decode_Suc
% 7.75/5.65 thf(fact_457_four__x__squared,axiom,
% 7.75/5.65 ! [X: real] :
% 7.75/5.65 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.65 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % four_x_squared
% 7.75/5.65 thf(fact_458_old_Onat_Oinject,axiom,
% 7.75/5.65 ! [Nat: nat,Nat2: nat] :
% 7.75/5.65 ( ( ( suc @ Nat )
% 7.75/5.65 = ( suc @ Nat2 ) )
% 7.75/5.65 = ( Nat = Nat2 ) ) ).
% 7.75/5.65
% 7.75/5.65 % old.nat.inject
% 7.75/5.65 thf(fact_459_nat_Oinject,axiom,
% 7.75/5.65 ! [X22: nat,Y22: nat] :
% 7.75/5.65 ( ( ( suc @ X22 )
% 7.75/5.65 = ( suc @ Y22 ) )
% 7.75/5.65 = ( X22 = Y22 ) ) ).
% 7.75/5.65
% 7.75/5.65 % nat.inject
% 7.75/5.65 thf(fact_460_real__divide__square__eq,axiom,
% 7.75/5.65 ! [R2: real,A: real] :
% 7.75/5.65 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 7.75/5.65 = ( divide_divide_real @ A @ R2 ) ) ).
% 7.75/5.65
% 7.75/5.65 % real_divide_square_eq
% 7.75/5.65 thf(fact_461_semiring__norm_I6_J,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 7.75/5.65 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % semiring_norm(6)
% 7.75/5.65 thf(fact_462_semiring__norm_I2_J,axiom,
% 7.75/5.65 ( ( plus_plus_num @ one @ one )
% 7.75/5.65 = ( bit0 @ one ) ) ).
% 7.75/5.65
% 7.75/5.65 % semiring_norm(2)
% 7.75/5.65 thf(fact_463_triangle__Suc,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( nat_triangle @ ( suc @ N ) )
% 7.75/5.65 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % triangle_Suc
% 7.75/5.65 thf(fact_464_Suc__numeral,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % Suc_numeral
% 7.75/5.65 thf(fact_465_power__add__numeral2,axiom,
% 7.75/5.65 ! [A: assn,M: num,N: num,B: assn] :
% 7.75/5.65 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 7.75/5.65 = ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral2
% 7.75/5.65 thf(fact_466_power__add__numeral2,axiom,
% 7.75/5.65 ! [A: real,M: num,N: num,B: real] :
% 7.75/5.65 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 7.75/5.65 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral2
% 7.75/5.65 thf(fact_467_power__add__numeral2,axiom,
% 7.75/5.65 ! [A: nat,M: num,N: num,B: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 7.75/5.65 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral2
% 7.75/5.65 thf(fact_468_power__add__numeral2,axiom,
% 7.75/5.65 ! [A: int,M: num,N: num,B: int] :
% 7.75/5.65 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 7.75/5.65 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral2
% 7.75/5.65 thf(fact_469_power__add__numeral2,axiom,
% 7.75/5.65 ! [A: code_integer,M: num,N: num,B: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 7.75/5.65 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral2
% 7.75/5.65 thf(fact_470_power__add__numeral2,axiom,
% 7.75/5.65 ! [A: complex,M: num,N: num,B: complex] :
% 7.75/5.65 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 7.75/5.65 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral2
% 7.75/5.65 thf(fact_471_power__add__numeral,axiom,
% 7.75/5.65 ! [A: assn,M: num,N: num] :
% 7.75/5.65 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N ) ) )
% 7.75/5.65 = ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral
% 7.75/5.65 thf(fact_472_power__add__numeral,axiom,
% 7.75/5.65 ! [A: real,M: num,N: num] :
% 7.75/5.65 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 7.75/5.65 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral
% 7.75/5.65 thf(fact_473_power__add__numeral,axiom,
% 7.75/5.65 ! [A: nat,M: num,N: num] :
% 7.75/5.65 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 7.75/5.65 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral
% 7.75/5.65 thf(fact_474_power__add__numeral,axiom,
% 7.75/5.65 ! [A: int,M: num,N: num] :
% 7.75/5.65 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 7.75/5.65 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral
% 7.75/5.65 thf(fact_475_power__add__numeral,axiom,
% 7.75/5.65 ! [A: code_integer,M: num,N: num] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) )
% 7.75/5.65 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral
% 7.75/5.65 thf(fact_476_power__add__numeral,axiom,
% 7.75/5.65 ! [A: complex,M: num,N: num] :
% 7.75/5.65 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 7.75/5.65 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_add_numeral
% 7.75/5.65 thf(fact_477_add__One__commute,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( plus_plus_num @ one @ N )
% 7.75/5.65 = ( plus_plus_num @ N @ one ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_One_commute
% 7.75/5.65 thf(fact_478_n__not__Suc__n,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( N
% 7.75/5.65 != ( suc @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % n_not_Suc_n
% 7.75/5.65 thf(fact_479_Suc__inject,axiom,
% 7.75/5.65 ! [X: nat,Y: nat] :
% 7.75/5.65 ( ( ( suc @ X )
% 7.75/5.65 = ( suc @ Y ) )
% 7.75/5.65 => ( X = Y ) ) ).
% 7.75/5.65
% 7.75/5.65 % Suc_inject
% 7.75/5.65 thf(fact_480_gcd__nat_Oasym,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ( A != B ) )
% 7.75/5.65 => ~ ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.65 & ( B != A ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.asym
% 7.75/5.65 thf(fact_481_gcd__nat_Orefl,axiom,
% 7.75/5.65 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.refl
% 7.75/5.65 thf(fact_482_gcd__nat_Otrans,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ B @ C )
% 7.75/5.65 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.trans
% 7.75/5.65 thf(fact_483_gcd__nat_Oeq__iff,axiom,
% 7.75/5.65 ( ( ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 ) )
% 7.75/5.65 = ( ^ [A3: nat,B4: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A3 @ B4 )
% 7.75/5.65 & ( dvd_dvd_nat @ B4 @ A3 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.eq_iff
% 7.75/5.65 thf(fact_484_gcd__nat_Oirrefl,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ~ ( ( dvd_dvd_nat @ A @ A )
% 7.75/5.65 & ( A != A ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.irrefl
% 7.75/5.65 thf(fact_485_gcd__nat_Oantisym,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.65 => ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.antisym
% 7.75/5.65 thf(fact_486_gcd__nat_Ostrict__trans,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ( A != B ) )
% 7.75/5.65 => ( ( ( dvd_dvd_nat @ B @ C )
% 7.75/5.65 & ( B != C ) )
% 7.75/5.65 => ( ( dvd_dvd_nat @ A @ C )
% 7.75/5.65 & ( A != C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.strict_trans
% 7.75/5.65 thf(fact_487_gcd__nat_Ostrict__trans1,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( ( dvd_dvd_nat @ B @ C )
% 7.75/5.65 & ( B != C ) )
% 7.75/5.65 => ( ( dvd_dvd_nat @ A @ C )
% 7.75/5.65 & ( A != C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.strict_trans1
% 7.75/5.65 thf(fact_488_gcd__nat_Ostrict__trans2,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ( A != B ) )
% 7.75/5.65 => ( ( dvd_dvd_nat @ B @ C )
% 7.75/5.65 => ( ( dvd_dvd_nat @ A @ C )
% 7.75/5.65 & ( A != C ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.strict_trans2
% 7.75/5.65 thf(fact_489_gcd__nat_Ostrict__iff__not,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ( A != B ) )
% 7.75/5.65 = ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.strict_iff_not
% 7.75/5.65 thf(fact_490_gcd__nat_Oorder__iff__strict,axiom,
% 7.75/5.65 ( dvd_dvd_nat
% 7.75/5.65 = ( ^ [A3: nat,B4: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ A3 @ B4 )
% 7.75/5.65 & ( A3 != B4 ) )
% 7.75/5.65 | ( A3 = B4 ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.order_iff_strict
% 7.75/5.65 thf(fact_491_gcd__nat_Ostrict__iff__order,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ( A != B ) )
% 7.75/5.65 = ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ( A != B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.strict_iff_order
% 7.75/5.65 thf(fact_492_gcd__nat_Ostrict__implies__order,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ( A != B ) )
% 7.75/5.65 => ( dvd_dvd_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.strict_implies_order
% 7.75/5.65 thf(fact_493_gcd__nat_Ostrict__implies__not__eq,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ( A != B ) )
% 7.75/5.65 => ( A != B ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.strict_implies_not_eq
% 7.75/5.65 thf(fact_494_gcd__nat_Onot__eq__order__implies__strict,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( A != B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 => ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.65 & ( A != B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % gcd_nat.not_eq_order_implies_strict
% 7.75/5.65 thf(fact_495_dvd__antisym,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ M @ N )
% 7.75/5.65 => ( ( dvd_dvd_nat @ N @ M )
% 7.75/5.65 => ( M = N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_antisym
% 7.75/5.65 thf(fact_496_Suc__nat__number__of__add,axiom,
% 7.75/5.65 ! [V: num,N: nat] :
% 7.75/5.65 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 7.75/5.65 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % Suc_nat_number_of_add
% 7.75/5.65 thf(fact_497_division__decomp,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 7.75/5.65 => ? [B5: nat,C2: nat] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( times_times_nat @ B5 @ C2 ) )
% 7.75/5.65 & ( dvd_dvd_nat @ B5 @ B )
% 7.75/5.65 & ( dvd_dvd_nat @ C2 @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % division_decomp
% 7.75/5.65 thf(fact_498_division__decomp,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 7.75/5.65 => ? [B5: int,C2: int] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( times_times_int @ B5 @ C2 ) )
% 7.75/5.65 & ( dvd_dvd_int @ B5 @ B )
% 7.75/5.65 & ( dvd_dvd_int @ C2 @ C ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % division_decomp
% 7.75/5.65 thf(fact_499_dvd__productE,axiom,
% 7.75/5.65 ! [P4: nat,A: nat,B: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ P4 @ ( times_times_nat @ A @ B ) )
% 7.75/5.65 => ~ ! [X3: nat,Y3: nat] :
% 7.75/5.65 ( ( P4
% 7.75/5.65 = ( times_times_nat @ X3 @ Y3 ) )
% 7.75/5.65 => ( ( dvd_dvd_nat @ X3 @ A )
% 7.75/5.65 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_productE
% 7.75/5.65 thf(fact_500_dvd__productE,axiom,
% 7.75/5.65 ! [P4: int,A: int,B: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ P4 @ ( times_times_int @ A @ B ) )
% 7.75/5.65 => ~ ! [X3: int,Y3: int] :
% 7.75/5.65 ( ( P4
% 7.75/5.65 = ( times_times_int @ X3 @ Y3 ) )
% 7.75/5.65 => ( ( dvd_dvd_int @ X3 @ A )
% 7.75/5.65 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_productE
% 7.75/5.65 thf(fact_501_add__Suc__shift,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 7.75/5.65 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_Suc_shift
% 7.75/5.65 thf(fact_502_add__Suc,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 7.75/5.65 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_Suc
% 7.75/5.65 thf(fact_503_nat__arith_Osuc1,axiom,
% 7.75/5.65 ! [A2: nat,K: nat,A: nat] :
% 7.75/5.65 ( ( A2
% 7.75/5.65 = ( plus_plus_nat @ K @ A ) )
% 7.75/5.65 => ( ( suc @ A2 )
% 7.75/5.65 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % nat_arith.suc1
% 7.75/5.65 thf(fact_504_Suc__mult__cancel1,axiom,
% 7.75/5.65 ! [K: nat,M: nat,N: nat] :
% 7.75/5.65 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 7.75/5.65 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 7.75/5.65 = ( M = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % Suc_mult_cancel1
% 7.75/5.65 thf(fact_505_add__mult__distrib2,axiom,
% 7.75/5.65 ! [K: nat,M: nat,N: nat] :
% 7.75/5.65 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_mult_distrib2
% 7.75/5.65 thf(fact_506_add__mult__distrib,axiom,
% 7.75/5.65 ! [M: nat,N: nat,K: nat] :
% 7.75/5.65 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 7.75/5.65 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_mult_distrib
% 7.75/5.65 thf(fact_507_high__inv,axiom,
% 7.75/5.65 ! [X: nat,N: nat,Y: nat] :
% 7.75/5.65 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.65 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 7.75/5.65 = Y ) ) ).
% 7.75/5.65
% 7.75/5.65 % high_inv
% 7.75/5.65 thf(fact_508_high__bound__aux,axiom,
% 7.75/5.65 ! [Ma: nat,N: nat,M: nat] :
% 7.75/5.65 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 7.75/5.65 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % high_bound_aux
% 7.75/5.65 thf(fact_509_VEBT__internal_OT__vebt__buildupi_Oelims,axiom,
% 7.75/5.65 ! [X: nat,Y: nat] :
% 7.75/5.65 ( ( ( vEBT_V441764108873111860ildupi @ X )
% 7.75/5.65 = Y )
% 7.75/5.65 => ( ( ( X = zero_zero_nat )
% 7.75/5.65 => ( Y
% 7.75/5.65 != ( suc @ zero_zero_nat ) ) )
% 7.75/5.65 => ( ( ( X
% 7.75/5.65 = ( suc @ zero_zero_nat ) )
% 7.75/5.65 => ( Y
% 7.75/5.65 != ( suc @ zero_zero_nat ) ) )
% 7.75/5.65 => ~ ! [N2: nat] :
% 7.75/5.65 ( ( X
% 7.75/5.65 = ( suc @ ( suc @ N2 ) ) )
% 7.75/5.65 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 7.75/5.65 => ( Y
% 7.75/5.65 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.65 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 7.75/5.65 => ( Y
% 7.75/5.65 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % VEBT_internal.T_vebt_buildupi.elims
% 7.75/5.65 thf(fact_510_power__numeral,axiom,
% 7.75/5.65 ! [K: num,L: num] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ K ) @ ( numeral_numeral_nat @ L ) )
% 7.75/5.65 = ( numera6620942414471956472nteger @ ( pow @ K @ L ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_numeral
% 7.75/5.65 thf(fact_511_power__numeral,axiom,
% 7.75/5.65 ! [K: num,L: num] :
% 7.75/5.65 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 7.75/5.65 = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_numeral
% 7.75/5.65 thf(fact_512_power__numeral,axiom,
% 7.75/5.65 ! [K: num,L: num] :
% 7.75/5.65 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 7.75/5.65 = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_numeral
% 7.75/5.65 thf(fact_513_power__numeral,axiom,
% 7.75/5.65 ! [K: num,L: num] :
% 7.75/5.65 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L ) )
% 7.75/5.65 = ( numeral_numeral_rat @ ( pow @ K @ L ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_numeral
% 7.75/5.65 thf(fact_514_power__numeral,axiom,
% 7.75/5.65 ! [K: num,L: num] :
% 7.75/5.65 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 7.75/5.65 = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_numeral
% 7.75/5.65 thf(fact_515_power__numeral,axiom,
% 7.75/5.65 ! [K: num,L: num] :
% 7.75/5.65 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 7.75/5.65 = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % power_numeral
% 7.75/5.65 thf(fact_516_odd__two__times__div__two__succ,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 7.75/5.65 = A ) ) ).
% 7.75/5.65
% 7.75/5.65 % odd_two_times_div_two_succ
% 7.75/5.65 thf(fact_517_odd__two__times__div__two__succ,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 7.75/5.65 = A ) ) ).
% 7.75/5.65
% 7.75/5.65 % odd_two_times_div_two_succ
% 7.75/5.65 thf(fact_518_odd__two__times__div__two__succ,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.65 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 7.75/5.65 = A ) ) ).
% 7.75/5.65
% 7.75/5.65 % odd_two_times_div_two_succ
% 7.75/5.65 thf(fact_519_add__left__cancel,axiom,
% 7.75/5.65 ! [A: real,B: real,C: real] :
% 7.75/5.65 ( ( ( plus_plus_real @ A @ B )
% 7.75/5.65 = ( plus_plus_real @ A @ C ) )
% 7.75/5.65 = ( B = C ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_left_cancel
% 7.75/5.65 thf(fact_520_add__left__cancel,axiom,
% 7.75/5.65 ! [A: rat,B: rat,C: rat] :
% 7.75/5.65 ( ( ( plus_plus_rat @ A @ B )
% 7.75/5.65 = ( plus_plus_rat @ A @ C ) )
% 7.75/5.65 = ( B = C ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_left_cancel
% 7.75/5.65 thf(fact_521_add__left__cancel,axiom,
% 7.75/5.65 ! [A: nat,B: nat,C: nat] :
% 7.75/5.65 ( ( ( plus_plus_nat @ A @ B )
% 7.75/5.65 = ( plus_plus_nat @ A @ C ) )
% 7.75/5.65 = ( B = C ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_left_cancel
% 7.75/5.65 thf(fact_522_add__left__cancel,axiom,
% 7.75/5.65 ! [A: int,B: int,C: int] :
% 7.75/5.65 ( ( ( plus_plus_int @ A @ B )
% 7.75/5.65 = ( plus_plus_int @ A @ C ) )
% 7.75/5.65 = ( B = C ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_left_cancel
% 7.75/5.65 thf(fact_523_add__right__cancel,axiom,
% 7.75/5.65 ! [B: real,A: real,C: real] :
% 7.75/5.65 ( ( ( plus_plus_real @ B @ A )
% 7.75/5.65 = ( plus_plus_real @ C @ A ) )
% 7.75/5.65 = ( B = C ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_right_cancel
% 7.75/5.65 thf(fact_524_add__right__cancel,axiom,
% 7.75/5.65 ! [B: rat,A: rat,C: rat] :
% 7.75/5.65 ( ( ( plus_plus_rat @ B @ A )
% 7.75/5.65 = ( plus_plus_rat @ C @ A ) )
% 7.75/5.65 = ( B = C ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_right_cancel
% 7.75/5.65 thf(fact_525_add__right__cancel,axiom,
% 7.75/5.65 ! [B: nat,A: nat,C: nat] :
% 7.75/5.65 ( ( ( plus_plus_nat @ B @ A )
% 7.75/5.65 = ( plus_plus_nat @ C @ A ) )
% 7.75/5.65 = ( B = C ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_right_cancel
% 7.75/5.65 thf(fact_526_add__right__cancel,axiom,
% 7.75/5.65 ! [B: int,A: int,C: int] :
% 7.75/5.65 ( ( ( plus_plus_int @ B @ A )
% 7.75/5.65 = ( plus_plus_int @ C @ A ) )
% 7.75/5.65 = ( B = C ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_right_cancel
% 7.75/5.65 thf(fact_527_verit__eq__simplify_I8_J,axiom,
% 7.75/5.65 ! [X22: num,Y22: num] :
% 7.75/5.65 ( ( ( bit0 @ X22 )
% 7.75/5.65 = ( bit0 @ Y22 ) )
% 7.75/5.65 = ( X22 = Y22 ) ) ).
% 7.75/5.65
% 7.75/5.65 % verit_eq_simplify(8)
% 7.75/5.65 thf(fact_528_zdiv__numeral__Bit0,axiom,
% 7.75/5.65 ! [V: num,W: num] :
% 7.75/5.65 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 7.75/5.65 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % zdiv_numeral_Bit0
% 7.75/5.65 thf(fact_529_lowi__def,axiom,
% 7.75/5.65 ( vEBT_VEBT_lowi
% 7.75/5.65 = ( ^ [X2: nat,N3: nat] : ( heap_Time_return_nat @ ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % lowi_def
% 7.75/5.65 thf(fact_530_list__assn__mono,axiom,
% 7.75/5.65 ! [P: vEBT_VEBT > vEBT_VEBTi > assn,P3: vEBT_VEBT > vEBT_VEBTi > assn,L: list_VEBT_VEBT,L3: list_VEBT_VEBTi] :
% 7.75/5.65 ( ! [X3: vEBT_VEBT,X4: vEBT_VEBTi] : ( entails @ ( P @ X3 @ X4 ) @ ( P3 @ X3 @ X4 ) )
% 7.75/5.65 => ( entails @ ( vEBT_L6296928887356842470_VEBTi @ P @ L @ L3 ) @ ( vEBT_L6296928887356842470_VEBTi @ P3 @ L @ L3 ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % list_assn_mono
% 7.75/5.65 thf(fact_531_buildup__nothing__in__min__max,axiom,
% 7.75/5.65 ! [N: nat,X: nat] :
% 7.75/5.65 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 7.75/5.65
% 7.75/5.65 % buildup_nothing_in_min_max
% 7.75/5.65 thf(fact_532_power__one__right,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( power_power_nat @ A @ one_one_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % power_one_right
% 7.75/5.65 thf(fact_533_power__one__right,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( power_power_real @ A @ one_one_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % power_one_right
% 7.75/5.65 thf(fact_534_power__one__right,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( power_power_int @ A @ one_one_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % power_one_right
% 7.75/5.65 thf(fact_535_power__one__right,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( power_power_complex @ A @ one_one_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % power_one_right
% 7.75/5.65 thf(fact_536_power__one__right,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ A @ one_one_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % power_one_right
% 7.75/5.65 thf(fact_537_power__one__right,axiom,
% 7.75/5.65 ! [A: assn] :
% 7.75/5.65 ( ( power_power_assn @ A @ one_one_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % power_one_right
% 7.75/5.65 thf(fact_538_mod__mod__trivial,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 7.75/5.65 = ( modulo_modulo_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_mod_trivial
% 7.75/5.65 thf(fact_539_mod__mod__trivial,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 7.75/5.65 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_mod_trivial
% 7.75/5.65 thf(fact_540_mod__mod__trivial,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer] :
% 7.75/5.65 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 7.75/5.65 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_mod_trivial
% 7.75/5.65 thf(fact_541_nat__1__eq__mult__iff,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( one_one_nat
% 7.75/5.65 = ( times_times_nat @ M @ N ) )
% 7.75/5.65 = ( ( M = one_one_nat )
% 7.75/5.65 & ( N = one_one_nat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % nat_1_eq_mult_iff
% 7.75/5.65 thf(fact_542_nat__mult__eq__1__iff,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( ( times_times_nat @ M @ N )
% 7.75/5.65 = one_one_nat )
% 7.75/5.65 = ( ( M = one_one_nat )
% 7.75/5.65 & ( N = one_one_nat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % nat_mult_eq_1_iff
% 7.75/5.65 thf(fact_543_nat__dvd__1__iff__1,axiom,
% 7.75/5.65 ! [M: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 7.75/5.65 = ( M = one_one_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % nat_dvd_1_iff_1
% 7.75/5.65 thf(fact_544_pure__true,axiom,
% 7.75/5.65 ( ( pure_assn @ $true )
% 7.75/5.65 = one_one_assn ) ).
% 7.75/5.65
% 7.75/5.65 % pure_true
% 7.75/5.65 thf(fact_545_pure__assn__eq__emp__iff,axiom,
% 7.75/5.65 ! [P: $o] :
% 7.75/5.65 ( ( ( pure_assn @ P )
% 7.75/5.65 = one_one_assn )
% 7.75/5.65 = P ) ).
% 7.75/5.65
% 7.75/5.65 % pure_assn_eq_emp_iff
% 7.75/5.65 thf(fact_546_not__gr__zero,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 7.75/5.65 = ( N = zero_zero_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % not_gr_zero
% 7.75/5.65 thf(fact_547_numeral__less__iff,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.65 = ( ord_less_num @ M @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_less_iff
% 7.75/5.65 thf(fact_548_numeral__less__iff,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 7.75/5.65 = ( ord_less_num @ M @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_less_iff
% 7.75/5.65 thf(fact_549_numeral__less__iff,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( ord_less_num @ M @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_less_iff
% 7.75/5.65 thf(fact_550_numeral__less__iff,axiom,
% 7.75/5.65 ! [M: num,N: num] :
% 7.75/5.65 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 7.75/5.65 = ( ord_less_num @ M @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_less_iff
% 7.75/5.65 thf(fact_551_add__0,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add_0
% 7.75/5.65 thf(fact_552_add__0,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( plus_plus_real @ zero_zero_real @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add_0
% 7.75/5.65 thf(fact_553_add__0,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add_0
% 7.75/5.65 thf(fact_554_add__0,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add_0
% 7.75/5.65 thf(fact_555_add__0,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( plus_plus_int @ zero_zero_int @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add_0
% 7.75/5.65 thf(fact_556_zero__eq__add__iff__both__eq__0,axiom,
% 7.75/5.65 ! [X: nat,Y: nat] :
% 7.75/5.65 ( ( zero_zero_nat
% 7.75/5.65 = ( plus_plus_nat @ X @ Y ) )
% 7.75/5.65 = ( ( X = zero_zero_nat )
% 7.75/5.65 & ( Y = zero_zero_nat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % zero_eq_add_iff_both_eq_0
% 7.75/5.65 thf(fact_557_add__eq__0__iff__both__eq__0,axiom,
% 7.75/5.65 ! [X: nat,Y: nat] :
% 7.75/5.65 ( ( ( plus_plus_nat @ X @ Y )
% 7.75/5.65 = zero_zero_nat )
% 7.75/5.65 = ( ( X = zero_zero_nat )
% 7.75/5.65 & ( Y = zero_zero_nat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_eq_0_iff_both_eq_0
% 7.75/5.65 thf(fact_558_add__cancel__right__right,axiom,
% 7.75/5.65 ! [A: complex,B: complex] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_complex @ A @ B ) )
% 7.75/5.65 = ( B = zero_zero_complex ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_right
% 7.75/5.65 thf(fact_559_add__cancel__right__right,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_real @ A @ B ) )
% 7.75/5.65 = ( B = zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_right
% 7.75/5.65 thf(fact_560_add__cancel__right__right,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_rat @ A @ B ) )
% 7.75/5.65 = ( B = zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_right
% 7.75/5.65 thf(fact_561_add__cancel__right__right,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_nat @ A @ B ) )
% 7.75/5.65 = ( B = zero_zero_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_right
% 7.75/5.65 thf(fact_562_add__cancel__right__right,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_int @ A @ B ) )
% 7.75/5.65 = ( B = zero_zero_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_right
% 7.75/5.65 thf(fact_563_add__cancel__right__left,axiom,
% 7.75/5.65 ! [A: complex,B: complex] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_complex @ B @ A ) )
% 7.75/5.65 = ( B = zero_zero_complex ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_left
% 7.75/5.65 thf(fact_564_add__cancel__right__left,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_real @ B @ A ) )
% 7.75/5.65 = ( B = zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_left
% 7.75/5.65 thf(fact_565_add__cancel__right__left,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_rat @ B @ A ) )
% 7.75/5.65 = ( B = zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_left
% 7.75/5.65 thf(fact_566_add__cancel__right__left,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_nat @ B @ A ) )
% 7.75/5.65 = ( B = zero_zero_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_left
% 7.75/5.65 thf(fact_567_add__cancel__right__left,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( A
% 7.75/5.65 = ( plus_plus_int @ B @ A ) )
% 7.75/5.65 = ( B = zero_zero_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_right_left
% 7.75/5.65 thf(fact_568_add__cancel__left__right,axiom,
% 7.75/5.65 ! [A: complex,B: complex] :
% 7.75/5.65 ( ( ( plus_plus_complex @ A @ B )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_complex ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_right
% 7.75/5.65 thf(fact_569_add__cancel__left__right,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( ( plus_plus_real @ A @ B )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_right
% 7.75/5.65 thf(fact_570_add__cancel__left__right,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( ( plus_plus_rat @ A @ B )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_right
% 7.75/5.65 thf(fact_571_add__cancel__left__right,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ( plus_plus_nat @ A @ B )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_right
% 7.75/5.65 thf(fact_572_add__cancel__left__right,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( ( plus_plus_int @ A @ B )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_right
% 7.75/5.65 thf(fact_573_add__cancel__left__left,axiom,
% 7.75/5.65 ! [B: complex,A: complex] :
% 7.75/5.65 ( ( ( plus_plus_complex @ B @ A )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_complex ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_left
% 7.75/5.65 thf(fact_574_add__cancel__left__left,axiom,
% 7.75/5.65 ! [B: real,A: real] :
% 7.75/5.65 ( ( ( plus_plus_real @ B @ A )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_left
% 7.75/5.65 thf(fact_575_add__cancel__left__left,axiom,
% 7.75/5.65 ! [B: rat,A: rat] :
% 7.75/5.65 ( ( ( plus_plus_rat @ B @ A )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_left
% 7.75/5.65 thf(fact_576_add__cancel__left__left,axiom,
% 7.75/5.65 ! [B: nat,A: nat] :
% 7.75/5.65 ( ( ( plus_plus_nat @ B @ A )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_left
% 7.75/5.65 thf(fact_577_add__cancel__left__left,axiom,
% 7.75/5.65 ! [B: int,A: int] :
% 7.75/5.65 ( ( ( plus_plus_int @ B @ A )
% 7.75/5.65 = A )
% 7.75/5.65 = ( B = zero_zero_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_cancel_left_left
% 7.75/5.65 thf(fact_578_double__zero__sym,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( zero_zero_real
% 7.75/5.65 = ( plus_plus_real @ A @ A ) )
% 7.75/5.65 = ( A = zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % double_zero_sym
% 7.75/5.65 thf(fact_579_double__zero__sym,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( zero_zero_rat
% 7.75/5.65 = ( plus_plus_rat @ A @ A ) )
% 7.75/5.65 = ( A = zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % double_zero_sym
% 7.75/5.65 thf(fact_580_double__zero__sym,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( zero_zero_int
% 7.75/5.65 = ( plus_plus_int @ A @ A ) )
% 7.75/5.65 = ( A = zero_zero_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % double_zero_sym
% 7.75/5.65 thf(fact_581_add_Oright__neutral,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add.right_neutral
% 7.75/5.65 thf(fact_582_add_Oright__neutral,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( plus_plus_real @ A @ zero_zero_real )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add.right_neutral
% 7.75/5.65 thf(fact_583_add_Oright__neutral,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add.right_neutral
% 7.75/5.65 thf(fact_584_add_Oright__neutral,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add.right_neutral
% 7.75/5.65 thf(fact_585_add_Oright__neutral,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( plus_plus_int @ A @ zero_zero_int )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % add.right_neutral
% 7.75/5.65 thf(fact_586_mult__zero__left,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( times_times_rat @ zero_zero_rat @ A )
% 7.75/5.65 = zero_zero_rat ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_left
% 7.75/5.65 thf(fact_587_mult__zero__left,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( times_times_real @ zero_zero_real @ A )
% 7.75/5.65 = zero_zero_real ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_left
% 7.75/5.65 thf(fact_588_mult__zero__left,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( times_times_nat @ zero_zero_nat @ A )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_left
% 7.75/5.65 thf(fact_589_mult__zero__left,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( times_times_int @ zero_zero_int @ A )
% 7.75/5.65 = zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_left
% 7.75/5.65 thf(fact_590_mult__zero__left,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.65 = zero_z3403309356797280102nteger ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_left
% 7.75/5.65 thf(fact_591_mult__zero__left,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( times_times_complex @ zero_zero_complex @ A )
% 7.75/5.65 = zero_zero_complex ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_left
% 7.75/5.65 thf(fact_592_mult__zero__right,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( times_times_rat @ A @ zero_zero_rat )
% 7.75/5.65 = zero_zero_rat ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_right
% 7.75/5.65 thf(fact_593_mult__zero__right,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( times_times_real @ A @ zero_zero_real )
% 7.75/5.65 = zero_zero_real ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_right
% 7.75/5.65 thf(fact_594_mult__zero__right,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( times_times_nat @ A @ zero_zero_nat )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_right
% 7.75/5.65 thf(fact_595_mult__zero__right,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( times_times_int @ A @ zero_zero_int )
% 7.75/5.65 = zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_right
% 7.75/5.65 thf(fact_596_mult__zero__right,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.65 = zero_z3403309356797280102nteger ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_right
% 7.75/5.65 thf(fact_597_mult__zero__right,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( times_times_complex @ A @ zero_zero_complex )
% 7.75/5.65 = zero_zero_complex ) ).
% 7.75/5.65
% 7.75/5.65 % mult_zero_right
% 7.75/5.65 thf(fact_598_mult__eq__0__iff,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( ( times_times_rat @ A @ B )
% 7.75/5.65 = zero_zero_rat )
% 7.75/5.65 = ( ( A = zero_zero_rat )
% 7.75/5.65 | ( B = zero_zero_rat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_eq_0_iff
% 7.75/5.65 thf(fact_599_mult__eq__0__iff,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( ( times_times_real @ A @ B )
% 7.75/5.65 = zero_zero_real )
% 7.75/5.65 = ( ( A = zero_zero_real )
% 7.75/5.65 | ( B = zero_zero_real ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_eq_0_iff
% 7.75/5.65 thf(fact_600_mult__eq__0__iff,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ( times_times_nat @ A @ B )
% 7.75/5.65 = zero_zero_nat )
% 7.75/5.65 = ( ( A = zero_zero_nat )
% 7.75/5.65 | ( B = zero_zero_nat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_eq_0_iff
% 7.75/5.65 thf(fact_601_mult__eq__0__iff,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( ( times_times_int @ A @ B )
% 7.75/5.65 = zero_zero_int )
% 7.75/5.65 = ( ( A = zero_zero_int )
% 7.75/5.65 | ( B = zero_zero_int ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_eq_0_iff
% 7.75/5.65 thf(fact_602_mult__eq__0__iff,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer] :
% 7.75/5.65 ( ( ( times_3573771949741848930nteger @ A @ B )
% 7.75/5.65 = zero_z3403309356797280102nteger )
% 7.75/5.65 = ( ( A = zero_z3403309356797280102nteger )
% 7.75/5.65 | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_eq_0_iff
% 7.75/5.65 thf(fact_603_mult__eq__0__iff,axiom,
% 7.75/5.65 ! [A: complex,B: complex] :
% 7.75/5.65 ( ( ( times_times_complex @ A @ B )
% 7.75/5.65 = zero_zero_complex )
% 7.75/5.65 = ( ( A = zero_zero_complex )
% 7.75/5.65 | ( B = zero_zero_complex ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_eq_0_iff
% 7.75/5.65 thf(fact_604_mult__cancel__left,axiom,
% 7.75/5.65 ! [C: rat,A: rat,B: rat] :
% 7.75/5.65 ( ( ( times_times_rat @ C @ A )
% 7.75/5.65 = ( times_times_rat @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_rat )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left
% 7.75/5.65 thf(fact_605_mult__cancel__left,axiom,
% 7.75/5.65 ! [C: real,A: real,B: real] :
% 7.75/5.65 ( ( ( times_times_real @ C @ A )
% 7.75/5.65 = ( times_times_real @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_real )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left
% 7.75/5.65 thf(fact_606_mult__cancel__left,axiom,
% 7.75/5.65 ! [C: nat,A: nat,B: nat] :
% 7.75/5.65 ( ( ( times_times_nat @ C @ A )
% 7.75/5.65 = ( times_times_nat @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_nat )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left
% 7.75/5.65 thf(fact_607_mult__cancel__left,axiom,
% 7.75/5.65 ! [C: int,A: int,B: int] :
% 7.75/5.65 ( ( ( times_times_int @ C @ A )
% 7.75/5.65 = ( times_times_int @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_int )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left
% 7.75/5.65 thf(fact_608_mult__cancel__left,axiom,
% 7.75/5.65 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.65 ( ( ( times_3573771949741848930nteger @ C @ A )
% 7.75/5.65 = ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_z3403309356797280102nteger )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left
% 7.75/5.65 thf(fact_609_mult__cancel__left,axiom,
% 7.75/5.65 ! [C: complex,A: complex,B: complex] :
% 7.75/5.65 ( ( ( times_times_complex @ C @ A )
% 7.75/5.65 = ( times_times_complex @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_complex )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left
% 7.75/5.65 thf(fact_610_mult__cancel__right,axiom,
% 7.75/5.65 ! [A: rat,C: rat,B: rat] :
% 7.75/5.65 ( ( ( times_times_rat @ A @ C )
% 7.75/5.65 = ( times_times_rat @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_rat )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right
% 7.75/5.65 thf(fact_611_mult__cancel__right,axiom,
% 7.75/5.65 ! [A: real,C: real,B: real] :
% 7.75/5.65 ( ( ( times_times_real @ A @ C )
% 7.75/5.65 = ( times_times_real @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_real )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right
% 7.75/5.65 thf(fact_612_mult__cancel__right,axiom,
% 7.75/5.65 ! [A: nat,C: nat,B: nat] :
% 7.75/5.65 ( ( ( times_times_nat @ A @ C )
% 7.75/5.65 = ( times_times_nat @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_nat )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right
% 7.75/5.65 thf(fact_613_mult__cancel__right,axiom,
% 7.75/5.65 ! [A: int,C: int,B: int] :
% 7.75/5.65 ( ( ( times_times_int @ A @ C )
% 7.75/5.65 = ( times_times_int @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_int )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right
% 7.75/5.65 thf(fact_614_mult__cancel__right,axiom,
% 7.75/5.65 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.65 ( ( ( times_3573771949741848930nteger @ A @ C )
% 7.75/5.65 = ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_z3403309356797280102nteger )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right
% 7.75/5.65 thf(fact_615_mult__cancel__right,axiom,
% 7.75/5.65 ! [A: complex,C: complex,B: complex] :
% 7.75/5.65 ( ( ( times_times_complex @ A @ C )
% 7.75/5.65 = ( times_times_complex @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_complex )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right
% 7.75/5.65 thf(fact_616_add__less__cancel__right,axiom,
% 7.75/5.65 ! [A: real,C: real,B: real] :
% 7.75/5.65 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 7.75/5.65 = ( ord_less_real @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_cancel_right
% 7.75/5.65 thf(fact_617_add__less__cancel__right,axiom,
% 7.75/5.65 ! [A: rat,C: rat,B: rat] :
% 7.75/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.65 = ( ord_less_rat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_cancel_right
% 7.75/5.65 thf(fact_618_add__less__cancel__right,axiom,
% 7.75/5.65 ! [A: nat,C: nat,B: nat] :
% 7.75/5.65 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 7.75/5.65 = ( ord_less_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_cancel_right
% 7.75/5.65 thf(fact_619_add__less__cancel__right,axiom,
% 7.75/5.65 ! [A: int,C: int,B: int] :
% 7.75/5.65 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 7.75/5.65 = ( ord_less_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_cancel_right
% 7.75/5.65 thf(fact_620_add__less__cancel__left,axiom,
% 7.75/5.65 ! [C: real,A: real,B: real] :
% 7.75/5.65 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 7.75/5.65 = ( ord_less_real @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_cancel_left
% 7.75/5.65 thf(fact_621_add__less__cancel__left,axiom,
% 7.75/5.65 ! [C: rat,A: rat,B: rat] :
% 7.75/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 7.75/5.65 = ( ord_less_rat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_cancel_left
% 7.75/5.65 thf(fact_622_add__less__cancel__left,axiom,
% 7.75/5.65 ! [C: nat,A: nat,B: nat] :
% 7.75/5.65 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 7.75/5.65 = ( ord_less_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_cancel_left
% 7.75/5.65 thf(fact_623_add__less__cancel__left,axiom,
% 7.75/5.65 ! [C: int,A: int,B: int] :
% 7.75/5.65 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 7.75/5.65 = ( ord_less_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_cancel_left
% 7.75/5.65 thf(fact_624_div__0,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 7.75/5.65 = zero_zero_complex ) ).
% 7.75/5.65
% 7.75/5.65 % div_0
% 7.75/5.65 thf(fact_625_div__0,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( divide_divide_real @ zero_zero_real @ A )
% 7.75/5.65 = zero_zero_real ) ).
% 7.75/5.65
% 7.75/5.65 % div_0
% 7.75/5.65 thf(fact_626_div__0,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 7.75/5.65 = zero_zero_rat ) ).
% 7.75/5.65
% 7.75/5.65 % div_0
% 7.75/5.65 thf(fact_627_div__0,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % div_0
% 7.75/5.65 thf(fact_628_div__0,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( divide_divide_int @ zero_zero_int @ A )
% 7.75/5.65 = zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % div_0
% 7.75/5.65 thf(fact_629_div__by__0,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 7.75/5.65 = zero_zero_complex ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_0
% 7.75/5.65 thf(fact_630_div__by__0,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( divide_divide_real @ A @ zero_zero_real )
% 7.75/5.65 = zero_zero_real ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_0
% 7.75/5.65 thf(fact_631_div__by__0,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 7.75/5.65 = zero_zero_rat ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_0
% 7.75/5.65 thf(fact_632_div__by__0,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_0
% 7.75/5.65 thf(fact_633_div__by__0,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( divide_divide_int @ A @ zero_zero_int )
% 7.75/5.65 = zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_0
% 7.75/5.65 thf(fact_634_bits__div__0,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % bits_div_0
% 7.75/5.65 thf(fact_635_bits__div__0,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( divide_divide_int @ zero_zero_int @ A )
% 7.75/5.65 = zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % bits_div_0
% 7.75/5.65 thf(fact_636_bits__div__by__0,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % bits_div_by_0
% 7.75/5.65 thf(fact_637_bits__div__by__0,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( divide_divide_int @ A @ zero_zero_int )
% 7.75/5.65 = zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % bits_div_by_0
% 7.75/5.65 thf(fact_638_divide__eq__0__iff,axiom,
% 7.75/5.65 ! [A: complex,B: complex] :
% 7.75/5.65 ( ( ( divide1717551699836669952omplex @ A @ B )
% 7.75/5.65 = zero_zero_complex )
% 7.75/5.65 = ( ( A = zero_zero_complex )
% 7.75/5.65 | ( B = zero_zero_complex ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_eq_0_iff
% 7.75/5.65 thf(fact_639_divide__eq__0__iff,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( ( divide_divide_real @ A @ B )
% 7.75/5.65 = zero_zero_real )
% 7.75/5.65 = ( ( A = zero_zero_real )
% 7.75/5.65 | ( B = zero_zero_real ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_eq_0_iff
% 7.75/5.65 thf(fact_640_divide__eq__0__iff,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( ( divide_divide_rat @ A @ B )
% 7.75/5.65 = zero_zero_rat )
% 7.75/5.65 = ( ( A = zero_zero_rat )
% 7.75/5.65 | ( B = zero_zero_rat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_eq_0_iff
% 7.75/5.65 thf(fact_641_divide__cancel__left,axiom,
% 7.75/5.65 ! [C: complex,A: complex,B: complex] :
% 7.75/5.65 ( ( ( divide1717551699836669952omplex @ C @ A )
% 7.75/5.65 = ( divide1717551699836669952omplex @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_complex )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_cancel_left
% 7.75/5.65 thf(fact_642_divide__cancel__left,axiom,
% 7.75/5.65 ! [C: real,A: real,B: real] :
% 7.75/5.65 ( ( ( divide_divide_real @ C @ A )
% 7.75/5.65 = ( divide_divide_real @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_real )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_cancel_left
% 7.75/5.65 thf(fact_643_divide__cancel__left,axiom,
% 7.75/5.65 ! [C: rat,A: rat,B: rat] :
% 7.75/5.65 ( ( ( divide_divide_rat @ C @ A )
% 7.75/5.65 = ( divide_divide_rat @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_rat )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_cancel_left
% 7.75/5.65 thf(fact_644_divide__cancel__right,axiom,
% 7.75/5.65 ! [A: complex,C: complex,B: complex] :
% 7.75/5.65 ( ( ( divide1717551699836669952omplex @ A @ C )
% 7.75/5.65 = ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_complex )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_cancel_right
% 7.75/5.65 thf(fact_645_divide__cancel__right,axiom,
% 7.75/5.65 ! [A: real,C: real,B: real] :
% 7.75/5.65 ( ( ( divide_divide_real @ A @ C )
% 7.75/5.65 = ( divide_divide_real @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_real )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_cancel_right
% 7.75/5.65 thf(fact_646_divide__cancel__right,axiom,
% 7.75/5.65 ! [A: rat,C: rat,B: rat] :
% 7.75/5.65 ( ( ( divide_divide_rat @ A @ C )
% 7.75/5.65 = ( divide_divide_rat @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_rat )
% 7.75/5.65 | ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_cancel_right
% 7.75/5.65 thf(fact_647_division__ring__divide__zero,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 7.75/5.65 = zero_zero_complex ) ).
% 7.75/5.65
% 7.75/5.65 % division_ring_divide_zero
% 7.75/5.65 thf(fact_648_division__ring__divide__zero,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( divide_divide_real @ A @ zero_zero_real )
% 7.75/5.65 = zero_zero_real ) ).
% 7.75/5.65
% 7.75/5.65 % division_ring_divide_zero
% 7.75/5.65 thf(fact_649_division__ring__divide__zero,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 7.75/5.65 = zero_zero_rat ) ).
% 7.75/5.65
% 7.75/5.65 % division_ring_divide_zero
% 7.75/5.65 thf(fact_650_mult_Oright__neutral,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( times_times_rat @ A @ one_one_rat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult.right_neutral
% 7.75/5.65 thf(fact_651_mult_Oright__neutral,axiom,
% 7.75/5.65 ! [A: assn] :
% 7.75/5.65 ( ( times_times_assn @ A @ one_one_assn )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult.right_neutral
% 7.75/5.65 thf(fact_652_mult_Oright__neutral,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( times_times_real @ A @ one_one_real )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult.right_neutral
% 7.75/5.65 thf(fact_653_mult_Oright__neutral,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( times_times_nat @ A @ one_one_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult.right_neutral
% 7.75/5.65 thf(fact_654_mult_Oright__neutral,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( times_times_int @ A @ one_one_int )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult.right_neutral
% 7.75/5.65 thf(fact_655_mult_Oright__neutral,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult.right_neutral
% 7.75/5.65 thf(fact_656_mult_Oright__neutral,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( times_times_complex @ A @ one_one_complex )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult.right_neutral
% 7.75/5.65 thf(fact_657_mult__1,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( times_times_rat @ one_one_rat @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_1
% 7.75/5.65 thf(fact_658_mult__1,axiom,
% 7.75/5.65 ! [A: assn] :
% 7.75/5.65 ( ( times_times_assn @ one_one_assn @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_1
% 7.75/5.65 thf(fact_659_mult__1,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( times_times_real @ one_one_real @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_1
% 7.75/5.65 thf(fact_660_mult__1,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( times_times_nat @ one_one_nat @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_1
% 7.75/5.65 thf(fact_661_mult__1,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( times_times_int @ one_one_int @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_1
% 7.75/5.65 thf(fact_662_mult__1,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_1
% 7.75/5.65 thf(fact_663_mult__1,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( times_times_complex @ one_one_complex @ A )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mult_1
% 7.75/5.65 thf(fact_664_div__by__1,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_1
% 7.75/5.65 thf(fact_665_div__by__1,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( divide_divide_real @ A @ one_one_real )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_1
% 7.75/5.65 thf(fact_666_div__by__1,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( divide_divide_rat @ A @ one_one_rat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_1
% 7.75/5.65 thf(fact_667_div__by__1,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ A @ one_one_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_1
% 7.75/5.65 thf(fact_668_div__by__1,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( divide_divide_int @ A @ one_one_int )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % div_by_1
% 7.75/5.65 thf(fact_669_bits__div__by__1,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( divide_divide_nat @ A @ one_one_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % bits_div_by_1
% 7.75/5.65 thf(fact_670_bits__div__by__1,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( divide_divide_int @ A @ one_one_int )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % bits_div_by_1
% 7.75/5.65 thf(fact_671_power__one,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( power_power_rat @ one_one_rat @ N )
% 7.75/5.65 = one_one_rat ) ).
% 7.75/5.65
% 7.75/5.65 % power_one
% 7.75/5.65 thf(fact_672_power__one,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( power_power_nat @ one_one_nat @ N )
% 7.75/5.65 = one_one_nat ) ).
% 7.75/5.65
% 7.75/5.65 % power_one
% 7.75/5.65 thf(fact_673_power__one,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( power_power_real @ one_one_real @ N )
% 7.75/5.65 = one_one_real ) ).
% 7.75/5.65
% 7.75/5.65 % power_one
% 7.75/5.65 thf(fact_674_power__one,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( power_power_int @ one_one_int @ N )
% 7.75/5.65 = one_one_int ) ).
% 7.75/5.65
% 7.75/5.65 % power_one
% 7.75/5.65 thf(fact_675_power__one,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( power_power_complex @ one_one_complex @ N )
% 7.75/5.65 = one_one_complex ) ).
% 7.75/5.65
% 7.75/5.65 % power_one
% 7.75/5.65 thf(fact_676_power__one,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N )
% 7.75/5.65 = one_one_Code_integer ) ).
% 7.75/5.65
% 7.75/5.65 % power_one
% 7.75/5.65 thf(fact_677_power__one,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( power_power_assn @ one_one_assn @ N )
% 7.75/5.65 = one_one_assn ) ).
% 7.75/5.65
% 7.75/5.65 % power_one
% 7.75/5.65 thf(fact_678_dvd__0__left__iff,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 7.75/5.65 = ( A = zero_zero_complex ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_left_iff
% 7.75/5.65 thf(fact_679_dvd__0__left__iff,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 7.75/5.65 = ( A = zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_left_iff
% 7.75/5.65 thf(fact_680_dvd__0__left__iff,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 7.75/5.65 = ( A = zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_left_iff
% 7.75/5.65 thf(fact_681_dvd__0__left__iff,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 7.75/5.65 = ( A = zero_zero_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_left_iff
% 7.75/5.65 thf(fact_682_dvd__0__left__iff,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 7.75/5.65 = ( A = zero_zero_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_left_iff
% 7.75/5.65 thf(fact_683_dvd__0__right,axiom,
% 7.75/5.65 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_right
% 7.75/5.65 thf(fact_684_dvd__0__right,axiom,
% 7.75/5.65 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_right
% 7.75/5.65 thf(fact_685_dvd__0__right,axiom,
% 7.75/5.65 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_right
% 7.75/5.65 thf(fact_686_dvd__0__right,axiom,
% 7.75/5.65 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_right
% 7.75/5.65 thf(fact_687_dvd__0__right,axiom,
% 7.75/5.65 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % dvd_0_right
% 7.75/5.65 thf(fact_688_lessI,axiom,
% 7.75/5.65 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % lessI
% 7.75/5.65 thf(fact_689_Suc__mono,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( ord_less_nat @ M @ N )
% 7.75/5.65 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % Suc_mono
% 7.75/5.65 thf(fact_690_Suc__less__eq,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 7.75/5.65 = ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % Suc_less_eq
% 7.75/5.65 thf(fact_691_mod__0,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % mod_0
% 7.75/5.65 thf(fact_692_mod__0,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 7.75/5.65 = zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % mod_0
% 7.75/5.65 thf(fact_693_mod__0,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.65 = zero_z3403309356797280102nteger ) ).
% 7.75/5.65
% 7.75/5.65 % mod_0
% 7.75/5.65 thf(fact_694_mod__by__0,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mod_by_0
% 7.75/5.65 thf(fact_695_mod__by__0,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mod_by_0
% 7.75/5.65 thf(fact_696_mod__by__0,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.65 = A ) ).
% 7.75/5.65
% 7.75/5.65 % mod_by_0
% 7.75/5.65 thf(fact_697_mod__self,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( modulo_modulo_nat @ A @ A )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % mod_self
% 7.75/5.65 thf(fact_698_mod__self,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( modulo_modulo_int @ A @ A )
% 7.75/5.65 = zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % mod_self
% 7.75/5.65 thf(fact_699_mod__self,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( modulo364778990260209775nteger @ A @ A )
% 7.75/5.65 = zero_z3403309356797280102nteger ) ).
% 7.75/5.65
% 7.75/5.65 % mod_self
% 7.75/5.65 thf(fact_700_bits__mod__0,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % bits_mod_0
% 7.75/5.65 thf(fact_701_bits__mod__0,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 7.75/5.65 = zero_zero_int ) ).
% 7.75/5.65
% 7.75/5.65 % bits_mod_0
% 7.75/5.65 thf(fact_702_bits__mod__0,axiom,
% 7.75/5.65 ! [A: code_integer] :
% 7.75/5.65 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.65 = zero_z3403309356797280102nteger ) ).
% 7.75/5.65
% 7.75/5.65 % bits_mod_0
% 7.75/5.65 thf(fact_703_bot__nat__0_Onot__eq__extremum,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( A != zero_zero_nat )
% 7.75/5.65 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % bot_nat_0.not_eq_extremum
% 7.75/5.65 thf(fact_704_less__one,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( ord_less_nat @ N @ one_one_nat )
% 7.75/5.65 = ( N = zero_zero_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % less_one
% 7.75/5.65 thf(fact_705_neq0__conv,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ( ( N != zero_zero_nat )
% 7.75/5.65 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % neq0_conv
% 7.75/5.65 thf(fact_706_less__nat__zero__code,axiom,
% 7.75/5.65 ! [N: nat] :
% 7.75/5.65 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % less_nat_zero_code
% 7.75/5.65 thf(fact_707_mod__add__self1,axiom,
% 7.75/5.65 ! [B: nat,A: nat] :
% 7.75/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 7.75/5.65 = ( modulo_modulo_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_add_self1
% 7.75/5.65 thf(fact_708_mod__add__self1,axiom,
% 7.75/5.65 ! [B: int,A: int] :
% 7.75/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 7.75/5.65 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_add_self1
% 7.75/5.65 thf(fact_709_mod__add__self1,axiom,
% 7.75/5.65 ! [B: code_integer,A: code_integer] :
% 7.75/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 7.75/5.65 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_add_self1
% 7.75/5.65 thf(fact_710_mod__add__self2,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 7.75/5.65 = ( modulo_modulo_nat @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_add_self2
% 7.75/5.65 thf(fact_711_mod__add__self2,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 7.75/5.65 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_add_self2
% 7.75/5.65 thf(fact_712_mod__add__self2,axiom,
% 7.75/5.65 ! [A: code_integer,B: code_integer] :
% 7.75/5.65 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 7.75/5.65 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_add_self2
% 7.75/5.65 thf(fact_713_Nat_Oadd__0__right,axiom,
% 7.75/5.65 ! [M: nat] :
% 7.75/5.65 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 7.75/5.65 = M ) ).
% 7.75/5.65
% 7.75/5.65 % Nat.add_0_right
% 7.75/5.65 thf(fact_714_add__is__0,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( ( plus_plus_nat @ M @ N )
% 7.75/5.65 = zero_zero_nat )
% 7.75/5.65 = ( ( M = zero_zero_nat )
% 7.75/5.65 & ( N = zero_zero_nat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_is_0
% 7.75/5.65 thf(fact_715_nat__add__left__cancel__less,axiom,
% 7.75/5.65 ! [K: nat,M: nat,N: nat] :
% 7.75/5.65 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 7.75/5.65 = ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.65
% 7.75/5.65 % nat_add_left_cancel_less
% 7.75/5.65 thf(fact_716_mult__is__0,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( ( times_times_nat @ M @ N )
% 7.75/5.65 = zero_zero_nat )
% 7.75/5.65 = ( ( M = zero_zero_nat )
% 7.75/5.65 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_is_0
% 7.75/5.65 thf(fact_717_mult__0__right,axiom,
% 7.75/5.65 ! [M: nat] :
% 7.75/5.65 ( ( times_times_nat @ M @ zero_zero_nat )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % mult_0_right
% 7.75/5.65 thf(fact_718_mult__cancel1,axiom,
% 7.75/5.65 ! [K: nat,M: nat,N: nat] :
% 7.75/5.65 ( ( ( times_times_nat @ K @ M )
% 7.75/5.65 = ( times_times_nat @ K @ N ) )
% 7.75/5.65 = ( ( M = N )
% 7.75/5.65 | ( K = zero_zero_nat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel1
% 7.75/5.65 thf(fact_719_mult__cancel2,axiom,
% 7.75/5.65 ! [M: nat,K: nat,N: nat] :
% 7.75/5.65 ( ( ( times_times_nat @ M @ K )
% 7.75/5.65 = ( times_times_nat @ N @ K ) )
% 7.75/5.65 = ( ( M = N )
% 7.75/5.65 | ( K = zero_zero_nat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel2
% 7.75/5.65 thf(fact_720_mod__less,axiom,
% 7.75/5.65 ! [M: nat,N: nat] :
% 7.75/5.65 ( ( ord_less_nat @ M @ N )
% 7.75/5.65 => ( ( modulo_modulo_nat @ M @ N )
% 7.75/5.65 = M ) ) ).
% 7.75/5.65
% 7.75/5.65 % mod_less
% 7.75/5.65 thf(fact_721_ent__pure__pre__iff__sng,axiom,
% 7.75/5.65 ! [B: $o,Q: assn] :
% 7.75/5.65 ( ( entails @ ( pure_assn @ B ) @ Q )
% 7.75/5.65 = ( B
% 7.75/5.65 => ( entails @ one_one_assn @ Q ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % ent_pure_pre_iff_sng
% 7.75/5.65 thf(fact_722_triangle__0,axiom,
% 7.75/5.65 ( ( nat_triangle @ zero_zero_nat )
% 7.75/5.65 = zero_zero_nat ) ).
% 7.75/5.65
% 7.75/5.65 % triangle_0
% 7.75/5.65 thf(fact_723_zero__less__double__add__iff__zero__less__single__add,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 7.75/5.65 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % zero_less_double_add_iff_zero_less_single_add
% 7.75/5.65 thf(fact_724_zero__less__double__add__iff__zero__less__single__add,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 7.75/5.65 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % zero_less_double_add_iff_zero_less_single_add
% 7.75/5.65 thf(fact_725_zero__less__double__add__iff__zero__less__single__add,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 7.75/5.65 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 7.75/5.65
% 7.75/5.65 % zero_less_double_add_iff_zero_less_single_add
% 7.75/5.65 thf(fact_726_double__add__less__zero__iff__single__add__less__zero,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 7.75/5.65 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % double_add_less_zero_iff_single_add_less_zero
% 7.75/5.65 thf(fact_727_double__add__less__zero__iff__single__add__less__zero,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 7.75/5.65 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % double_add_less_zero_iff_single_add_less_zero
% 7.75/5.65 thf(fact_728_double__add__less__zero__iff__single__add__less__zero,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 7.75/5.65 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % double_add_less_zero_iff_single_add_less_zero
% 7.75/5.65 thf(fact_729_less__add__same__cancel2,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 7.75/5.65 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % less_add_same_cancel2
% 7.75/5.65 thf(fact_730_less__add__same__cancel2,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 7.75/5.65 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % less_add_same_cancel2
% 7.75/5.65 thf(fact_731_less__add__same__cancel2,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 7.75/5.65 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % less_add_same_cancel2
% 7.75/5.65 thf(fact_732_less__add__same__cancel2,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 7.75/5.65 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % less_add_same_cancel2
% 7.75/5.65 thf(fact_733_less__add__same__cancel1,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 7.75/5.65 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % less_add_same_cancel1
% 7.75/5.65 thf(fact_734_less__add__same__cancel1,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.65 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % less_add_same_cancel1
% 7.75/5.65 thf(fact_735_less__add__same__cancel1,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 7.75/5.65 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % less_add_same_cancel1
% 7.75/5.65 thf(fact_736_less__add__same__cancel1,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 7.75/5.65 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 7.75/5.65
% 7.75/5.65 % less_add_same_cancel1
% 7.75/5.65 thf(fact_737_add__less__same__cancel2,axiom,
% 7.75/5.65 ! [A: real,B: real] :
% 7.75/5.65 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 7.75/5.65 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_same_cancel2
% 7.75/5.65 thf(fact_738_add__less__same__cancel2,axiom,
% 7.75/5.65 ! [A: rat,B: rat] :
% 7.75/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 7.75/5.65 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_same_cancel2
% 7.75/5.65 thf(fact_739_add__less__same__cancel2,axiom,
% 7.75/5.65 ! [A: nat,B: nat] :
% 7.75/5.65 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 7.75/5.65 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_same_cancel2
% 7.75/5.65 thf(fact_740_add__less__same__cancel2,axiom,
% 7.75/5.65 ! [A: int,B: int] :
% 7.75/5.65 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 7.75/5.65 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_same_cancel2
% 7.75/5.65 thf(fact_741_add__less__same__cancel1,axiom,
% 7.75/5.65 ! [B: real,A: real] :
% 7.75/5.65 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 7.75/5.65 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_same_cancel1
% 7.75/5.65 thf(fact_742_add__less__same__cancel1,axiom,
% 7.75/5.65 ! [B: rat,A: rat] :
% 7.75/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 7.75/5.65 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_same_cancel1
% 7.75/5.65 thf(fact_743_add__less__same__cancel1,axiom,
% 7.75/5.65 ! [B: nat,A: nat] :
% 7.75/5.65 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 7.75/5.65 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_same_cancel1
% 7.75/5.65 thf(fact_744_add__less__same__cancel1,axiom,
% 7.75/5.65 ! [B: int,A: int] :
% 7.75/5.65 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 7.75/5.65 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % add_less_same_cancel1
% 7.75/5.65 thf(fact_745_sum__squares__eq__zero__iff,axiom,
% 7.75/5.65 ! [X: rat,Y: rat] :
% 7.75/5.65 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 7.75/5.65 = zero_zero_rat )
% 7.75/5.65 = ( ( X = zero_zero_rat )
% 7.75/5.65 & ( Y = zero_zero_rat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % sum_squares_eq_zero_iff
% 7.75/5.65 thf(fact_746_sum__squares__eq__zero__iff,axiom,
% 7.75/5.65 ! [X: real,Y: real] :
% 7.75/5.65 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 7.75/5.65 = zero_zero_real )
% 7.75/5.65 = ( ( X = zero_zero_real )
% 7.75/5.65 & ( Y = zero_zero_real ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % sum_squares_eq_zero_iff
% 7.75/5.65 thf(fact_747_sum__squares__eq__zero__iff,axiom,
% 7.75/5.65 ! [X: int,Y: int] :
% 7.75/5.65 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 7.75/5.65 = zero_zero_int )
% 7.75/5.65 = ( ( X = zero_zero_int )
% 7.75/5.65 & ( Y = zero_zero_int ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % sum_squares_eq_zero_iff
% 7.75/5.65 thf(fact_748_sum__squares__eq__zero__iff,axiom,
% 7.75/5.65 ! [X: code_integer,Y: code_integer] :
% 7.75/5.65 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 7.75/5.65 = zero_z3403309356797280102nteger )
% 7.75/5.65 = ( ( X = zero_z3403309356797280102nteger )
% 7.75/5.65 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % sum_squares_eq_zero_iff
% 7.75/5.65 thf(fact_749_mult__cancel__left1,axiom,
% 7.75/5.65 ! [C: rat,B: rat] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_times_rat @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_rat )
% 7.75/5.65 | ( B = one_one_rat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left1
% 7.75/5.65 thf(fact_750_mult__cancel__left1,axiom,
% 7.75/5.65 ! [C: real,B: real] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_times_real @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_real )
% 7.75/5.65 | ( B = one_one_real ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left1
% 7.75/5.65 thf(fact_751_mult__cancel__left1,axiom,
% 7.75/5.65 ! [C: int,B: int] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_times_int @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_int )
% 7.75/5.65 | ( B = one_one_int ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left1
% 7.75/5.65 thf(fact_752_mult__cancel__left1,axiom,
% 7.75/5.65 ! [C: code_integer,B: code_integer] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_z3403309356797280102nteger )
% 7.75/5.65 | ( B = one_one_Code_integer ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left1
% 7.75/5.65 thf(fact_753_mult__cancel__left1,axiom,
% 7.75/5.65 ! [C: complex,B: complex] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_times_complex @ C @ B ) )
% 7.75/5.65 = ( ( C = zero_zero_complex )
% 7.75/5.65 | ( B = one_one_complex ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left1
% 7.75/5.65 thf(fact_754_mult__cancel__left2,axiom,
% 7.75/5.65 ! [C: rat,A: rat] :
% 7.75/5.65 ( ( ( times_times_rat @ C @ A )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_zero_rat )
% 7.75/5.65 | ( A = one_one_rat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left2
% 7.75/5.65 thf(fact_755_mult__cancel__left2,axiom,
% 7.75/5.65 ! [C: real,A: real] :
% 7.75/5.65 ( ( ( times_times_real @ C @ A )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_zero_real )
% 7.75/5.65 | ( A = one_one_real ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left2
% 7.75/5.65 thf(fact_756_mult__cancel__left2,axiom,
% 7.75/5.65 ! [C: int,A: int] :
% 7.75/5.65 ( ( ( times_times_int @ C @ A )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_zero_int )
% 7.75/5.65 | ( A = one_one_int ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left2
% 7.75/5.65 thf(fact_757_mult__cancel__left2,axiom,
% 7.75/5.65 ! [C: code_integer,A: code_integer] :
% 7.75/5.65 ( ( ( times_3573771949741848930nteger @ C @ A )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_z3403309356797280102nteger )
% 7.75/5.65 | ( A = one_one_Code_integer ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left2
% 7.75/5.65 thf(fact_758_mult__cancel__left2,axiom,
% 7.75/5.65 ! [C: complex,A: complex] :
% 7.75/5.65 ( ( ( times_times_complex @ C @ A )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_zero_complex )
% 7.75/5.65 | ( A = one_one_complex ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_left2
% 7.75/5.65 thf(fact_759_mult__cancel__right1,axiom,
% 7.75/5.65 ! [C: rat,B: rat] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_times_rat @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_rat )
% 7.75/5.65 | ( B = one_one_rat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right1
% 7.75/5.65 thf(fact_760_mult__cancel__right1,axiom,
% 7.75/5.65 ! [C: real,B: real] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_times_real @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_real )
% 7.75/5.65 | ( B = one_one_real ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right1
% 7.75/5.65 thf(fact_761_mult__cancel__right1,axiom,
% 7.75/5.65 ! [C: int,B: int] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_times_int @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_int )
% 7.75/5.65 | ( B = one_one_int ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right1
% 7.75/5.65 thf(fact_762_mult__cancel__right1,axiom,
% 7.75/5.65 ! [C: code_integer,B: code_integer] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_z3403309356797280102nteger )
% 7.75/5.65 | ( B = one_one_Code_integer ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right1
% 7.75/5.65 thf(fact_763_mult__cancel__right1,axiom,
% 7.75/5.65 ! [C: complex,B: complex] :
% 7.75/5.65 ( ( C
% 7.75/5.65 = ( times_times_complex @ B @ C ) )
% 7.75/5.65 = ( ( C = zero_zero_complex )
% 7.75/5.65 | ( B = one_one_complex ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right1
% 7.75/5.65 thf(fact_764_mult__cancel__right2,axiom,
% 7.75/5.65 ! [A: rat,C: rat] :
% 7.75/5.65 ( ( ( times_times_rat @ A @ C )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_zero_rat )
% 7.75/5.65 | ( A = one_one_rat ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right2
% 7.75/5.65 thf(fact_765_mult__cancel__right2,axiom,
% 7.75/5.65 ! [A: real,C: real] :
% 7.75/5.65 ( ( ( times_times_real @ A @ C )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_zero_real )
% 7.75/5.65 | ( A = one_one_real ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right2
% 7.75/5.65 thf(fact_766_mult__cancel__right2,axiom,
% 7.75/5.65 ! [A: int,C: int] :
% 7.75/5.65 ( ( ( times_times_int @ A @ C )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_zero_int )
% 7.75/5.65 | ( A = one_one_int ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right2
% 7.75/5.65 thf(fact_767_mult__cancel__right2,axiom,
% 7.75/5.65 ! [A: code_integer,C: code_integer] :
% 7.75/5.65 ( ( ( times_3573771949741848930nteger @ A @ C )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_z3403309356797280102nteger )
% 7.75/5.65 | ( A = one_one_Code_integer ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right2
% 7.75/5.65 thf(fact_768_mult__cancel__right2,axiom,
% 7.75/5.65 ! [A: complex,C: complex] :
% 7.75/5.65 ( ( ( times_times_complex @ A @ C )
% 7.75/5.65 = C )
% 7.75/5.65 = ( ( C = zero_zero_complex )
% 7.75/5.65 | ( A = one_one_complex ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % mult_cancel_right2
% 7.75/5.65 thf(fact_769_numeral__eq__one__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( ( numera6690914467698888265omplex @ N )
% 7.75/5.65 = one_one_complex )
% 7.75/5.65 = ( N = one ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_one_iff
% 7.75/5.65 thf(fact_770_numeral__eq__one__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( ( numeral_numeral_real @ N )
% 7.75/5.65 = one_one_real )
% 7.75/5.65 = ( N = one ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_one_iff
% 7.75/5.65 thf(fact_771_numeral__eq__one__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( ( numeral_numeral_rat @ N )
% 7.75/5.65 = one_one_rat )
% 7.75/5.65 = ( N = one ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_one_iff
% 7.75/5.65 thf(fact_772_numeral__eq__one__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( ( numeral_numeral_nat @ N )
% 7.75/5.65 = one_one_nat )
% 7.75/5.65 = ( N = one ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_one_iff
% 7.75/5.65 thf(fact_773_numeral__eq__one__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( ( numeral_numeral_int @ N )
% 7.75/5.65 = one_one_int )
% 7.75/5.65 = ( N = one ) ) ).
% 7.75/5.65
% 7.75/5.65 % numeral_eq_one_iff
% 7.75/5.65 thf(fact_774_one__eq__numeral__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( one_one_complex
% 7.75/5.65 = ( numera6690914467698888265omplex @ N ) )
% 7.75/5.65 = ( one = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % one_eq_numeral_iff
% 7.75/5.65 thf(fact_775_one__eq__numeral__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( one_one_real
% 7.75/5.65 = ( numeral_numeral_real @ N ) )
% 7.75/5.65 = ( one = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % one_eq_numeral_iff
% 7.75/5.65 thf(fact_776_one__eq__numeral__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( one_one_rat
% 7.75/5.65 = ( numeral_numeral_rat @ N ) )
% 7.75/5.65 = ( one = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % one_eq_numeral_iff
% 7.75/5.65 thf(fact_777_one__eq__numeral__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( one_one_nat
% 7.75/5.65 = ( numeral_numeral_nat @ N ) )
% 7.75/5.65 = ( one = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % one_eq_numeral_iff
% 7.75/5.65 thf(fact_778_one__eq__numeral__iff,axiom,
% 7.75/5.65 ! [N: num] :
% 7.75/5.65 ( ( one_one_int
% 7.75/5.65 = ( numeral_numeral_int @ N ) )
% 7.75/5.65 = ( one = N ) ) ).
% 7.75/5.65
% 7.75/5.65 % one_eq_numeral_iff
% 7.75/5.65 thf(fact_779_div__self,axiom,
% 7.75/5.65 ! [A: complex] :
% 7.75/5.65 ( ( A != zero_zero_complex )
% 7.75/5.65 => ( ( divide1717551699836669952omplex @ A @ A )
% 7.75/5.65 = one_one_complex ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_self
% 7.75/5.65 thf(fact_780_div__self,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( A != zero_zero_real )
% 7.75/5.65 => ( ( divide_divide_real @ A @ A )
% 7.75/5.65 = one_one_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_self
% 7.75/5.65 thf(fact_781_div__self,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( A != zero_zero_rat )
% 7.75/5.65 => ( ( divide_divide_rat @ A @ A )
% 7.75/5.65 = one_one_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_self
% 7.75/5.65 thf(fact_782_div__self,axiom,
% 7.75/5.65 ! [A: nat] :
% 7.75/5.65 ( ( A != zero_zero_nat )
% 7.75/5.65 => ( ( divide_divide_nat @ A @ A )
% 7.75/5.65 = one_one_nat ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_self
% 7.75/5.65 thf(fact_783_div__self,axiom,
% 7.75/5.65 ! [A: int] :
% 7.75/5.65 ( ( A != zero_zero_int )
% 7.75/5.65 => ( ( divide_divide_int @ A @ A )
% 7.75/5.65 = one_one_int ) ) ).
% 7.75/5.65
% 7.75/5.65 % div_self
% 7.75/5.65 thf(fact_784_zero__eq__1__divide__iff,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( zero_zero_real
% 7.75/5.65 = ( divide_divide_real @ one_one_real @ A ) )
% 7.75/5.65 = ( A = zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % zero_eq_1_divide_iff
% 7.75/5.65 thf(fact_785_zero__eq__1__divide__iff,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( zero_zero_rat
% 7.75/5.65 = ( divide_divide_rat @ one_one_rat @ A ) )
% 7.75/5.65 = ( A = zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % zero_eq_1_divide_iff
% 7.75/5.65 thf(fact_786_one__divide__eq__0__iff,axiom,
% 7.75/5.65 ! [A: real] :
% 7.75/5.65 ( ( ( divide_divide_real @ one_one_real @ A )
% 7.75/5.65 = zero_zero_real )
% 7.75/5.65 = ( A = zero_zero_real ) ) ).
% 7.75/5.65
% 7.75/5.65 % one_divide_eq_0_iff
% 7.75/5.65 thf(fact_787_one__divide__eq__0__iff,axiom,
% 7.75/5.65 ! [A: rat] :
% 7.75/5.65 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 7.75/5.65 = zero_zero_rat )
% 7.75/5.65 = ( A = zero_zero_rat ) ) ).
% 7.75/5.65
% 7.75/5.65 % one_divide_eq_0_iff
% 7.75/5.65 thf(fact_788_eq__divide__eq__1,axiom,
% 7.75/5.65 ! [B: real,A: real] :
% 7.75/5.65 ( ( one_one_real
% 7.75/5.65 = ( divide_divide_real @ B @ A ) )
% 7.75/5.65 = ( ( A != zero_zero_real )
% 7.75/5.65 & ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % eq_divide_eq_1
% 7.75/5.65 thf(fact_789_eq__divide__eq__1,axiom,
% 7.75/5.65 ! [B: rat,A: rat] :
% 7.75/5.65 ( ( one_one_rat
% 7.75/5.65 = ( divide_divide_rat @ B @ A ) )
% 7.75/5.65 = ( ( A != zero_zero_rat )
% 7.75/5.65 & ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % eq_divide_eq_1
% 7.75/5.65 thf(fact_790_divide__eq__eq__1,axiom,
% 7.75/5.65 ! [B: real,A: real] :
% 7.75/5.65 ( ( ( divide_divide_real @ B @ A )
% 7.75/5.65 = one_one_real )
% 7.75/5.65 = ( ( A != zero_zero_real )
% 7.75/5.65 & ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_eq_eq_1
% 7.75/5.65 thf(fact_791_divide__eq__eq__1,axiom,
% 7.75/5.65 ! [B: rat,A: rat] :
% 7.75/5.65 ( ( ( divide_divide_rat @ B @ A )
% 7.75/5.65 = one_one_rat )
% 7.75/5.65 = ( ( A != zero_zero_rat )
% 7.75/5.65 & ( A = B ) ) ) ).
% 7.75/5.65
% 7.75/5.65 % divide_eq_eq_1
% 7.75/5.65 thf(fact_792_divide__self__if,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( ( A = zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ A @ A )
% 7.75/5.66 = zero_zero_complex ) )
% 7.75/5.66 & ( ( A != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ A @ A )
% 7.75/5.66 = one_one_complex ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_self_if
% 7.75/5.66 thf(fact_793_divide__self__if,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( ( A = zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ A @ A )
% 7.75/5.66 = zero_zero_real ) )
% 7.75/5.66 & ( ( A != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ A @ A )
% 7.75/5.66 = one_one_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_self_if
% 7.75/5.66 thf(fact_794_divide__self__if,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( ( A = zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ A @ A )
% 7.75/5.66 = zero_zero_rat ) )
% 7.75/5.66 & ( ( A != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ A @ A )
% 7.75/5.66 = one_one_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_self_if
% 7.75/5.66 thf(fact_795_divide__self,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( A != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ A @ A )
% 7.75/5.66 = one_one_complex ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_self
% 7.75/5.66 thf(fact_796_divide__self,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( A != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ A @ A )
% 7.75/5.66 = one_one_real ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_self
% 7.75/5.66 thf(fact_797_divide__self,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( A != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ A @ A )
% 7.75/5.66 = one_one_rat ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_self
% 7.75/5.66 thf(fact_798_one__eq__divide__iff,axiom,
% 7.75/5.66 ! [A: complex,B: complex] :
% 7.75/5.66 ( ( one_one_complex
% 7.75/5.66 = ( divide1717551699836669952omplex @ A @ B ) )
% 7.75/5.66 = ( ( B != zero_zero_complex )
% 7.75/5.66 & ( A = B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_eq_divide_iff
% 7.75/5.66 thf(fact_799_one__eq__divide__iff,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( one_one_real
% 7.75/5.66 = ( divide_divide_real @ A @ B ) )
% 7.75/5.66 = ( ( B != zero_zero_real )
% 7.75/5.66 & ( A = B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_eq_divide_iff
% 7.75/5.66 thf(fact_800_one__eq__divide__iff,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( one_one_rat
% 7.75/5.66 = ( divide_divide_rat @ A @ B ) )
% 7.75/5.66 = ( ( B != zero_zero_rat )
% 7.75/5.66 & ( A = B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_eq_divide_iff
% 7.75/5.66 thf(fact_801_divide__eq__1__iff,axiom,
% 7.75/5.66 ! [A: complex,B: complex] :
% 7.75/5.66 ( ( ( divide1717551699836669952omplex @ A @ B )
% 7.75/5.66 = one_one_complex )
% 7.75/5.66 = ( ( B != zero_zero_complex )
% 7.75/5.66 & ( A = B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_eq_1_iff
% 7.75/5.66 thf(fact_802_divide__eq__1__iff,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ( divide_divide_real @ A @ B )
% 7.75/5.66 = one_one_real )
% 7.75/5.66 = ( ( B != zero_zero_real )
% 7.75/5.66 & ( A = B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_eq_1_iff
% 7.75/5.66 thf(fact_803_divide__eq__1__iff,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ( divide_divide_rat @ A @ B )
% 7.75/5.66 = one_one_rat )
% 7.75/5.66 = ( ( B != zero_zero_rat )
% 7.75/5.66 & ( A = B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_eq_1_iff
% 7.75/5.66 thf(fact_804_nonzero__mult__div__cancel__left,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 7.75/5.66 = B ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_left
% 7.75/5.66 thf(fact_805_nonzero__mult__div__cancel__left,axiom,
% 7.75/5.66 ! [A: complex,B: complex] :
% 7.75/5.66 ( ( A != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 7.75/5.66 = B ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_left
% 7.75/5.66 thf(fact_806_nonzero__mult__div__cancel__left,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( A != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 7.75/5.66 = B ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_left
% 7.75/5.66 thf(fact_807_nonzero__mult__div__cancel__left,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( A != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 7.75/5.66 = B ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_left
% 7.75/5.66 thf(fact_808_nonzero__mult__div__cancel__left,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( A != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 7.75/5.66 = B ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_left
% 7.75/5.66 thf(fact_809_nonzero__mult__div__cancel__left,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( A != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 7.75/5.66 = B ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_left
% 7.75/5.66 thf(fact_810_nonzero__mult__div__cancel__right,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer] :
% 7.75/5.66 ( ( B != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 7.75/5.66 = A ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_right
% 7.75/5.66 thf(fact_811_nonzero__mult__div__cancel__right,axiom,
% 7.75/5.66 ! [B: complex,A: complex] :
% 7.75/5.66 ( ( B != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 7.75/5.66 = A ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_right
% 7.75/5.66 thf(fact_812_nonzero__mult__div__cancel__right,axiom,
% 7.75/5.66 ! [B: real,A: real] :
% 7.75/5.66 ( ( B != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 7.75/5.66 = A ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_right
% 7.75/5.66 thf(fact_813_nonzero__mult__div__cancel__right,axiom,
% 7.75/5.66 ! [B: rat,A: rat] :
% 7.75/5.66 ( ( B != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 7.75/5.66 = A ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_right
% 7.75/5.66 thf(fact_814_nonzero__mult__div__cancel__right,axiom,
% 7.75/5.66 ! [B: nat,A: nat] :
% 7.75/5.66 ( ( B != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 7.75/5.66 = A ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_right
% 7.75/5.66 thf(fact_815_nonzero__mult__div__cancel__right,axiom,
% 7.75/5.66 ! [B: int,A: int] :
% 7.75/5.66 ( ( B != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 7.75/5.66 = A ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_div_cancel_right
% 7.75/5.66 thf(fact_816_mult__divide__mult__cancel__left__if,axiom,
% 7.75/5.66 ! [C: complex,A: complex,B: complex] :
% 7.75/5.66 ( ( ( C = zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 7.75/5.66 = zero_zero_complex ) )
% 7.75/5.66 & ( ( C != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 7.75/5.66 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_divide_mult_cancel_left_if
% 7.75/5.66 thf(fact_817_mult__divide__mult__cancel__left__if,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( ( C = zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.66 = zero_zero_real ) )
% 7.75/5.66 & ( ( C != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.66 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_divide_mult_cancel_left_if
% 7.75/5.66 thf(fact_818_mult__divide__mult__cancel__left__if,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( ( C = zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.66 = zero_zero_rat ) )
% 7.75/5.66 & ( ( C != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.66 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_divide_mult_cancel_left_if
% 7.75/5.66 thf(fact_819_nonzero__mult__divide__mult__cancel__left,axiom,
% 7.75/5.66 ! [C: complex,A: complex,B: complex] :
% 7.75/5.66 ( ( C != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 7.75/5.66 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_left
% 7.75/5.66 thf(fact_820_nonzero__mult__divide__mult__cancel__left,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( C != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.66 = ( divide_divide_real @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_left
% 7.75/5.66 thf(fact_821_nonzero__mult__divide__mult__cancel__left,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( C != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.66 = ( divide_divide_rat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_left
% 7.75/5.66 thf(fact_822_nonzero__mult__divide__mult__cancel__left2,axiom,
% 7.75/5.66 ! [C: complex,A: complex,B: complex] :
% 7.75/5.66 ( ( C != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 7.75/5.66 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_left2
% 7.75/5.66 thf(fact_823_nonzero__mult__divide__mult__cancel__left2,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( C != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 7.75/5.66 = ( divide_divide_real @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_left2
% 7.75/5.66 thf(fact_824_nonzero__mult__divide__mult__cancel__left2,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( C != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 7.75/5.66 = ( divide_divide_rat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_left2
% 7.75/5.66 thf(fact_825_nonzero__mult__divide__mult__cancel__right,axiom,
% 7.75/5.66 ! [C: complex,A: complex,B: complex] :
% 7.75/5.66 ( ( C != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 7.75/5.66 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_right
% 7.75/5.66 thf(fact_826_nonzero__mult__divide__mult__cancel__right,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( C != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 7.75/5.66 = ( divide_divide_real @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_right
% 7.75/5.66 thf(fact_827_nonzero__mult__divide__mult__cancel__right,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( C != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 7.75/5.66 = ( divide_divide_rat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_right
% 7.75/5.66 thf(fact_828_nonzero__mult__divide__mult__cancel__right2,axiom,
% 7.75/5.66 ! [C: complex,A: complex,B: complex] :
% 7.75/5.66 ( ( C != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 7.75/5.66 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_right2
% 7.75/5.66 thf(fact_829_nonzero__mult__divide__mult__cancel__right2,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( C != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 7.75/5.66 = ( divide_divide_real @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_right2
% 7.75/5.66 thf(fact_830_nonzero__mult__divide__mult__cancel__right2,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( C != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.66 = ( divide_divide_rat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_mult_divide_mult_cancel_right2
% 7.75/5.66 thf(fact_831_div__mult__mult1,axiom,
% 7.75/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( C != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.66 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_mult1
% 7.75/5.66 thf(fact_832_div__mult__mult1,axiom,
% 7.75/5.66 ! [C: nat,A: nat,B: nat] :
% 7.75/5.66 ( ( C != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 7.75/5.66 = ( divide_divide_nat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_mult1
% 7.75/5.66 thf(fact_833_div__mult__mult1,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( C != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.66 = ( divide_divide_int @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_mult1
% 7.75/5.66 thf(fact_834_div__mult__mult2,axiom,
% 7.75/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( C != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.66 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_mult2
% 7.75/5.66 thf(fact_835_div__mult__mult2,axiom,
% 7.75/5.66 ! [C: nat,A: nat,B: nat] :
% 7.75/5.66 ( ( C != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 7.75/5.66 = ( divide_divide_nat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_mult2
% 7.75/5.66 thf(fact_836_div__mult__mult2,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( C != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 7.75/5.66 = ( divide_divide_int @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_mult2
% 7.75/5.66 thf(fact_837_div__mult__mult1__if,axiom,
% 7.75/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ( C = zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.66 = zero_z3403309356797280102nteger ) )
% 7.75/5.66 & ( ( C != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.66 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_mult1_if
% 7.75/5.66 thf(fact_838_div__mult__mult1__if,axiom,
% 7.75/5.66 ! [C: nat,A: nat,B: nat] :
% 7.75/5.66 ( ( ( C = zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 7.75/5.66 = zero_zero_nat ) )
% 7.75/5.66 & ( ( C != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 7.75/5.66 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_mult1_if
% 7.75/5.66 thf(fact_839_div__mult__mult1__if,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( ( C = zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.66 = zero_zero_int ) )
% 7.75/5.66 & ( ( C != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.66 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_mult1_if
% 7.75/5.66 thf(fact_840_power__inject__exp,axiom,
% 7.75/5.66 ! [A: code_integer,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 7.75/5.66 => ( ( ( power_8256067586552552935nteger @ A @ M )
% 7.75/5.66 = ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.66 = ( M = N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_inject_exp
% 7.75/5.66 thf(fact_841_power__inject__exp,axiom,
% 7.75/5.66 ! [A: real,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.66 => ( ( ( power_power_real @ A @ M )
% 7.75/5.66 = ( power_power_real @ A @ N ) )
% 7.75/5.66 = ( M = N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_inject_exp
% 7.75/5.66 thf(fact_842_power__inject__exp,axiom,
% 7.75/5.66 ! [A: rat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ A )
% 7.75/5.66 => ( ( ( power_power_rat @ A @ M )
% 7.75/5.66 = ( power_power_rat @ A @ N ) )
% 7.75/5.66 = ( M = N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_inject_exp
% 7.75/5.66 thf(fact_843_power__inject__exp,axiom,
% 7.75/5.66 ! [A: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ A )
% 7.75/5.66 => ( ( ( power_power_nat @ A @ M )
% 7.75/5.66 = ( power_power_nat @ A @ N ) )
% 7.75/5.66 = ( M = N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_inject_exp
% 7.75/5.66 thf(fact_844_power__inject__exp,axiom,
% 7.75/5.66 ! [A: int,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ one_one_int @ A )
% 7.75/5.66 => ( ( ( power_power_int @ A @ M )
% 7.75/5.66 = ( power_power_int @ A @ N ) )
% 7.75/5.66 = ( M = N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_inject_exp
% 7.75/5.66 thf(fact_845_power__0__Suc,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 7.75/5.66 = zero_zero_rat ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_Suc
% 7.75/5.66 thf(fact_846_power__0__Suc,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_Suc
% 7.75/5.66 thf(fact_847_power__0__Suc,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 7.75/5.66 = zero_zero_real ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_Suc
% 7.75/5.66 thf(fact_848_power__0__Suc,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_Suc
% 7.75/5.66 thf(fact_849_power__0__Suc,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 7.75/5.66 = zero_zero_complex ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_Suc
% 7.75/5.66 thf(fact_850_power__0__Suc,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( suc @ N ) )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_Suc
% 7.75/5.66 thf(fact_851_power__zero__numeral,axiom,
% 7.75/5.66 ! [K: num] :
% 7.75/5.66 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 7.75/5.66 = zero_zero_rat ) ).
% 7.75/5.66
% 7.75/5.66 % power_zero_numeral
% 7.75/5.66 thf(fact_852_power__zero__numeral,axiom,
% 7.75/5.66 ! [K: num] :
% 7.75/5.66 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % power_zero_numeral
% 7.75/5.66 thf(fact_853_power__zero__numeral,axiom,
% 7.75/5.66 ! [K: num] :
% 7.75/5.66 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 7.75/5.66 = zero_zero_real ) ).
% 7.75/5.66
% 7.75/5.66 % power_zero_numeral
% 7.75/5.66 thf(fact_854_power__zero__numeral,axiom,
% 7.75/5.66 ! [K: num] :
% 7.75/5.66 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % power_zero_numeral
% 7.75/5.66 thf(fact_855_power__zero__numeral,axiom,
% 7.75/5.66 ! [K: num] :
% 7.75/5.66 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 7.75/5.66 = zero_zero_complex ) ).
% 7.75/5.66
% 7.75/5.66 % power_zero_numeral
% 7.75/5.66 thf(fact_856_power__zero__numeral,axiom,
% 7.75/5.66 ! [K: num] :
% 7.75/5.66 ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( numeral_numeral_nat @ K ) )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % power_zero_numeral
% 7.75/5.66 thf(fact_857_dvd__times__right__cancel__iff,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( A != zero_zero_nat )
% 7.75/5.66 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 7.75/5.66 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_times_right_cancel_iff
% 7.75/5.66 thf(fact_858_dvd__times__right__cancel__iff,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( A != zero_zero_int )
% 7.75/5.66 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 7.75/5.66 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_times_right_cancel_iff
% 7.75/5.66 thf(fact_859_dvd__times__right__cancel__iff,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.66 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 7.75/5.66 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_times_right_cancel_iff
% 7.75/5.66 thf(fact_860_dvd__times__left__cancel__iff,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( A != zero_zero_nat )
% 7.75/5.66 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 7.75/5.66 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_times_left_cancel_iff
% 7.75/5.66 thf(fact_861_dvd__times__left__cancel__iff,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( A != zero_zero_int )
% 7.75/5.66 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 7.75/5.66 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_times_left_cancel_iff
% 7.75/5.66 thf(fact_862_dvd__times__left__cancel__iff,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.66 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 7.75/5.66 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_times_left_cancel_iff
% 7.75/5.66 thf(fact_863_dvd__mult__cancel__right,axiom,
% 7.75/5.66 ! [A: rat,C: rat,B: rat] :
% 7.75/5.66 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 7.75/5.66 = ( ( C = zero_zero_rat )
% 7.75/5.66 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_right
% 7.75/5.66 thf(fact_864_dvd__mult__cancel__right,axiom,
% 7.75/5.66 ! [A: real,C: real,B: real] :
% 7.75/5.66 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 7.75/5.66 = ( ( C = zero_zero_real )
% 7.75/5.66 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_right
% 7.75/5.66 thf(fact_865_dvd__mult__cancel__right,axiom,
% 7.75/5.66 ! [A: int,C: int,B: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 7.75/5.66 = ( ( C = zero_zero_int )
% 7.75/5.66 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_right
% 7.75/5.66 thf(fact_866_dvd__mult__cancel__right,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.66 = ( ( C = zero_z3403309356797280102nteger )
% 7.75/5.66 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_right
% 7.75/5.66 thf(fact_867_dvd__mult__cancel__right,axiom,
% 7.75/5.66 ! [A: complex,C: complex,B: complex] :
% 7.75/5.66 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 7.75/5.66 = ( ( C = zero_zero_complex )
% 7.75/5.66 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_right
% 7.75/5.66 thf(fact_868_dvd__mult__cancel__left,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.66 = ( ( C = zero_zero_rat )
% 7.75/5.66 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_left
% 7.75/5.66 thf(fact_869_dvd__mult__cancel__left,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.66 = ( ( C = zero_zero_real )
% 7.75/5.66 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_left
% 7.75/5.66 thf(fact_870_dvd__mult__cancel__left,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.66 = ( ( C = zero_zero_int )
% 7.75/5.66 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_left
% 7.75/5.66 thf(fact_871_dvd__mult__cancel__left,axiom,
% 7.75/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.66 = ( ( C = zero_z3403309356797280102nteger )
% 7.75/5.66 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_left
% 7.75/5.66 thf(fact_872_dvd__mult__cancel__left,axiom,
% 7.75/5.66 ! [C: complex,A: complex,B: complex] :
% 7.75/5.66 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 7.75/5.66 = ( ( C = zero_zero_complex )
% 7.75/5.66 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel_left
% 7.75/5.66 thf(fact_873_mod__by__1,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % mod_by_1
% 7.75/5.66 thf(fact_874_mod__by__1,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ A @ one_one_int )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % mod_by_1
% 7.75/5.66 thf(fact_875_mod__by__1,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % mod_by_1
% 7.75/5.66 thf(fact_876_bits__mod__by__1,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % bits_mod_by_1
% 7.75/5.66 thf(fact_877_bits__mod__by__1,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ A @ one_one_int )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % bits_mod_by_1
% 7.75/5.66 thf(fact_878_bits__mod__by__1,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % bits_mod_by_1
% 7.75/5.66 thf(fact_879_mod__mult__self2__is__0,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self2_is_0
% 7.75/5.66 thf(fact_880_mod__mult__self2__is__0,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self2_is_0
% 7.75/5.66 thf(fact_881_mod__mult__self2__is__0,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self2_is_0
% 7.75/5.66 thf(fact_882_mod__mult__self1__is__0,axiom,
% 7.75/5.66 ! [B: nat,A: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self1_is_0
% 7.75/5.66 thf(fact_883_mod__mult__self1__is__0,axiom,
% 7.75/5.66 ! [B: int,A: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self1_is_0
% 7.75/5.66 thf(fact_884_mod__mult__self1__is__0,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self1_is_0
% 7.75/5.66 thf(fact_885_unit__prod,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.66 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.66 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_prod
% 7.75/5.66 thf(fact_886_unit__prod,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.66 => ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.66 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_prod
% 7.75/5.66 thf(fact_887_unit__prod,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.66 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.66 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_prod
% 7.75/5.66 thf(fact_888_power__Suc0__right,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc0_right
% 7.75/5.66 thf(fact_889_power__Suc0__right,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc0_right
% 7.75/5.66 thf(fact_890_power__Suc0__right,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc0_right
% 7.75/5.66 thf(fact_891_power__Suc0__right,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc0_right
% 7.75/5.66 thf(fact_892_power__Suc0__right,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( power_8256067586552552935nteger @ A @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc0_right
% 7.75/5.66 thf(fact_893_power__Suc0__right,axiom,
% 7.75/5.66 ! [A: assn] :
% 7.75/5.66 ( ( power_power_assn @ A @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc0_right
% 7.75/5.66 thf(fact_894_zero__less__Suc,axiom,
% 7.75/5.66 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_Suc
% 7.75/5.66 thf(fact_895_less__Suc0,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = ( N = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_Suc0
% 7.75/5.66 thf(fact_896_bits__mod__div__trivial,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % bits_mod_div_trivial
% 7.75/5.66 thf(fact_897_bits__mod__div__trivial,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % bits_mod_div_trivial
% 7.75/5.66 thf(fact_898_bits__mod__div__trivial,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % bits_mod_div_trivial
% 7.75/5.66 thf(fact_899_mod__div__trivial,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % mod_div_trivial
% 7.75/5.66 thf(fact_900_mod__div__trivial,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % mod_div_trivial
% 7.75/5.66 thf(fact_901_mod__div__trivial,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % mod_div_trivial
% 7.75/5.66 thf(fact_902_mod__mult__self4,axiom,
% 7.75/5.66 ! [B: nat,C: nat,A: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 7.75/5.66 = ( modulo_modulo_nat @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self4
% 7.75/5.66 thf(fact_903_mod__mult__self4,axiom,
% 7.75/5.66 ! [B: int,C: int,A: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 7.75/5.66 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self4
% 7.75/5.66 thf(fact_904_mod__mult__self4,axiom,
% 7.75/5.66 ! [B: code_integer,C: code_integer,A: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 7.75/5.66 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self4
% 7.75/5.66 thf(fact_905_mod__mult__self3,axiom,
% 7.75/5.66 ! [C: nat,B: nat,A: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 7.75/5.66 = ( modulo_modulo_nat @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self3
% 7.75/5.66 thf(fact_906_mod__mult__self3,axiom,
% 7.75/5.66 ! [C: int,B: int,A: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 7.75/5.66 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self3
% 7.75/5.66 thf(fact_907_mod__mult__self3,axiom,
% 7.75/5.66 ! [C: code_integer,B: code_integer,A: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 7.75/5.66 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self3
% 7.75/5.66 thf(fact_908_mod__mult__self2,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 7.75/5.66 = ( modulo_modulo_nat @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self2
% 7.75/5.66 thf(fact_909_mod__mult__self2,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 7.75/5.66 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self2
% 7.75/5.66 thf(fact_910_mod__mult__self2,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 7.75/5.66 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self2
% 7.75/5.66 thf(fact_911_mod__mult__self1,axiom,
% 7.75/5.66 ! [A: nat,C: nat,B: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 7.75/5.66 = ( modulo_modulo_nat @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self1
% 7.75/5.66 thf(fact_912_mod__mult__self1,axiom,
% 7.75/5.66 ! [A: int,C: int,B: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 7.75/5.66 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self1
% 7.75/5.66 thf(fact_913_mod__mult__self1,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 7.75/5.66 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_self1
% 7.75/5.66 thf(fact_914_unit__div__1__div__1,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 7.75/5.66 = A ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div_1_div_1
% 7.75/5.66 thf(fact_915_unit__div__1__div__1,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.66 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 7.75/5.66 = A ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div_1_div_1
% 7.75/5.66 thf(fact_916_unit__div__1__unit,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.66 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div_1_unit
% 7.75/5.66 thf(fact_917_unit__div__1__unit,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.66 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div_1_unit
% 7.75/5.66 thf(fact_918_unit__div,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.66 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.66 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div
% 7.75/5.66 thf(fact_919_unit__div,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.66 => ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.66 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div
% 7.75/5.66 thf(fact_920_dvd__imp__mod__0,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.66 => ( ( modulo_modulo_nat @ B @ A )
% 7.75/5.66 = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_imp_mod_0
% 7.75/5.66 thf(fact_921_dvd__imp__mod__0,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.66 => ( ( modulo_modulo_int @ B @ A )
% 7.75/5.66 = zero_zero_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_imp_mod_0
% 7.75/5.66 thf(fact_922_dvd__imp__mod__0,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ A @ B )
% 7.75/5.66 => ( ( modulo364778990260209775nteger @ B @ A )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_imp_mod_0
% 7.75/5.66 thf(fact_923_add__gr__0,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.66 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.66 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_gr_0
% 7.75/5.66 thf(fact_924_div__by__Suc__0,axiom,
% 7.75/5.66 ! [M: nat] :
% 7.75/5.66 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = M ) ).
% 7.75/5.66
% 7.75/5.66 % div_by_Suc_0
% 7.75/5.66 thf(fact_925_mult__eq__1__iff,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ( times_times_nat @ M @ N )
% 7.75/5.66 = ( suc @ zero_zero_nat ) )
% 7.75/5.66 = ( ( M
% 7.75/5.66 = ( suc @ zero_zero_nat ) )
% 7.75/5.66 & ( N
% 7.75/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_eq_1_iff
% 7.75/5.66 thf(fact_926_one__eq__mult__iff,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ( suc @ zero_zero_nat )
% 7.75/5.66 = ( times_times_nat @ M @ N ) )
% 7.75/5.66 = ( ( M
% 7.75/5.66 = ( suc @ zero_zero_nat ) )
% 7.75/5.66 & ( N
% 7.75/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_eq_mult_iff
% 7.75/5.66 thf(fact_927_power__Suc__0,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.75/5.66 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_0
% 7.75/5.66 thf(fact_928_nat__power__eq__Suc__0__iff,axiom,
% 7.75/5.66 ! [X: nat,M: nat] :
% 7.75/5.66 ( ( ( power_power_nat @ X @ M )
% 7.75/5.66 = ( suc @ zero_zero_nat ) )
% 7.75/5.66 = ( ( M = zero_zero_nat )
% 7.75/5.66 | ( X
% 7.75/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_power_eq_Suc_0_iff
% 7.75/5.66 thf(fact_929_div__eq__dividend__iff,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.66 => ( ( ( divide_divide_nat @ M @ N )
% 7.75/5.66 = M )
% 7.75/5.66 = ( N = one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_eq_dividend_iff
% 7.75/5.66 thf(fact_930_div__less,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M @ N )
% 7.75/5.66 => ( ( divide_divide_nat @ M @ N )
% 7.75/5.66 = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_less
% 7.75/5.66 thf(fact_931_nat__mult__less__cancel__disj,axiom,
% 7.75/5.66 ! [K: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.66 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.66 & ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_mult_less_cancel_disj
% 7.75/5.66 thf(fact_932_nat__0__less__mult__iff,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 7.75/5.66 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_0_less_mult_iff
% 7.75/5.66 thf(fact_933_mult__less__cancel2,axiom,
% 7.75/5.66 ! [M: nat,K: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 7.75/5.66 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.66 & ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel2
% 7.75/5.66 thf(fact_934_nat__zero__less__power__iff,axiom,
% 7.75/5.66 ! [X: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 7.75/5.66 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 7.75/5.66 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_zero_less_power_iff
% 7.75/5.66 thf(fact_935_dvd__1__iff__1,axiom,
% 7.75/5.66 ! [M: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = ( M
% 7.75/5.66 = ( suc @ zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_1_iff_1
% 7.75/5.66 thf(fact_936_dvd__1__left,axiom,
% 7.75/5.66 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_1_left
% 7.75/5.66 thf(fact_937_mod__by__Suc__0,axiom,
% 7.75/5.66 ! [M: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % mod_by_Suc_0
% 7.75/5.66 thf(fact_938_nat__mult__div__cancel__disj,axiom,
% 7.75/5.66 ! [K: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ( K = zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.66 = zero_zero_nat ) )
% 7.75/5.66 & ( ( K != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.66 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_mult_div_cancel_disj
% 7.75/5.66 thf(fact_939_nat__mult__dvd__cancel__disj,axiom,
% 7.75/5.66 ! [K: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.66 = ( ( K = zero_zero_nat )
% 7.75/5.66 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_mult_dvd_cancel_disj
% 7.75/5.66 thf(fact_940_one__less__numeral__iff,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 7.75/5.66 = ( ord_less_num @ one @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_numeral_iff
% 7.75/5.66 thf(fact_941_one__less__numeral__iff,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 7.75/5.66 = ( ord_less_num @ one @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_numeral_iff
% 7.75/5.66 thf(fact_942_one__less__numeral__iff,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 7.75/5.66 = ( ord_less_num @ one @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_numeral_iff
% 7.75/5.66 thf(fact_943_one__less__numeral__iff,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 7.75/5.66 = ( ord_less_num @ one @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_numeral_iff
% 7.75/5.66 thf(fact_944_divide__less__0__1__iff,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 7.75/5.66 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_0_1_iff
% 7.75/5.66 thf(fact_945_divide__less__0__1__iff,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 7.75/5.66 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_0_1_iff
% 7.75/5.66 thf(fact_946_divide__less__eq__1__neg,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 7.75/5.66 = ( ord_less_real @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq_1_neg
% 7.75/5.66 thf(fact_947_divide__less__eq__1__neg,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 7.75/5.66 = ( ord_less_rat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq_1_neg
% 7.75/5.66 thf(fact_948_divide__less__eq__1__pos,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 7.75/5.66 = ( ord_less_real @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq_1_pos
% 7.75/5.66 thf(fact_949_divide__less__eq__1__pos,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 7.75/5.66 = ( ord_less_rat @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq_1_pos
% 7.75/5.66 thf(fact_950_less__divide__eq__1__neg,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 7.75/5.66 = ( ord_less_real @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq_1_neg
% 7.75/5.66 thf(fact_951_less__divide__eq__1__neg,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 7.75/5.66 = ( ord_less_rat @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq_1_neg
% 7.75/5.66 thf(fact_952_less__divide__eq__1__pos,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 7.75/5.66 = ( ord_less_real @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq_1_pos
% 7.75/5.66 thf(fact_953_less__divide__eq__1__pos,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 7.75/5.66 = ( ord_less_rat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq_1_pos
% 7.75/5.66 thf(fact_954_zero__less__divide__1__iff,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 7.75/5.66 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_divide_1_iff
% 7.75/5.66 thf(fact_955_zero__less__divide__1__iff,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 7.75/5.66 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_divide_1_iff
% 7.75/5.66 thf(fact_956_divide__eq__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [B: complex,W: num,A: complex] :
% 7.75/5.66 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.66 = A )
% 7.75/5.66 = ( ( ( ( numera6690914467698888265omplex @ W )
% 7.75/5.66 != zero_zero_complex )
% 7.75/5.66 => ( B
% 7.75/5.66 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 7.75/5.66 & ( ( ( numera6690914467698888265omplex @ W )
% 7.75/5.66 = zero_zero_complex )
% 7.75/5.66 => ( A = zero_zero_complex ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_eq_eq_numeral1(1)
% 7.75/5.66 thf(fact_957_divide__eq__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [B: real,W: num,A: real] :
% 7.75/5.66 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 7.75/5.66 = A )
% 7.75/5.66 = ( ( ( ( numeral_numeral_real @ W )
% 7.75/5.66 != zero_zero_real )
% 7.75/5.66 => ( B
% 7.75/5.66 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 7.75/5.66 & ( ( ( numeral_numeral_real @ W )
% 7.75/5.66 = zero_zero_real )
% 7.75/5.66 => ( A = zero_zero_real ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_eq_eq_numeral1(1)
% 7.75/5.66 thf(fact_958_divide__eq__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [B: rat,W: num,A: rat] :
% 7.75/5.66 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 7.75/5.66 = A )
% 7.75/5.66 = ( ( ( ( numeral_numeral_rat @ W )
% 7.75/5.66 != zero_zero_rat )
% 7.75/5.66 => ( B
% 7.75/5.66 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 7.75/5.66 & ( ( ( numeral_numeral_rat @ W )
% 7.75/5.66 = zero_zero_rat )
% 7.75/5.66 => ( A = zero_zero_rat ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_eq_eq_numeral1(1)
% 7.75/5.66 thf(fact_959_eq__divide__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [A: complex,B: complex,W: num] :
% 7.75/5.66 ( ( A
% 7.75/5.66 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 7.75/5.66 = ( ( ( ( numera6690914467698888265omplex @ W )
% 7.75/5.66 != zero_zero_complex )
% 7.75/5.66 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.66 = B ) )
% 7.75/5.66 & ( ( ( numera6690914467698888265omplex @ W )
% 7.75/5.66 = zero_zero_complex )
% 7.75/5.66 => ( A = zero_zero_complex ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % eq_divide_eq_numeral1(1)
% 7.75/5.66 thf(fact_960_eq__divide__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [A: real,B: real,W: num] :
% 7.75/5.66 ( ( A
% 7.75/5.66 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.66 = ( ( ( ( numeral_numeral_real @ W )
% 7.75/5.66 != zero_zero_real )
% 7.75/5.66 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 7.75/5.66 = B ) )
% 7.75/5.66 & ( ( ( numeral_numeral_real @ W )
% 7.75/5.66 = zero_zero_real )
% 7.75/5.66 => ( A = zero_zero_real ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % eq_divide_eq_numeral1(1)
% 7.75/5.66 thf(fact_961_eq__divide__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [A: rat,B: rat,W: num] :
% 7.75/5.66 ( ( A
% 7.75/5.66 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 7.75/5.66 = ( ( ( ( numeral_numeral_rat @ W )
% 7.75/5.66 != zero_zero_rat )
% 7.75/5.66 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 7.75/5.66 = B ) )
% 7.75/5.66 & ( ( ( numeral_numeral_rat @ W )
% 7.75/5.66 = zero_zero_rat )
% 7.75/5.66 => ( A = zero_zero_rat ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % eq_divide_eq_numeral1(1)
% 7.75/5.66 thf(fact_962_divide__less__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [B: real,W: num,A: real] :
% 7.75/5.66 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 7.75/5.66 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq_numeral1(1)
% 7.75/5.66 thf(fact_963_divide__less__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [B: rat,W: num,A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 7.75/5.66 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq_numeral1(1)
% 7.75/5.66 thf(fact_964_less__divide__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [A: real,B: real,W: num] :
% 7.75/5.66 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.66 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq_numeral1(1)
% 7.75/5.66 thf(fact_965_less__divide__eq__numeral1_I1_J,axiom,
% 7.75/5.66 ! [A: rat,B: rat,W: num] :
% 7.75/5.66 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 7.75/5.66 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq_numeral1(1)
% 7.75/5.66 thf(fact_966_div__mult__self1,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.66 ( ( B != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 7.75/5.66 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self1
% 7.75/5.66 thf(fact_967_div__mult__self1,axiom,
% 7.75/5.66 ! [B: nat,A: nat,C: nat] :
% 7.75/5.66 ( ( B != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 7.75/5.66 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self1
% 7.75/5.66 thf(fact_968_div__mult__self1,axiom,
% 7.75/5.66 ! [B: int,A: int,C: int] :
% 7.75/5.66 ( ( B != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 7.75/5.66 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self1
% 7.75/5.66 thf(fact_969_div__mult__self2,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.66 ( ( B != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 7.75/5.66 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self2
% 7.75/5.66 thf(fact_970_div__mult__self2,axiom,
% 7.75/5.66 ! [B: nat,A: nat,C: nat] :
% 7.75/5.66 ( ( B != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 7.75/5.66 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self2
% 7.75/5.66 thf(fact_971_div__mult__self2,axiom,
% 7.75/5.66 ! [B: int,A: int,C: int] :
% 7.75/5.66 ( ( B != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 7.75/5.66 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self2
% 7.75/5.66 thf(fact_972_div__mult__self3,axiom,
% 7.75/5.66 ! [B: code_integer,C: code_integer,A: code_integer] :
% 7.75/5.66 ( ( B != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 7.75/5.66 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self3
% 7.75/5.66 thf(fact_973_div__mult__self3,axiom,
% 7.75/5.66 ! [B: nat,C: nat,A: nat] :
% 7.75/5.66 ( ( B != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 7.75/5.66 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self3
% 7.75/5.66 thf(fact_974_div__mult__self3,axiom,
% 7.75/5.66 ! [B: int,C: int,A: int] :
% 7.75/5.66 ( ( B != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 7.75/5.66 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self3
% 7.75/5.66 thf(fact_975_div__mult__self4,axiom,
% 7.75/5.66 ! [B: code_integer,C: code_integer,A: code_integer] :
% 7.75/5.66 ( ( B != zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 7.75/5.66 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self4
% 7.75/5.66 thf(fact_976_div__mult__self4,axiom,
% 7.75/5.66 ! [B: nat,C: nat,A: nat] :
% 7.75/5.66 ( ( B != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 7.75/5.66 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self4
% 7.75/5.66 thf(fact_977_div__mult__self4,axiom,
% 7.75/5.66 ! [B: int,C: int,A: int] :
% 7.75/5.66 ( ( B != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 7.75/5.66 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self4
% 7.75/5.66 thf(fact_978_nonzero__divide__mult__cancel__left,axiom,
% 7.75/5.66 ! [A: complex,B: complex] :
% 7.75/5.66 ( ( A != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 7.75/5.66 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_divide_mult_cancel_left
% 7.75/5.66 thf(fact_979_nonzero__divide__mult__cancel__left,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( A != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 7.75/5.66 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_divide_mult_cancel_left
% 7.75/5.66 thf(fact_980_nonzero__divide__mult__cancel__left,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( A != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 7.75/5.66 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_divide_mult_cancel_left
% 7.75/5.66 thf(fact_981_nonzero__divide__mult__cancel__right,axiom,
% 7.75/5.66 ! [B: complex,A: complex] :
% 7.75/5.66 ( ( B != zero_zero_complex )
% 7.75/5.66 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 7.75/5.66 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_divide_mult_cancel_right
% 7.75/5.66 thf(fact_982_nonzero__divide__mult__cancel__right,axiom,
% 7.75/5.66 ! [B: real,A: real] :
% 7.75/5.66 ( ( B != zero_zero_real )
% 7.75/5.66 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 7.75/5.66 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_divide_mult_cancel_right
% 7.75/5.66 thf(fact_983_nonzero__divide__mult__cancel__right,axiom,
% 7.75/5.66 ! [B: rat,A: rat] :
% 7.75/5.66 ( ( B != zero_zero_rat )
% 7.75/5.66 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 7.75/5.66 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nonzero_divide_mult_cancel_right
% 7.75/5.66 thf(fact_984_Suc__1,axiom,
% 7.75/5.66 ( ( suc @ one_one_nat )
% 7.75/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_1
% 7.75/5.66 thf(fact_985_power__strict__increasing__iff,axiom,
% 7.75/5.66 ! [B: code_integer,X: nat,Y: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 7.75/5.66 = ( ord_less_nat @ X @ Y ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing_iff
% 7.75/5.66 thf(fact_986_power__strict__increasing__iff,axiom,
% 7.75/5.66 ! [B: real,X: nat,Y: nat] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.66 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 7.75/5.66 = ( ord_less_nat @ X @ Y ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing_iff
% 7.75/5.66 thf(fact_987_power__strict__increasing__iff,axiom,
% 7.75/5.66 ! [B: rat,X: nat,Y: nat] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ B )
% 7.75/5.66 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 7.75/5.66 = ( ord_less_nat @ X @ Y ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing_iff
% 7.75/5.66 thf(fact_988_power__strict__increasing__iff,axiom,
% 7.75/5.66 ! [B: nat,X: nat,Y: nat] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ B )
% 7.75/5.66 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 7.75/5.66 = ( ord_less_nat @ X @ Y ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing_iff
% 7.75/5.66 thf(fact_989_power__strict__increasing__iff,axiom,
% 7.75/5.66 ! [B: int,X: nat,Y: nat] :
% 7.75/5.66 ( ( ord_less_int @ one_one_int @ B )
% 7.75/5.66 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 7.75/5.66 = ( ord_less_nat @ X @ Y ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing_iff
% 7.75/5.66 thf(fact_990_power__eq__0__iff,axiom,
% 7.75/5.66 ! [A: rat,N: nat] :
% 7.75/5.66 ( ( ( power_power_rat @ A @ N )
% 7.75/5.66 = zero_zero_rat )
% 7.75/5.66 = ( ( A = zero_zero_rat )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_eq_0_iff
% 7.75/5.66 thf(fact_991_power__eq__0__iff,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( ( power_power_nat @ A @ N )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 = ( ( A = zero_zero_nat )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_eq_0_iff
% 7.75/5.66 thf(fact_992_power__eq__0__iff,axiom,
% 7.75/5.66 ! [A: real,N: nat] :
% 7.75/5.66 ( ( ( power_power_real @ A @ N )
% 7.75/5.66 = zero_zero_real )
% 7.75/5.66 = ( ( A = zero_zero_real )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_eq_0_iff
% 7.75/5.66 thf(fact_993_power__eq__0__iff,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( ( power_power_int @ A @ N )
% 7.75/5.66 = zero_zero_int )
% 7.75/5.66 = ( ( A = zero_zero_int )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_eq_0_iff
% 7.75/5.66 thf(fact_994_power__eq__0__iff,axiom,
% 7.75/5.66 ! [A: complex,N: nat] :
% 7.75/5.66 ( ( ( power_power_complex @ A @ N )
% 7.75/5.66 = zero_zero_complex )
% 7.75/5.66 = ( ( A = zero_zero_complex )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_eq_0_iff
% 7.75/5.66 thf(fact_995_power__eq__0__iff,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( ( power_8256067586552552935nteger @ A @ N )
% 7.75/5.66 = zero_z3403309356797280102nteger )
% 7.75/5.66 = ( ( A = zero_z3403309356797280102nteger )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_eq_0_iff
% 7.75/5.66 thf(fact_996_unit__mult__div__div,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.66 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 7.75/5.66 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_mult_div_div
% 7.75/5.66 thf(fact_997_unit__mult__div__div,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.66 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 7.75/5.66 = ( divide_divide_nat @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_mult_div_div
% 7.75/5.66 thf(fact_998_unit__mult__div__div,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.66 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 7.75/5.66 = ( divide_divide_int @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_mult_div_div
% 7.75/5.66 thf(fact_999_unit__div__mult__self,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.66 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 7.75/5.66 = B ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div_mult_self
% 7.75/5.66 thf(fact_1000_unit__div__mult__self,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.66 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 7.75/5.66 = B ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div_mult_self
% 7.75/5.66 thf(fact_1001_unit__div__mult__self,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.66 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 7.75/5.66 = B ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div_mult_self
% 7.75/5.66 thf(fact_1002_pow__divides__pow__iff,axiom,
% 7.75/5.66 ! [N: nat,A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 7.75/5.66 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pow_divides_pow_iff
% 7.75/5.66 thf(fact_1003_pow__divides__pow__iff,axiom,
% 7.75/5.66 ! [N: nat,A: int,B: int] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 7.75/5.66 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pow_divides_pow_iff
% 7.75/5.66 thf(fact_1004_div__mult__self__is__m,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 7.75/5.66 = M ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self_is_m
% 7.75/5.66 thf(fact_1005_div__mult__self1__is__m,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 7.75/5.66 = M ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_mult_self1_is_m
% 7.75/5.66 thf(fact_1006_Suc__times__numeral__mod__eq,axiom,
% 7.75/5.66 ! [K: num,N: nat] :
% 7.75/5.66 ( ( ( numeral_numeral_nat @ K )
% 7.75/5.66 != one_one_nat )
% 7.75/5.66 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 7.75/5.66 = one_one_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_times_numeral_mod_eq
% 7.75/5.66 thf(fact_1007_Suc__mod__mult__self1,axiom,
% 7.75/5.66 ! [M: nat,K: nat,N: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 7.75/5.66 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_mod_mult_self1
% 7.75/5.66 thf(fact_1008_Suc__mod__mult__self2,axiom,
% 7.75/5.66 ! [M: nat,N: nat,K: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 7.75/5.66 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_mod_mult_self2
% 7.75/5.66 thf(fact_1009_Suc__mod__mult__self3,axiom,
% 7.75/5.66 ! [K: nat,N: nat,M: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 7.75/5.66 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_mod_mult_self3
% 7.75/5.66 thf(fact_1010_Suc__mod__mult__self4,axiom,
% 7.75/5.66 ! [N: nat,K: nat,M: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 7.75/5.66 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_mod_mult_self4
% 7.75/5.66 thf(fact_1011_one__add__one,axiom,
% 7.75/5.66 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 7.75/5.66 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_add_one
% 7.75/5.66 thf(fact_1012_one__add__one,axiom,
% 7.75/5.66 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 7.75/5.66 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_add_one
% 7.75/5.66 thf(fact_1013_one__add__one,axiom,
% 7.75/5.66 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 7.75/5.66 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_add_one
% 7.75/5.66 thf(fact_1014_one__add__one,axiom,
% 7.75/5.66 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 7.75/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_add_one
% 7.75/5.66 thf(fact_1015_one__add__one,axiom,
% 7.75/5.66 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 7.75/5.66 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_add_one
% 7.75/5.66 thf(fact_1016_power__strict__decreasing__iff,axiom,
% 7.75/5.66 ! [B: code_integer,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing_iff
% 7.75/5.66 thf(fact_1017_power__strict__decreasing__iff,axiom,
% 7.75/5.66 ! [B: real,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.66 => ( ( ord_less_real @ B @ one_one_real )
% 7.75/5.66 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing_iff
% 7.75/5.66 thf(fact_1018_power__strict__decreasing__iff,axiom,
% 7.75/5.66 ! [B: rat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ B )
% 7.75/5.66 => ( ( ord_less_rat @ B @ one_one_rat )
% 7.75/5.66 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing_iff
% 7.75/5.66 thf(fact_1019_power__strict__decreasing__iff,axiom,
% 7.75/5.66 ! [B: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.66 => ( ( ord_less_nat @ B @ one_one_nat )
% 7.75/5.66 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing_iff
% 7.75/5.66 thf(fact_1020_power__strict__decreasing__iff,axiom,
% 7.75/5.66 ! [B: int,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.66 => ( ( ord_less_int @ B @ one_one_int )
% 7.75/5.66 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing_iff
% 7.75/5.66 thf(fact_1021_zero__eq__power2,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_rat )
% 7.75/5.66 = ( A = zero_zero_rat ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_eq_power2
% 7.75/5.66 thf(fact_1022_zero__eq__power2,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 = ( A = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_eq_power2
% 7.75/5.66 thf(fact_1023_zero__eq__power2,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_real )
% 7.75/5.66 = ( A = zero_zero_real ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_eq_power2
% 7.75/5.66 thf(fact_1024_zero__eq__power2,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_int )
% 7.75/5.66 = ( A = zero_zero_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_eq_power2
% 7.75/5.66 thf(fact_1025_zero__eq__power2,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_complex )
% 7.75/5.66 = ( A = zero_zero_complex ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_eq_power2
% 7.75/5.66 thf(fact_1026_zero__eq__power2,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_z3403309356797280102nteger )
% 7.75/5.66 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_eq_power2
% 7.75/5.66 thf(fact_1027_bits__one__mod__two__eq__one,axiom,
% 7.75/5.66 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_nat ) ).
% 7.75/5.66
% 7.75/5.66 % bits_one_mod_two_eq_one
% 7.75/5.66 thf(fact_1028_bits__one__mod__two__eq__one,axiom,
% 7.75/5.66 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_int ) ).
% 7.75/5.66
% 7.75/5.66 % bits_one_mod_two_eq_one
% 7.75/5.66 thf(fact_1029_bits__one__mod__two__eq__one,axiom,
% 7.75/5.66 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_Code_integer ) ).
% 7.75/5.66
% 7.75/5.66 % bits_one_mod_two_eq_one
% 7.75/5.66 thf(fact_1030_one__mod__two__eq__one,axiom,
% 7.75/5.66 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_nat ) ).
% 7.75/5.66
% 7.75/5.66 % one_mod_two_eq_one
% 7.75/5.66 thf(fact_1031_one__mod__two__eq__one,axiom,
% 7.75/5.66 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_int ) ).
% 7.75/5.66
% 7.75/5.66 % one_mod_two_eq_one
% 7.75/5.66 thf(fact_1032_one__mod__two__eq__one,axiom,
% 7.75/5.66 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_Code_integer ) ).
% 7.75/5.66
% 7.75/5.66 % one_mod_two_eq_one
% 7.75/5.66 thf(fact_1033_even__mod__2__iff,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_mod_2_iff
% 7.75/5.66 thf(fact_1034_even__mod__2__iff,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_mod_2_iff
% 7.75/5.66 thf(fact_1035_even__mod__2__iff,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_mod_2_iff
% 7.75/5.66 thf(fact_1036_mod2__Suc__Suc,axiom,
% 7.75/5.66 ! [M: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod2_Suc_Suc
% 7.75/5.66 thf(fact_1037_numeral__plus__one,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 7.75/5.66 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % numeral_plus_one
% 7.75/5.66 thf(fact_1038_numeral__plus__one,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 7.75/5.66 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % numeral_plus_one
% 7.75/5.66 thf(fact_1039_numeral__plus__one,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 7.75/5.66 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % numeral_plus_one
% 7.75/5.66 thf(fact_1040_numeral__plus__one,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 7.75/5.66 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % numeral_plus_one
% 7.75/5.66 thf(fact_1041_numeral__plus__one,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 7.75/5.66 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % numeral_plus_one
% 7.75/5.66 thf(fact_1042_one__plus__numeral,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 7.75/5.66 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_plus_numeral
% 7.75/5.66 thf(fact_1043_one__plus__numeral,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 7.75/5.66 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_plus_numeral
% 7.75/5.66 thf(fact_1044_one__plus__numeral,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 7.75/5.66 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_plus_numeral
% 7.75/5.66 thf(fact_1045_one__plus__numeral,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 7.75/5.66 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_plus_numeral
% 7.75/5.66 thf(fact_1046_one__plus__numeral,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 7.75/5.66 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_plus_numeral
% 7.75/5.66 thf(fact_1047_bits__1__div__2,axiom,
% 7.75/5.66 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % bits_1_div_2
% 7.75/5.66 thf(fact_1048_bits__1__div__2,axiom,
% 7.75/5.66 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % bits_1_div_2
% 7.75/5.66 thf(fact_1049_one__div__two__eq__zero,axiom,
% 7.75/5.66 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % one_div_two_eq_zero
% 7.75/5.66 thf(fact_1050_one__div__two__eq__zero,axiom,
% 7.75/5.66 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % one_div_two_eq_zero
% 7.75/5.66 thf(fact_1051_zero__less__power2,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = ( A != zero_z3403309356797280102nteger ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power2
% 7.75/5.66 thf(fact_1052_zero__less__power2,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = ( A != zero_zero_real ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power2
% 7.75/5.66 thf(fact_1053_zero__less__power2,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = ( A != zero_zero_rat ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power2
% 7.75/5.66 thf(fact_1054_zero__less__power2,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = ( A != zero_zero_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power2
% 7.75/5.66 thf(fact_1055_sum__power2__eq__zero__iff,axiom,
% 7.75/5.66 ! [X: rat,Y: rat] :
% 7.75/5.66 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = zero_zero_rat )
% 7.75/5.66 = ( ( X = zero_zero_rat )
% 7.75/5.66 & ( Y = zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % sum_power2_eq_zero_iff
% 7.75/5.66 thf(fact_1056_sum__power2__eq__zero__iff,axiom,
% 7.75/5.66 ! [X: real,Y: real] :
% 7.75/5.66 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = zero_zero_real )
% 7.75/5.66 = ( ( X = zero_zero_real )
% 7.75/5.66 & ( Y = zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % sum_power2_eq_zero_iff
% 7.75/5.66 thf(fact_1057_sum__power2__eq__zero__iff,axiom,
% 7.75/5.66 ! [X: int,Y: int] :
% 7.75/5.66 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = zero_zero_int )
% 7.75/5.66 = ( ( X = zero_zero_int )
% 7.75/5.66 & ( Y = zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % sum_power2_eq_zero_iff
% 7.75/5.66 thf(fact_1058_sum__power2__eq__zero__iff,axiom,
% 7.75/5.66 ! [X: code_integer,Y: code_integer] :
% 7.75/5.66 ( ( ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = zero_z3403309356797280102nteger )
% 7.75/5.66 = ( ( X = zero_z3403309356797280102nteger )
% 7.75/5.66 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % sum_power2_eq_zero_iff
% 7.75/5.66 thf(fact_1059_not__mod__2__eq__0__eq__1,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 != zero_zero_nat )
% 7.75/5.66 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_mod_2_eq_0_eq_1
% 7.75/5.66 thf(fact_1060_not__mod__2__eq__0__eq__1,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 != zero_zero_int )
% 7.75/5.66 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_mod_2_eq_0_eq_1
% 7.75/5.66 thf(fact_1061_not__mod__2__eq__0__eq__1,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.66 != zero_z3403309356797280102nteger )
% 7.75/5.66 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_Code_integer ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_mod_2_eq_0_eq_1
% 7.75/5.66 thf(fact_1062_not__mod__2__eq__1__eq__0,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 != one_one_nat )
% 7.75/5.66 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_mod_2_eq_1_eq_0
% 7.75/5.66 thf(fact_1063_not__mod__2__eq__1__eq__0,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 != one_one_int )
% 7.75/5.66 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_mod_2_eq_1_eq_0
% 7.75/5.66 thf(fact_1064_not__mod__2__eq__1__eq__0,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.66 != one_one_Code_integer )
% 7.75/5.66 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_mod_2_eq_1_eq_0
% 7.75/5.66 thf(fact_1065_even__plus__one__iff,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_plus_one_iff
% 7.75/5.66 thf(fact_1066_even__plus__one__iff,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 7.75/5.66 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_plus_one_iff
% 7.75/5.66 thf(fact_1067_not__mod2__eq__Suc__0__eq__0,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 != ( suc @ zero_zero_nat ) )
% 7.75/5.66 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_mod2_eq_Suc_0_eq_0
% 7.75/5.66 thf(fact_1068_mod2__gr__0,axiom,
% 7.75/5.66 ! [M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.66 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = one_one_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod2_gr_0
% 7.75/5.66 thf(fact_1069_add__self__mod__2,axiom,
% 7.75/5.66 ! [M: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % add_self_mod_2
% 7.75/5.66 thf(fact_1070_set__decode__0,axiom,
% 7.75/5.66 ! [X: nat] :
% 7.75/5.66 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % set_decode_0
% 7.75/5.66 thf(fact_1071_even__succ__div__2,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_div_2
% 7.75/5.66 thf(fact_1072_even__succ__div__2,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_div_2
% 7.75/5.66 thf(fact_1073_odd__succ__div__two,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % odd_succ_div_two
% 7.75/5.66 thf(fact_1074_odd__succ__div__two,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % odd_succ_div_two
% 7.75/5.66 thf(fact_1075_even__succ__div__two,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.66 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_div_two
% 7.75/5.66 thf(fact_1076_even__succ__div__two,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.66 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_div_two
% 7.75/5.66 thf(fact_1077_even__power,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.66 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_power
% 7.75/5.66 thf(fact_1078_even__power,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 7.75/5.66 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_power
% 7.75/5.66 thf(fact_1079_even__power,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 7.75/5.66 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_power
% 7.75/5.66 thf(fact_1080_power__less__zero__eq,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ zero_z3403309356797280102nteger )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_zero_eq
% 7.75/5.66 thf(fact_1081_power__less__zero__eq,axiom,
% 7.75/5.66 ! [A: real,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.66 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_zero_eq
% 7.75/5.66 thf(fact_1082_power__less__zero__eq,axiom,
% 7.75/5.66 ! [A: rat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.66 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_zero_eq
% 7.75/5.66 thf(fact_1083_power__less__zero__eq,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.66 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_zero_eq
% 7.75/5.66 thf(fact_1084_power__less__zero__eq__numeral,axiom,
% 7.75/5.66 ! [A: code_integer,W: num] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) @ zero_z3403309356797280102nteger )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_zero_eq_numeral
% 7.75/5.66 thf(fact_1085_power__less__zero__eq__numeral,axiom,
% 7.75/5.66 ! [A: real,W: num] :
% 7.75/5.66 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_zero_eq_numeral
% 7.75/5.66 thf(fact_1086_power__less__zero__eq__numeral,axiom,
% 7.75/5.66 ! [A: rat,W: num] :
% 7.75/5.66 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_zero_eq_numeral
% 7.75/5.66 thf(fact_1087_power__less__zero__eq__numeral,axiom,
% 7.75/5.66 ! [A: int,W: num] :
% 7.75/5.66 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_zero_eq_numeral
% 7.75/5.66 thf(fact_1088_zero__less__power__eq__numeral,axiom,
% 7.75/5.66 ! [A: code_integer,W: num] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) )
% 7.75/5.66 = ( ( ( numeral_numeral_nat @ W )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( A != zero_z3403309356797280102nteger ) )
% 7.75/5.66 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power_eq_numeral
% 7.75/5.66 thf(fact_1089_zero__less__power__eq__numeral,axiom,
% 7.75/5.66 ! [A: real,W: num] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 7.75/5.66 = ( ( ( numeral_numeral_nat @ W )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( A != zero_zero_real ) )
% 7.75/5.66 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power_eq_numeral
% 7.75/5.66 thf(fact_1090_zero__less__power__eq__numeral,axiom,
% 7.75/5.66 ! [A: rat,W: num] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 7.75/5.66 = ( ( ( numeral_numeral_nat @ W )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( A != zero_zero_rat ) )
% 7.75/5.66 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power_eq_numeral
% 7.75/5.66 thf(fact_1091_zero__less__power__eq__numeral,axiom,
% 7.75/5.66 ! [A: int,W: num] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 7.75/5.66 = ( ( ( numeral_numeral_nat @ W )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( A != zero_zero_int ) )
% 7.75/5.66 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.66 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power_eq_numeral
% 7.75/5.66 thf(fact_1092_even__succ__div__exp,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.66 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_div_exp
% 7.75/5.66 thf(fact_1093_even__succ__div__exp,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.66 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_div_exp
% 7.75/5.66 thf(fact_1094_even__succ__div__exp,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.66 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_div_exp
% 7.75/5.66 thf(fact_1095_even__succ__mod__exp,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.66 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_mod_exp
% 7.75/5.66 thf(fact_1096_even__succ__mod__exp,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.66 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_mod_exp
% 7.75/5.66 thf(fact_1097_even__succ__mod__exp,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.66 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % even_succ_mod_exp
% 7.75/5.66 thf(fact_1098_mod__eq__0D,axiom,
% 7.75/5.66 ! [M: nat,D2: nat] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ M @ D2 )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 => ? [Q5: nat] :
% 7.75/5.66 ( M
% 7.75/5.66 = ( times_times_nat @ D2 @ Q5 ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_eq_0D
% 7.75/5.66 thf(fact_1099_pos__add__strict,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ B @ C )
% 7.75/5.66 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pos_add_strict
% 7.75/5.66 thf(fact_1100_pos__add__strict,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ B @ C )
% 7.75/5.66 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pos_add_strict
% 7.75/5.66 thf(fact_1101_pos__add__strict,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ B @ C )
% 7.75/5.66 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pos_add_strict
% 7.75/5.66 thf(fact_1102_pos__add__strict,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ( ord_less_int @ B @ C )
% 7.75/5.66 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pos_add_strict
% 7.75/5.66 thf(fact_1103_zero__less__two,axiom,
% 7.75/5.66 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_two
% 7.75/5.66 thf(fact_1104_zero__less__two,axiom,
% 7.75/5.66 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_two
% 7.75/5.66 thf(fact_1105_zero__less__two,axiom,
% 7.75/5.66 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_two
% 7.75/5.66 thf(fact_1106_zero__less__two,axiom,
% 7.75/5.66 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_two
% 7.75/5.66 thf(fact_1107_canonically__ordered__monoid__add__class_OlessE,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ B )
% 7.75/5.66 => ~ ! [C3: nat] :
% 7.75/5.66 ( ( B
% 7.75/5.66 = ( plus_plus_nat @ A @ C3 ) )
% 7.75/5.66 => ( C3 = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % canonically_ordered_monoid_add_class.lessE
% 7.75/5.66 thf(fact_1108_add__pos__pos,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.66 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_pos_pos
% 7.75/5.66 thf(fact_1109_add__pos__pos,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 7.75/5.66 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_pos_pos
% 7.75/5.66 thf(fact_1110_add__pos__pos,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.66 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_pos_pos
% 7.75/5.66 thf(fact_1111_add__pos__pos,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.66 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_pos_pos
% 7.75/5.66 thf(fact_1112_add__neg__neg,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ B @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_neg_neg
% 7.75/5.66 thf(fact_1113_add__neg__neg,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_neg_neg
% 7.75/5.66 thf(fact_1114_add__neg__neg,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ zero_zero_nat )
% 7.75/5.66 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 7.75/5.66 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_neg_neg
% 7.75/5.66 thf(fact_1115_add__neg__neg,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.66 => ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.66 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_neg_neg
% 7.75/5.66 thf(fact_1116_bot__nat__0_Oextremum__strict,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % bot_nat_0.extremum_strict
% 7.75/5.66 thf(fact_1117_gr0I,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( N != zero_zero_nat )
% 7.75/5.66 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % gr0I
% 7.75/5.66 thf(fact_1118_not__gr0,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 7.75/5.66 = ( N = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_gr0
% 7.75/5.66 thf(fact_1119_not__less0,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % not_less0
% 7.75/5.66 thf(fact_1120_less__zeroE,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % less_zeroE
% 7.75/5.66 thf(fact_1121_nat__neq__iff,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( M != N )
% 7.75/5.66 = ( ( ord_less_nat @ M @ N )
% 7.75/5.66 | ( ord_less_nat @ N @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_neq_iff
% 7.75/5.66 thf(fact_1122_less__not__refl,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ~ ( ord_less_nat @ N @ N ) ).
% 7.75/5.66
% 7.75/5.66 % less_not_refl
% 7.75/5.66 thf(fact_1123_gcd__nat__induct,axiom,
% 7.75/5.66 ! [P: nat > nat > $o,M: nat,N: nat] :
% 7.75/5.66 ( ! [M2: nat] : ( P @ M2 @ zero_zero_nat )
% 7.75/5.66 => ( ! [M2: nat,N2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 7.75/5.66 => ( ( P @ N2 @ ( modulo_modulo_nat @ M2 @ N2 ) )
% 7.75/5.66 => ( P @ M2 @ N2 ) ) )
% 7.75/5.66 => ( P @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % gcd_nat_induct
% 7.75/5.66 thf(fact_1124_less__not__refl2,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ N @ M )
% 7.75/5.66 => ( M != N ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_not_refl2
% 7.75/5.66 thf(fact_1125_less__not__refl3,axiom,
% 7.75/5.66 ! [S: nat,T: nat] :
% 7.75/5.66 ( ( ord_less_nat @ S @ T )
% 7.75/5.66 => ( S != T ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_not_refl3
% 7.75/5.66 thf(fact_1126_gr__implies__not0,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M @ N )
% 7.75/5.66 => ( N != zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % gr_implies_not0
% 7.75/5.66 thf(fact_1127_less__irrefl__nat,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ~ ( ord_less_nat @ N @ N ) ).
% 7.75/5.66
% 7.75/5.66 % less_irrefl_nat
% 7.75/5.66 thf(fact_1128_nat__less__induct,axiom,
% 7.75/5.66 ! [P: nat > $o,N: nat] :
% 7.75/5.66 ( ! [N2: nat] :
% 7.75/5.66 ( ! [M3: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M3 @ N2 )
% 7.75/5.66 => ( P @ M3 ) )
% 7.75/5.66 => ( P @ N2 ) )
% 7.75/5.66 => ( P @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_less_induct
% 7.75/5.66 thf(fact_1129_infinite__descent,axiom,
% 7.75/5.66 ! [P: nat > $o,N: nat] :
% 7.75/5.66 ( ! [N2: nat] :
% 7.75/5.66 ( ~ ( P @ N2 )
% 7.75/5.66 => ? [M3: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M3 @ N2 )
% 7.75/5.66 & ~ ( P @ M3 ) ) )
% 7.75/5.66 => ( P @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % infinite_descent
% 7.75/5.66 thf(fact_1130_infinite__descent0,axiom,
% 7.75/5.66 ! [P: nat > $o,N: nat] :
% 7.75/5.66 ( ( P @ zero_zero_nat )
% 7.75/5.66 => ( ! [N2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 7.75/5.66 => ( ~ ( P @ N2 )
% 7.75/5.66 => ? [M3: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M3 @ N2 )
% 7.75/5.66 & ~ ( P @ M3 ) ) ) )
% 7.75/5.66 => ( P @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % infinite_descent0
% 7.75/5.66 thf(fact_1131_linorder__neqE__nat,axiom,
% 7.75/5.66 ! [X: nat,Y: nat] :
% 7.75/5.66 ( ( X != Y )
% 7.75/5.66 => ( ~ ( ord_less_nat @ X @ Y )
% 7.75/5.66 => ( ord_less_nat @ Y @ X ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % linorder_neqE_nat
% 7.75/5.66 thf(fact_1132_nat__induct__non__zero,axiom,
% 7.75/5.66 ! [N: nat,P: nat > $o] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( P @ one_one_nat )
% 7.75/5.66 => ( ! [N2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 7.75/5.66 => ( ( P @ N2 )
% 7.75/5.66 => ( P @ ( suc @ N2 ) ) ) )
% 7.75/5.66 => ( P @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_induct_non_zero
% 7.75/5.66 thf(fact_1133_field__lbound__gt__zero,axiom,
% 7.75/5.66 ! [D1: real,D22: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ D1 )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 7.75/5.66 => ? [E2: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ E2 )
% 7.75/5.66 & ( ord_less_real @ E2 @ D1 )
% 7.75/5.66 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % field_lbound_gt_zero
% 7.75/5.66 thf(fact_1134_field__lbound__gt__zero,axiom,
% 7.75/5.66 ! [D1: rat,D22: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 7.75/5.66 => ? [E2: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 7.75/5.66 & ( ord_less_rat @ E2 @ D1 )
% 7.75/5.66 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % field_lbound_gt_zero
% 7.75/5.66 thf(fact_1135_power__strict__increasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: code_integer] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing
% 7.75/5.66 thf(fact_1136_power__strict__increasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: real] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.66 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing
% 7.75/5.66 thf(fact_1137_power__strict__increasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: rat] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_less_rat @ one_one_rat @ A )
% 7.75/5.66 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing
% 7.75/5.66 thf(fact_1138_power__strict__increasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: nat] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_less_nat @ one_one_nat @ A )
% 7.75/5.66 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing
% 7.75/5.66 thf(fact_1139_power__strict__increasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: int] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_less_int @ one_one_int @ A )
% 7.75/5.66 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_increasing
% 7.75/5.66 thf(fact_1140_power__strict__decreasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: code_integer] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing
% 7.75/5.66 thf(fact_1141_power__strict__decreasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: real] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ A @ one_one_real )
% 7.75/5.66 => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing
% 7.75/5.66 thf(fact_1142_power__strict__decreasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: rat] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ A @ one_one_rat )
% 7.75/5.66 => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing
% 7.75/5.66 thf(fact_1143_power__strict__decreasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: nat] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ A @ one_one_nat )
% 7.75/5.66 => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing
% 7.75/5.66 thf(fact_1144_power__strict__decreasing,axiom,
% 7.75/5.66 ! [N: nat,N4: nat,A: int] :
% 7.75/5.66 ( ( ord_less_nat @ N @ N4 )
% 7.75/5.66 => ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ( ord_less_int @ A @ one_one_int )
% 7.75/5.66 => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_strict_decreasing
% 7.75/5.66 thf(fact_1145_power__less__imp__less__exp,axiom,
% 7.75/5.66 ! [A: code_integer,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.66 => ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_imp_less_exp
% 7.75/5.66 thf(fact_1146_power__less__imp__less__exp,axiom,
% 7.75/5.66 ! [A: real,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 7.75/5.66 => ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_imp_less_exp
% 7.75/5.66 thf(fact_1147_power__less__imp__less__exp,axiom,
% 7.75/5.66 ! [A: rat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 7.75/5.66 => ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_imp_less_exp
% 7.75/5.66 thf(fact_1148_power__less__imp__less__exp,axiom,
% 7.75/5.66 ! [A: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 7.75/5.66 => ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_imp_less_exp
% 7.75/5.66 thf(fact_1149_power__less__imp__less__exp,axiom,
% 7.75/5.66 ! [A: int,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ one_one_int @ A )
% 7.75/5.66 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 7.75/5.66 => ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_imp_less_exp
% 7.75/5.66 thf(fact_1150_one__less__power,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_power
% 7.75/5.66 thf(fact_1151_one__less__power,axiom,
% 7.75/5.66 ! [A: real,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_power
% 7.75/5.66 thf(fact_1152_one__less__power,axiom,
% 7.75/5.66 ! [A: rat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_power
% 7.75/5.66 thf(fact_1153_one__less__power,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_power
% 7.75/5.66 thf(fact_1154_one__less__power,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ one_one_int @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_power
% 7.75/5.66 thf(fact_1155_power__0__left,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ( N = zero_zero_nat )
% 7.75/5.66 => ( ( power_power_rat @ zero_zero_rat @ N )
% 7.75/5.66 = one_one_rat ) )
% 7.75/5.66 & ( ( N != zero_zero_nat )
% 7.75/5.66 => ( ( power_power_rat @ zero_zero_rat @ N )
% 7.75/5.66 = zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_left
% 7.75/5.66 thf(fact_1156_power__0__left,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ( N = zero_zero_nat )
% 7.75/5.66 => ( ( power_power_nat @ zero_zero_nat @ N )
% 7.75/5.66 = one_one_nat ) )
% 7.75/5.66 & ( ( N != zero_zero_nat )
% 7.75/5.66 => ( ( power_power_nat @ zero_zero_nat @ N )
% 7.75/5.66 = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_left
% 7.75/5.66 thf(fact_1157_power__0__left,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ( N = zero_zero_nat )
% 7.75/5.66 => ( ( power_power_real @ zero_zero_real @ N )
% 7.75/5.66 = one_one_real ) )
% 7.75/5.66 & ( ( N != zero_zero_nat )
% 7.75/5.66 => ( ( power_power_real @ zero_zero_real @ N )
% 7.75/5.66 = zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_left
% 7.75/5.66 thf(fact_1158_power__0__left,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ( N = zero_zero_nat )
% 7.75/5.66 => ( ( power_power_int @ zero_zero_int @ N )
% 7.75/5.66 = one_one_int ) )
% 7.75/5.66 & ( ( N != zero_zero_nat )
% 7.75/5.66 => ( ( power_power_int @ zero_zero_int @ N )
% 7.75/5.66 = zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_left
% 7.75/5.66 thf(fact_1159_power__0__left,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ( N = zero_zero_nat )
% 7.75/5.66 => ( ( power_power_complex @ zero_zero_complex @ N )
% 7.75/5.66 = one_one_complex ) )
% 7.75/5.66 & ( ( N != zero_zero_nat )
% 7.75/5.66 => ( ( power_power_complex @ zero_zero_complex @ N )
% 7.75/5.66 = zero_zero_complex ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_left
% 7.75/5.66 thf(fact_1160_power__0__left,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ( N = zero_zero_nat )
% 7.75/5.66 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 7.75/5.66 = one_one_Code_integer ) )
% 7.75/5.66 & ( ( N != zero_zero_nat )
% 7.75/5.66 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_0_left
% 7.75/5.66 thf(fact_1161_zero__power,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( power_power_rat @ zero_zero_rat @ N )
% 7.75/5.66 = zero_zero_rat ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_power
% 7.75/5.66 thf(fact_1162_zero__power,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( power_power_nat @ zero_zero_nat @ N )
% 7.75/5.66 = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_power
% 7.75/5.66 thf(fact_1163_zero__power,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( power_power_real @ zero_zero_real @ N )
% 7.75/5.66 = zero_zero_real ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_power
% 7.75/5.66 thf(fact_1164_zero__power,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( power_power_int @ zero_zero_int @ N )
% 7.75/5.66 = zero_zero_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_power
% 7.75/5.66 thf(fact_1165_zero__power,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( power_power_complex @ zero_zero_complex @ N )
% 7.75/5.66 = zero_zero_complex ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_power
% 7.75/5.66 thf(fact_1166_zero__power,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_power
% 7.75/5.66 thf(fact_1167_divide__less__eq__1,axiom,
% 7.75/5.66 ! [B: real,A: real] :
% 7.75/5.66 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 & ( ord_less_real @ B @ A ) )
% 7.75/5.66 | ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 & ( ord_less_real @ A @ B ) )
% 7.75/5.66 | ( A = zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq_1
% 7.75/5.66 thf(fact_1168_divide__less__eq__1,axiom,
% 7.75/5.66 ! [B: rat,A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 & ( ord_less_rat @ B @ A ) )
% 7.75/5.66 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 & ( ord_less_rat @ A @ B ) )
% 7.75/5.66 | ( A = zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq_1
% 7.75/5.66 thf(fact_1169_less__divide__eq__1,axiom,
% 7.75/5.66 ! [B: real,A: real] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 & ( ord_less_real @ A @ B ) )
% 7.75/5.66 | ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 & ( ord_less_real @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq_1
% 7.75/5.66 thf(fact_1170_less__divide__eq__1,axiom,
% 7.75/5.66 ! [B: rat,A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 & ( ord_less_rat @ A @ B ) )
% 7.75/5.66 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq_1
% 7.75/5.66 thf(fact_1171_linordered__field__no__lb,axiom,
% 7.75/5.66 ! [X5: real] :
% 7.75/5.66 ? [Y3: real] : ( ord_less_real @ Y3 @ X5 ) ).
% 7.75/5.66
% 7.75/5.66 % linordered_field_no_lb
% 7.75/5.66 thf(fact_1172_linordered__field__no__lb,axiom,
% 7.75/5.66 ! [X5: rat] :
% 7.75/5.66 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X5 ) ).
% 7.75/5.66
% 7.75/5.66 % linordered_field_no_lb
% 7.75/5.66 thf(fact_1173_linordered__field__no__ub,axiom,
% 7.75/5.66 ! [X5: real] :
% 7.75/5.66 ? [X_1: real] : ( ord_less_real @ X5 @ X_1 ) ).
% 7.75/5.66
% 7.75/5.66 % linordered_field_no_ub
% 7.75/5.66 thf(fact_1174_linordered__field__no__ub,axiom,
% 7.75/5.66 ! [X5: rat] :
% 7.75/5.66 ? [X_1: rat] : ( ord_less_rat @ X5 @ X_1 ) ).
% 7.75/5.66
% 7.75/5.66 % linordered_field_no_ub
% 7.75/5.66 thf(fact_1175_div__less__mono,axiom,
% 7.75/5.66 ! [A2: nat,B3: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A2 @ B3 )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 => ( ( ( modulo_modulo_nat @ B3 @ N )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B3 @ N ) ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_less_mono
% 7.75/5.66 thf(fact_1176_mod__less__divisor,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_less_divisor
% 7.75/5.66 thf(fact_1177_div__less__dividend,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ N )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.66 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_less_dividend
% 7.75/5.66 thf(fact_1178_zero__reorient,axiom,
% 7.75/5.66 ! [X: complex] :
% 7.75/5.66 ( ( zero_zero_complex = X )
% 7.75/5.66 = ( X = zero_zero_complex ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_reorient
% 7.75/5.66 thf(fact_1179_zero__reorient,axiom,
% 7.75/5.66 ! [X: real] :
% 7.75/5.66 ( ( zero_zero_real = X )
% 7.75/5.66 = ( X = zero_zero_real ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_reorient
% 7.75/5.66 thf(fact_1180_zero__reorient,axiom,
% 7.75/5.66 ! [X: rat] :
% 7.75/5.66 ( ( zero_zero_rat = X )
% 7.75/5.66 = ( X = zero_zero_rat ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_reorient
% 7.75/5.66 thf(fact_1181_zero__reorient,axiom,
% 7.75/5.66 ! [X: nat] :
% 7.75/5.66 ( ( zero_zero_nat = X )
% 7.75/5.66 = ( X = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_reorient
% 7.75/5.66 thf(fact_1182_zero__reorient,axiom,
% 7.75/5.66 ! [X: int] :
% 7.75/5.66 ( ( zero_zero_int = X )
% 7.75/5.66 = ( X = zero_zero_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_reorient
% 7.75/5.66 thf(fact_1183_one__reorient,axiom,
% 7.75/5.66 ! [X: assn] :
% 7.75/5.66 ( ( one_one_assn = X )
% 7.75/5.66 = ( X = one_one_assn ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_reorient
% 7.75/5.66 thf(fact_1184_one__reorient,axiom,
% 7.75/5.66 ! [X: real] :
% 7.75/5.66 ( ( one_one_real = X )
% 7.75/5.66 = ( X = one_one_real ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_reorient
% 7.75/5.66 thf(fact_1185_one__reorient,axiom,
% 7.75/5.66 ! [X: rat] :
% 7.75/5.66 ( ( one_one_rat = X )
% 7.75/5.66 = ( X = one_one_rat ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_reorient
% 7.75/5.66 thf(fact_1186_one__reorient,axiom,
% 7.75/5.66 ! [X: nat] :
% 7.75/5.66 ( ( one_one_nat = X )
% 7.75/5.66 = ( X = one_one_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_reorient
% 7.75/5.66 thf(fact_1187_one__reorient,axiom,
% 7.75/5.66 ! [X: int] :
% 7.75/5.66 ( ( one_one_int = X )
% 7.75/5.66 = ( X = one_one_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_reorient
% 7.75/5.66 thf(fact_1188_zero__less__iff__neq__zero,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 = ( N != zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_iff_neq_zero
% 7.75/5.66 thf(fact_1189_gr__implies__not__zero,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M @ N )
% 7.75/5.66 => ( N != zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % gr_implies_not_zero
% 7.75/5.66 thf(fact_1190_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 7.75/5.66 ! [B: nat,A: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.66 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 7.75/5.66 thf(fact_1191_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 7.75/5.66 ! [B: int,A: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.66 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 7.75/5.66 thf(fact_1192_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 7.75/5.66 thf(fact_1193_not__less__zero,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % not_less_zero
% 7.75/5.66 thf(fact_1194_gr__zeroI,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( N != zero_zero_nat )
% 7.75/5.66 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % gr_zeroI
% 7.75/5.66 thf(fact_1195_verit__comp__simplify1_I1_J,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ~ ( ord_less_real @ A @ A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_comp_simplify1(1)
% 7.75/5.66 thf(fact_1196_verit__comp__simplify1_I1_J,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ~ ( ord_less_rat @ A @ A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_comp_simplify1(1)
% 7.75/5.66 thf(fact_1197_verit__comp__simplify1_I1_J,axiom,
% 7.75/5.66 ! [A: num] :
% 7.75/5.66 ~ ( ord_less_num @ A @ A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_comp_simplify1(1)
% 7.75/5.66 thf(fact_1198_verit__comp__simplify1_I1_J,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ~ ( ord_less_nat @ A @ A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_comp_simplify1(1)
% 7.75/5.66 thf(fact_1199_verit__comp__simplify1_I1_J,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ~ ( ord_less_int @ A @ A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_comp_simplify1(1)
% 7.75/5.66 thf(fact_1200_less__numeral__extra_I4_J,axiom,
% 7.75/5.66 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(4)
% 7.75/5.66 thf(fact_1201_less__numeral__extra_I4_J,axiom,
% 7.75/5.66 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(4)
% 7.75/5.66 thf(fact_1202_less__numeral__extra_I4_J,axiom,
% 7.75/5.66 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(4)
% 7.75/5.66 thf(fact_1203_less__numeral__extra_I4_J,axiom,
% 7.75/5.66 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(4)
% 7.75/5.66 thf(fact_1204_less__numeral__extra_I3_J,axiom,
% 7.75/5.66 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(3)
% 7.75/5.66 thf(fact_1205_less__numeral__extra_I3_J,axiom,
% 7.75/5.66 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(3)
% 7.75/5.66 thf(fact_1206_less__numeral__extra_I3_J,axiom,
% 7.75/5.66 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(3)
% 7.75/5.66 thf(fact_1207_less__numeral__extra_I3_J,axiom,
% 7.75/5.66 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(3)
% 7.75/5.66 thf(fact_1208_less__numeral__extra_I1_J,axiom,
% 7.75/5.66 ord_less_real @ zero_zero_real @ one_one_real ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(1)
% 7.75/5.66 thf(fact_1209_less__numeral__extra_I1_J,axiom,
% 7.75/5.66 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(1)
% 7.75/5.66 thf(fact_1210_less__numeral__extra_I1_J,axiom,
% 7.75/5.66 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(1)
% 7.75/5.66 thf(fact_1211_less__numeral__extra_I1_J,axiom,
% 7.75/5.66 ord_less_int @ zero_zero_int @ one_one_int ).
% 7.75/5.66
% 7.75/5.66 % less_numeral_extra(1)
% 7.75/5.66 thf(fact_1212_zero__neq__one,axiom,
% 7.75/5.66 zero_zero_complex != one_one_complex ).
% 7.75/5.66
% 7.75/5.66 % zero_neq_one
% 7.75/5.66 thf(fact_1213_zero__neq__one,axiom,
% 7.75/5.66 zero_zero_real != one_one_real ).
% 7.75/5.66
% 7.75/5.66 % zero_neq_one
% 7.75/5.66 thf(fact_1214_zero__neq__one,axiom,
% 7.75/5.66 zero_zero_rat != one_one_rat ).
% 7.75/5.66
% 7.75/5.66 % zero_neq_one
% 7.75/5.66 thf(fact_1215_zero__neq__one,axiom,
% 7.75/5.66 zero_zero_nat != one_one_nat ).
% 7.75/5.66
% 7.75/5.66 % zero_neq_one
% 7.75/5.66 thf(fact_1216_zero__neq__one,axiom,
% 7.75/5.66 zero_zero_int != one_one_int ).
% 7.75/5.66
% 7.75/5.66 % zero_neq_one
% 7.75/5.66 thf(fact_1217_zero__less__one,axiom,
% 7.75/5.66 ord_less_real @ zero_zero_real @ one_one_real ).
% 7.75/5.66
% 7.75/5.66 % zero_less_one
% 7.75/5.66 thf(fact_1218_zero__less__one,axiom,
% 7.75/5.66 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 7.75/5.66
% 7.75/5.66 % zero_less_one
% 7.75/5.66 thf(fact_1219_zero__less__one,axiom,
% 7.75/5.66 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 7.75/5.66
% 7.75/5.66 % zero_less_one
% 7.75/5.66 thf(fact_1220_zero__less__one,axiom,
% 7.75/5.66 ord_less_int @ zero_zero_int @ one_one_int ).
% 7.75/5.66
% 7.75/5.66 % zero_less_one
% 7.75/5.66 thf(fact_1221_linorder__neqE__linordered__idom,axiom,
% 7.75/5.66 ! [X: real,Y: real] :
% 7.75/5.66 ( ( X != Y )
% 7.75/5.66 => ( ~ ( ord_less_real @ X @ Y )
% 7.75/5.66 => ( ord_less_real @ Y @ X ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % linorder_neqE_linordered_idom
% 7.75/5.66 thf(fact_1222_linorder__neqE__linordered__idom,axiom,
% 7.75/5.66 ! [X: rat,Y: rat] :
% 7.75/5.66 ( ( X != Y )
% 7.75/5.66 => ( ~ ( ord_less_rat @ X @ Y )
% 7.75/5.66 => ( ord_less_rat @ Y @ X ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % linorder_neqE_linordered_idom
% 7.75/5.66 thf(fact_1223_linorder__neqE__linordered__idom,axiom,
% 7.75/5.66 ! [X: int,Y: int] :
% 7.75/5.66 ( ( X != Y )
% 7.75/5.66 => ( ~ ( ord_less_int @ X @ Y )
% 7.75/5.66 => ( ord_less_int @ Y @ X ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % linorder_neqE_linordered_idom
% 7.75/5.66 thf(fact_1224_not__one__less__zero,axiom,
% 7.75/5.66 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 7.75/5.66
% 7.75/5.66 % not_one_less_zero
% 7.75/5.66 thf(fact_1225_not__one__less__zero,axiom,
% 7.75/5.66 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 7.75/5.66
% 7.75/5.66 % not_one_less_zero
% 7.75/5.66 thf(fact_1226_not__one__less__zero,axiom,
% 7.75/5.66 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % not_one_less_zero
% 7.75/5.66 thf(fact_1227_not__one__less__zero,axiom,
% 7.75/5.66 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % not_one_less_zero
% 7.75/5.66 thf(fact_1228_mod__greater__zero__iff__not__dvd,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 7.75/5.66 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_greater_zero_iff_not_dvd
% 7.75/5.66 thf(fact_1229_unit__imp__mod__eq__0,axiom,
% 7.75/5.66 ! [B: nat,A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.66 => ( ( modulo_modulo_nat @ A @ B )
% 7.75/5.66 = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_imp_mod_eq_0
% 7.75/5.66 thf(fact_1230_unit__imp__mod__eq__0,axiom,
% 7.75/5.66 ! [B: int,A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.66 => ( ( modulo_modulo_int @ A @ B )
% 7.75/5.66 = zero_zero_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_imp_mod_eq_0
% 7.75/5.66 thf(fact_1231_unit__imp__mod__eq__0,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.66 => ( ( modulo364778990260209775nteger @ A @ B )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_imp_mod_eq_0
% 7.75/5.66 thf(fact_1232_Suc__times__mod__eq,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 7.75/5.66 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 7.75/5.66 = one_one_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_times_mod_eq
% 7.75/5.66 thf(fact_1233_mod__induct,axiom,
% 7.75/5.66 ! [P: nat > $o,N: nat,P4: nat,M: nat] :
% 7.75/5.66 ( ( P @ N )
% 7.75/5.66 => ( ( ord_less_nat @ N @ P4 )
% 7.75/5.66 => ( ( ord_less_nat @ M @ P4 )
% 7.75/5.66 => ( ! [N2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ N2 @ P4 )
% 7.75/5.66 => ( ( P @ N2 )
% 7.75/5.66 => ( P @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P4 ) ) ) )
% 7.75/5.66 => ( P @ M ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_induct
% 7.75/5.66 thf(fact_1234_mod__eq__self__iff__div__eq__0,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ A @ B )
% 7.75/5.66 = A )
% 7.75/5.66 = ( ( divide_divide_nat @ A @ B )
% 7.75/5.66 = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_eq_self_iff_div_eq_0
% 7.75/5.66 thf(fact_1235_mod__eq__self__iff__div__eq__0,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.66 = A )
% 7.75/5.66 = ( ( divide_divide_int @ A @ B )
% 7.75/5.66 = zero_zero_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_eq_self_iff_div_eq_0
% 7.75/5.66 thf(fact_1236_mod__eq__self__iff__div__eq__0,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ( modulo364778990260209775nteger @ A @ B )
% 7.75/5.66 = A )
% 7.75/5.66 = ( ( divide6298287555418463151nteger @ A @ B )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_eq_self_iff_div_eq_0
% 7.75/5.66 thf(fact_1237_not__numeral__less__one,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 7.75/5.66
% 7.75/5.66 % not_numeral_less_one
% 7.75/5.66 thf(fact_1238_not__numeral__less__one,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 7.75/5.66
% 7.75/5.66 % not_numeral_less_one
% 7.75/5.66 thf(fact_1239_not__numeral__less__one,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 7.75/5.66
% 7.75/5.66 % not_numeral_less_one
% 7.75/5.66 thf(fact_1240_not__numeral__less__one,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 7.75/5.66
% 7.75/5.66 % not_numeral_less_one
% 7.75/5.66 thf(fact_1241_lift__Suc__mono__less__iff,axiom,
% 7.75/5.66 ! [F: nat > real,N: nat,M: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less_iff
% 7.75/5.66 thf(fact_1242_lift__Suc__mono__less__iff,axiom,
% 7.75/5.66 ! [F: nat > rat,N: nat,M: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less_iff
% 7.75/5.66 thf(fact_1243_lift__Suc__mono__less__iff,axiom,
% 7.75/5.66 ! [F: nat > num,N: nat,M: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less_iff
% 7.75/5.66 thf(fact_1244_lift__Suc__mono__less__iff,axiom,
% 7.75/5.66 ! [F: nat > nat,N: nat,M: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less_iff
% 7.75/5.66 thf(fact_1245_lift__Suc__mono__less__iff,axiom,
% 7.75/5.66 ! [F: nat > int,N: nat,M: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 7.75/5.66 = ( ord_less_nat @ N @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less_iff
% 7.75/5.66 thf(fact_1246_lift__Suc__mono__less,axiom,
% 7.75/5.66 ! [F: nat > real,N: nat,N5: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_nat @ N @ N5 )
% 7.75/5.66 => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less
% 7.75/5.66 thf(fact_1247_lift__Suc__mono__less,axiom,
% 7.75/5.66 ! [F: nat > rat,N: nat,N5: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_nat @ N @ N5 )
% 7.75/5.66 => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less
% 7.75/5.66 thf(fact_1248_lift__Suc__mono__less,axiom,
% 7.75/5.66 ! [F: nat > num,N: nat,N5: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_nat @ N @ N5 )
% 7.75/5.66 => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less
% 7.75/5.66 thf(fact_1249_lift__Suc__mono__less,axiom,
% 7.75/5.66 ! [F: nat > nat,N: nat,N5: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_nat @ N @ N5 )
% 7.75/5.66 => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less
% 7.75/5.66 thf(fact_1250_lift__Suc__mono__less,axiom,
% 7.75/5.66 ! [F: nat > int,N: nat,N5: nat] :
% 7.75/5.66 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.66 => ( ( ord_less_nat @ N @ N5 )
% 7.75/5.66 => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % lift_Suc_mono_less
% 7.75/5.66 thf(fact_1251_mod__0__imp__dvd,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ A @ B )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 => ( dvd_dvd_nat @ B @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_0_imp_dvd
% 7.75/5.66 thf(fact_1252_mod__0__imp__dvd,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.66 = zero_zero_int )
% 7.75/5.66 => ( dvd_dvd_int @ B @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_0_imp_dvd
% 7.75/5.66 thf(fact_1253_mod__0__imp__dvd,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ( modulo364778990260209775nteger @ A @ B )
% 7.75/5.66 = zero_z3403309356797280102nteger )
% 7.75/5.66 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_0_imp_dvd
% 7.75/5.66 thf(fact_1254_dvd__eq__mod__eq__0,axiom,
% 7.75/5.66 ( dvd_dvd_nat
% 7.75/5.66 = ( ^ [A3: nat,B4: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ B4 @ A3 )
% 7.75/5.66 = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_eq_mod_eq_0
% 7.75/5.66 thf(fact_1255_dvd__eq__mod__eq__0,axiom,
% 7.75/5.66 ( dvd_dvd_int
% 7.75/5.66 = ( ^ [A3: int,B4: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ B4 @ A3 )
% 7.75/5.66 = zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_eq_mod_eq_0
% 7.75/5.66 thf(fact_1256_dvd__eq__mod__eq__0,axiom,
% 7.75/5.66 ( dvd_dvd_Code_integer
% 7.75/5.66 = ( ^ [A3: code_integer,B4: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ B4 @ A3 )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_eq_mod_eq_0
% 7.75/5.66 thf(fact_1257_mod__eq__0__iff__dvd,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ A @ B )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 = ( dvd_dvd_nat @ B @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_eq_0_iff_dvd
% 7.75/5.66 thf(fact_1258_mod__eq__0__iff__dvd,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.66 = zero_zero_int )
% 7.75/5.66 = ( dvd_dvd_int @ B @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_eq_0_iff_dvd
% 7.75/5.66 thf(fact_1259_mod__eq__0__iff__dvd,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ( modulo364778990260209775nteger @ A @ B )
% 7.75/5.66 = zero_z3403309356797280102nteger )
% 7.75/5.66 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_eq_0_iff_dvd
% 7.75/5.66 thf(fact_1260_add__mono1,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono1
% 7.75/5.66 thf(fact_1261_add__mono1,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono1
% 7.75/5.66 thf(fact_1262_add__mono1,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ B )
% 7.75/5.66 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono1
% 7.75/5.66 thf(fact_1263_add__mono1,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ B )
% 7.75/5.66 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono1
% 7.75/5.66 thf(fact_1264_less__add__one,axiom,
% 7.75/5.66 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_add_one
% 7.75/5.66 thf(fact_1265_less__add__one,axiom,
% 7.75/5.66 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_add_one
% 7.75/5.66 thf(fact_1266_less__add__one,axiom,
% 7.75/5.66 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_add_one
% 7.75/5.66 thf(fact_1267_less__add__one,axiom,
% 7.75/5.66 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_add_one
% 7.75/5.66 thf(fact_1268_less__1__mult,axiom,
% 7.75/5.66 ! [M: code_integer,N: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_1_mult
% 7.75/5.66 thf(fact_1269_less__1__mult,axiom,
% 7.75/5.66 ! [M: real,N: real] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ M )
% 7.75/5.66 => ( ( ord_less_real @ one_one_real @ N )
% 7.75/5.66 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_1_mult
% 7.75/5.66 thf(fact_1270_less__1__mult,axiom,
% 7.75/5.66 ! [M: rat,N: rat] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ M )
% 7.75/5.66 => ( ( ord_less_rat @ one_one_rat @ N )
% 7.75/5.66 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_1_mult
% 7.75/5.66 thf(fact_1271_less__1__mult,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ M )
% 7.75/5.66 => ( ( ord_less_nat @ one_one_nat @ N )
% 7.75/5.66 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_1_mult
% 7.75/5.66 thf(fact_1272_less__1__mult,axiom,
% 7.75/5.66 ! [M: int,N: int] :
% 7.75/5.66 ( ( ord_less_int @ one_one_int @ M )
% 7.75/5.66 => ( ( ord_less_int @ one_one_int @ N )
% 7.75/5.66 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_1_mult
% 7.75/5.66 thf(fact_1273_mod__Suc,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 7.75/5.66 = N )
% 7.75/5.66 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 7.75/5.66 = zero_zero_nat ) )
% 7.75/5.66 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 7.75/5.66 != N )
% 7.75/5.66 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 7.75/5.66 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_Suc
% 7.75/5.66 thf(fact_1274_not__numeral__less__zero,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 7.75/5.66
% 7.75/5.66 % not_numeral_less_zero
% 7.75/5.66 thf(fact_1275_not__numeral__less__zero,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 7.75/5.66
% 7.75/5.66 % not_numeral_less_zero
% 7.75/5.66 thf(fact_1276_not__numeral__less__zero,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % not_numeral_less_zero
% 7.75/5.66 thf(fact_1277_not__numeral__less__zero,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % not_numeral_less_zero
% 7.75/5.66 thf(fact_1278_zero__less__numeral,axiom,
% 7.75/5.66 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_numeral
% 7.75/5.66 thf(fact_1279_zero__less__numeral,axiom,
% 7.75/5.66 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_numeral
% 7.75/5.66 thf(fact_1280_zero__less__numeral,axiom,
% 7.75/5.66 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_numeral
% 7.75/5.66 thf(fact_1281_zero__less__numeral,axiom,
% 7.75/5.66 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_numeral
% 7.75/5.66 thf(fact_1282_add__less__zeroD,axiom,
% 7.75/5.66 ! [X: real,Y: real] :
% 7.75/5.66 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ X @ zero_zero_real )
% 7.75/5.66 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_zeroD
% 7.75/5.66 thf(fact_1283_add__less__zeroD,axiom,
% 7.75/5.66 ! [X: rat,Y: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 7.75/5.66 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_zeroD
% 7.75/5.66 thf(fact_1284_add__less__zeroD,axiom,
% 7.75/5.66 ! [X: int,Y: int] :
% 7.75/5.66 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 7.75/5.66 => ( ( ord_less_int @ X @ zero_zero_int )
% 7.75/5.66 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_zeroD
% 7.75/5.66 thf(fact_1285_mult__neg__neg,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_neg_neg
% 7.75/5.66 thf(fact_1286_mult__neg__neg,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ B @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_neg_neg
% 7.75/5.66 thf(fact_1287_mult__neg__neg,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_neg_neg
% 7.75/5.66 thf(fact_1288_mult__neg__neg,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.66 => ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.66 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_neg_neg
% 7.75/5.66 thf(fact_1289_not__square__less__zero,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ A ) @ zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % not_square_less_zero
% 7.75/5.66 thf(fact_1290_not__square__less__zero,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 7.75/5.66
% 7.75/5.66 % not_square_less_zero
% 7.75/5.66 thf(fact_1291_not__square__less__zero,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 7.75/5.66
% 7.75/5.66 % not_square_less_zero
% 7.75/5.66 thf(fact_1292_not__square__less__zero,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % not_square_less_zero
% 7.75/5.66 thf(fact_1293_mult__less__0__iff,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 7.75/5.66 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) )
% 7.75/5.66 | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_0_iff
% 7.75/5.66 thf(fact_1294_mult__less__0__iff,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 & ( ord_less_real @ B @ zero_zero_real ) )
% 7.75/5.66 | ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_0_iff
% 7.75/5.66 thf(fact_1295_mult__less__0__iff,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 7.75/5.66 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_0_iff
% 7.75/5.66 thf(fact_1296_mult__less__0__iff,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 7.75/5.66 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 & ( ord_less_int @ B @ zero_zero_int ) )
% 7.75/5.66 | ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.66 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_0_iff
% 7.75/5.66 thf(fact_1297_mult__neg__pos,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_neg_pos
% 7.75/5.66 thf(fact_1298_mult__neg__pos,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_neg_pos
% 7.75/5.66 thf(fact_1299_mult__neg__pos,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_neg_pos
% 7.75/5.66 thf(fact_1300_mult__neg__pos,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ zero_zero_nat )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.66 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_neg_pos
% 7.75/5.66 thf(fact_1301_mult__neg__pos,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.66 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_neg_pos
% 7.75/5.66 thf(fact_1302_mult__pos__neg,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg
% 7.75/5.66 thf(fact_1303_mult__pos__neg,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ B @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg
% 7.75/5.66 thf(fact_1304_mult__pos__neg,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg
% 7.75/5.66 thf(fact_1305_mult__pos__neg,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 7.75/5.66 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg
% 7.75/5.66 thf(fact_1306_mult__pos__neg,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.66 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg
% 7.75/5.66 thf(fact_1307_mult__pos__pos,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_pos
% 7.75/5.66 thf(fact_1308_mult__pos__pos,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.66 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_pos
% 7.75/5.66 thf(fact_1309_mult__pos__pos,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 7.75/5.66 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_pos
% 7.75/5.66 thf(fact_1310_mult__pos__pos,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.66 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_pos
% 7.75/5.66 thf(fact_1311_mult__pos__pos,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.66 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_pos
% 7.75/5.66 thf(fact_1312_mult__pos__neg2,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg2
% 7.75/5.66 thf(fact_1313_mult__pos__neg2,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ B @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg2
% 7.75/5.66 thf(fact_1314_mult__pos__neg2,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg2
% 7.75/5.66 thf(fact_1315_mult__pos__neg2,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 7.75/5.66 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg2
% 7.75/5.66 thf(fact_1316_mult__pos__neg2,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.66 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_pos_neg2
% 7.75/5.66 thf(fact_1317_zero__less__mult__iff,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 7.75/5.66 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) )
% 7.75/5.66 | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_iff
% 7.75/5.66 thf(fact_1318_zero__less__mult__iff,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 & ( ord_less_real @ zero_zero_real @ B ) )
% 7.75/5.66 | ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_iff
% 7.75/5.66 thf(fact_1319_zero__less__mult__iff,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 7.75/5.66 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_iff
% 7.75/5.66 thf(fact_1320_zero__less__mult__iff,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 7.75/5.66 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 & ( ord_less_int @ zero_zero_int @ B ) )
% 7.75/5.66 | ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.66 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_iff
% 7.75/5.66 thf(fact_1321_zero__less__mult__pos,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos
% 7.75/5.66 thf(fact_1322_zero__less__mult__pos,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos
% 7.75/5.66 thf(fact_1323_zero__less__mult__pos,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos
% 7.75/5.66 thf(fact_1324_zero__less__mult__pos,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos
% 7.75/5.66 thf(fact_1325_zero__less__mult__pos,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 7.75/5.66 => ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos
% 7.75/5.66 thf(fact_1326_zero__less__mult__pos2,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B @ A ) )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos2
% 7.75/5.66 thf(fact_1327_zero__less__mult__pos2,axiom,
% 7.75/5.66 ! [B: real,A: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos2
% 7.75/5.66 thf(fact_1328_zero__less__mult__pos2,axiom,
% 7.75/5.66 ! [B: rat,A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos2
% 7.75/5.66 thf(fact_1329_zero__less__mult__pos2,axiom,
% 7.75/5.66 ! [B: nat,A: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos2
% 7.75/5.66 thf(fact_1330_zero__less__mult__pos2,axiom,
% 7.75/5.66 ! [B: int,A: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 7.75/5.66 => ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_mult_pos2
% 7.75/5.66 thf(fact_1331_mult__less__cancel__left__neg,axiom,
% 7.75/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.66 = ( ord_le6747313008572928689nteger @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_neg
% 7.75/5.66 thf(fact_1332_mult__less__cancel__left__neg,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.66 = ( ord_less_real @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_neg
% 7.75/5.66 thf(fact_1333_mult__less__cancel__left__neg,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.66 = ( ord_less_rat @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_neg
% 7.75/5.66 thf(fact_1334_mult__less__cancel__left__neg,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.66 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.66 = ( ord_less_int @ B @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_neg
% 7.75/5.66 thf(fact_1335_mult__less__cancel__left__pos,axiom,
% 7.75/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.66 = ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_pos
% 7.75/5.66 thf(fact_1336_mult__less__cancel__left__pos,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.66 = ( ord_less_real @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_pos
% 7.75/5.66 thf(fact_1337_mult__less__cancel__left__pos,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.66 = ( ord_less_rat @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_pos
% 7.75/5.66 thf(fact_1338_mult__less__cancel__left__pos,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.66 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.66 = ( ord_less_int @ A @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_pos
% 7.75/5.66 thf(fact_1339_mult__strict__left__mono__neg,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ B @ A )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_left_mono_neg
% 7.75/5.66 thf(fact_1340_mult__strict__left__mono__neg,axiom,
% 7.75/5.66 ! [B: real,A: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ B @ A )
% 7.75/5.66 => ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_left_mono_neg
% 7.75/5.66 thf(fact_1341_mult__strict__left__mono__neg,axiom,
% 7.75/5.66 ! [B: rat,A: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ B @ A )
% 7.75/5.66 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_left_mono_neg
% 7.75/5.66 thf(fact_1342_mult__strict__left__mono__neg,axiom,
% 7.75/5.66 ! [B: int,A: int,C: int] :
% 7.75/5.66 ( ( ord_less_int @ B @ A )
% 7.75/5.66 => ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.66 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_left_mono_neg
% 7.75/5.66 thf(fact_1343_mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_left_mono
% 7.75/5.66 thf(fact_1344_mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_left_mono
% 7.75/5.66 thf(fact_1345_mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_left_mono
% 7.75/5.66 thf(fact_1346_mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ B )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 7.75/5.66 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_left_mono
% 7.75/5.66 thf(fact_1347_mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ B )
% 7.75/5.66 => ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.66 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_left_mono
% 7.75/5.66 thf(fact_1348_mult__less__cancel__left__disj,axiom,
% 7.75/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.66 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ A @ B ) )
% 7.75/5.66 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_disj
% 7.75/5.66 thf(fact_1349_mult__less__cancel__left__disj,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 & ( ord_less_real @ A @ B ) )
% 7.75/5.66 | ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 & ( ord_less_real @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_disj
% 7.75/5.66 thf(fact_1350_mult__less__cancel__left__disj,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 & ( ord_less_rat @ A @ B ) )
% 7.75/5.66 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_disj
% 7.75/5.66 thf(fact_1351_mult__less__cancel__left__disj,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.66 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.66 & ( ord_less_int @ A @ B ) )
% 7.75/5.66 | ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.66 & ( ord_less_int @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_left_disj
% 7.75/5.66 thf(fact_1352_mult__strict__right__mono__neg,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ B @ A )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_right_mono_neg
% 7.75/5.66 thf(fact_1353_mult__strict__right__mono__neg,axiom,
% 7.75/5.66 ! [B: real,A: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ B @ A )
% 7.75/5.66 => ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_right_mono_neg
% 7.75/5.66 thf(fact_1354_mult__strict__right__mono__neg,axiom,
% 7.75/5.66 ! [B: rat,A: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ B @ A )
% 7.75/5.66 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_right_mono_neg
% 7.75/5.66 thf(fact_1355_mult__strict__right__mono__neg,axiom,
% 7.75/5.66 ! [B: int,A: int,C: int] :
% 7.75/5.66 ( ( ord_less_int @ B @ A )
% 7.75/5.66 => ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.66 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_right_mono_neg
% 7.75/5.66 thf(fact_1356_mult__strict__right__mono,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_right_mono
% 7.75/5.66 thf(fact_1357_mult__strict__right__mono,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_right_mono
% 7.75/5.66 thf(fact_1358_mult__strict__right__mono,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_right_mono
% 7.75/5.66 thf(fact_1359_mult__strict__right__mono,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ B )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 7.75/5.66 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_right_mono
% 7.75/5.66 thf(fact_1360_mult__strict__right__mono,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ B )
% 7.75/5.66 => ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.66 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_strict_right_mono
% 7.75/5.66 thf(fact_1361_mult__less__cancel__right__disj,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.66 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ A @ B ) )
% 7.75/5.66 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.66 & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_right_disj
% 7.75/5.66 thf(fact_1362_mult__less__cancel__right__disj,axiom,
% 7.75/5.66 ! [A: real,C: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 & ( ord_less_real @ A @ B ) )
% 7.75/5.66 | ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 & ( ord_less_real @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_right_disj
% 7.75/5.66 thf(fact_1363_mult__less__cancel__right__disj,axiom,
% 7.75/5.66 ! [A: rat,C: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 & ( ord_less_rat @ A @ B ) )
% 7.75/5.66 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_right_disj
% 7.75/5.66 thf(fact_1364_mult__less__cancel__right__disj,axiom,
% 7.75/5.66 ! [A: int,C: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 7.75/5.66 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.66 & ( ord_less_int @ A @ B ) )
% 7.75/5.66 | ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.66 & ( ord_less_int @ B @ A ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_cancel_right_disj
% 7.75/5.66 thf(fact_1365_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 7.75/5.66 thf(fact_1366_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 7.75/5.66 thf(fact_1367_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 7.75/5.66 thf(fact_1368_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ B )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 7.75/5.66 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 7.75/5.66 thf(fact_1369_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ B )
% 7.75/5.66 => ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.66 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 7.75/5.66 thf(fact_1370_divide__strict__right__mono__neg,axiom,
% 7.75/5.66 ! [B: real,A: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ B @ A )
% 7.75/5.66 => ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_strict_right_mono_neg
% 7.75/5.66 thf(fact_1371_divide__strict__right__mono__neg,axiom,
% 7.75/5.66 ! [B: rat,A: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ B @ A )
% 7.75/5.66 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_strict_right_mono_neg
% 7.75/5.66 thf(fact_1372_divide__strict__right__mono,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_strict_right_mono
% 7.75/5.66 thf(fact_1373_divide__strict__right__mono,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_strict_right_mono
% 7.75/5.66 thf(fact_1374_zero__less__divide__iff,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 & ( ord_less_real @ zero_zero_real @ B ) )
% 7.75/5.66 | ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_divide_iff
% 7.75/5.66 thf(fact_1375_zero__less__divide__iff,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 7.75/5.66 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_divide_iff
% 7.75/5.66 thf(fact_1376_divide__less__cancel,axiom,
% 7.75/5.66 ! [A: real,C: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ord_less_real @ A @ B ) )
% 7.75/5.66 & ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ B @ A ) )
% 7.75/5.66 & ( C != zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_cancel
% 7.75/5.66 thf(fact_1377_divide__less__cancel,axiom,
% 7.75/5.66 ! [A: rat,C: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ord_less_rat @ A @ B ) )
% 7.75/5.66 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ B @ A ) )
% 7.75/5.66 & ( C != zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_cancel
% 7.75/5.66 thf(fact_1378_divide__less__0__iff,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 & ( ord_less_real @ B @ zero_zero_real ) )
% 7.75/5.66 | ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.66 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_0_iff
% 7.75/5.66 thf(fact_1379_divide__less__0__iff,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 7.75/5.66 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.66 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_0_iff
% 7.75/5.66 thf(fact_1380_divide__pos__pos,axiom,
% 7.75/5.66 ! [X: real,Y: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.66 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_pos_pos
% 7.75/5.66 thf(fact_1381_divide__pos__pos,axiom,
% 7.75/5.66 ! [X: rat,Y: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ X )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 7.75/5.66 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_pos_pos
% 7.75/5.66 thf(fact_1382_divide__pos__neg,axiom,
% 7.75/5.66 ! [X: real,Y: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.66 => ( ( ord_less_real @ Y @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_pos_neg
% 7.75/5.66 thf(fact_1383_divide__pos__neg,axiom,
% 7.75/5.66 ! [X: rat,Y: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ X )
% 7.75/5.66 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_pos_neg
% 7.75/5.66 thf(fact_1384_divide__neg__pos,axiom,
% 7.75/5.66 ! [X: real,Y: real] :
% 7.75/5.66 ( ( ord_less_real @ X @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.66 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_neg_pos
% 7.75/5.66 thf(fact_1385_divide__neg__pos,axiom,
% 7.75/5.66 ! [X: rat,Y: rat] :
% 7.75/5.66 ( ( ord_less_rat @ X @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 7.75/5.66 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_neg_pos
% 7.75/5.66 thf(fact_1386_divide__neg__neg,axiom,
% 7.75/5.66 ! [X: real,Y: real] :
% 7.75/5.66 ( ( ord_less_real @ X @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ Y @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_neg_neg
% 7.75/5.66 thf(fact_1387_divide__neg__neg,axiom,
% 7.75/5.66 ! [X: rat,Y: rat] :
% 7.75/5.66 ( ( ord_less_rat @ X @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_neg_neg
% 7.75/5.66 thf(fact_1388_zero__less__power,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power
% 7.75/5.66 thf(fact_1389_zero__less__power,axiom,
% 7.75/5.66 ! [A: real,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power
% 7.75/5.66 thf(fact_1390_zero__less__power,axiom,
% 7.75/5.66 ! [A: rat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power
% 7.75/5.66 thf(fact_1391_zero__less__power,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power
% 7.75/5.66 thf(fact_1392_zero__less__power,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % zero_less_power
% 7.75/5.66 thf(fact_1393_less__Suc__eq__0__disj,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 7.75/5.66 = ( ( M = zero_zero_nat )
% 7.75/5.66 | ? [J2: nat] :
% 7.75/5.66 ( ( M
% 7.75/5.66 = ( suc @ J2 ) )
% 7.75/5.66 & ( ord_less_nat @ J2 @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_Suc_eq_0_disj
% 7.75/5.66 thf(fact_1394_gr0__implies__Suc,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ? [M2: nat] :
% 7.75/5.66 ( N
% 7.75/5.66 = ( suc @ M2 ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % gr0_implies_Suc
% 7.75/5.66 thf(fact_1395_All__less__Suc2,axiom,
% 7.75/5.66 ! [N: nat,P: nat > $o] :
% 7.75/5.66 ( ( ! [I2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 7.75/5.66 => ( P @ I2 ) ) )
% 7.75/5.66 = ( ( P @ zero_zero_nat )
% 7.75/5.66 & ! [I2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I2 @ N )
% 7.75/5.66 => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % All_less_Suc2
% 7.75/5.66 thf(fact_1396_gr0__conv__Suc,axiom,
% 7.75/5.66 ! [N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 = ( ? [M4: nat] :
% 7.75/5.66 ( N
% 7.75/5.66 = ( suc @ M4 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % gr0_conv_Suc
% 7.75/5.66 thf(fact_1397_Ex__less__Suc2,axiom,
% 7.75/5.66 ! [N: nat,P: nat > $o] :
% 7.75/5.66 ( ( ? [I2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 7.75/5.66 & ( P @ I2 ) ) )
% 7.75/5.66 = ( ( P @ zero_zero_nat )
% 7.75/5.66 | ? [I2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I2 @ N )
% 7.75/5.66 & ( P @ ( suc @ I2 ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % Ex_less_Suc2
% 7.75/5.66 thf(fact_1398_right__inverse__eq,axiom,
% 7.75/5.66 ! [B: complex,A: complex] :
% 7.75/5.66 ( ( B != zero_zero_complex )
% 7.75/5.66 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 7.75/5.66 = one_one_complex )
% 7.75/5.66 = ( A = B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % right_inverse_eq
% 7.75/5.66 thf(fact_1399_right__inverse__eq,axiom,
% 7.75/5.66 ! [B: real,A: real] :
% 7.75/5.66 ( ( B != zero_zero_real )
% 7.75/5.66 => ( ( ( divide_divide_real @ A @ B )
% 7.75/5.66 = one_one_real )
% 7.75/5.66 = ( A = B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % right_inverse_eq
% 7.75/5.66 thf(fact_1400_right__inverse__eq,axiom,
% 7.75/5.66 ! [B: rat,A: rat] :
% 7.75/5.66 ( ( B != zero_zero_rat )
% 7.75/5.66 => ( ( ( divide_divide_rat @ A @ B )
% 7.75/5.66 = one_one_rat )
% 7.75/5.66 = ( A = B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % right_inverse_eq
% 7.75/5.66 thf(fact_1401_power__0,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( power_power_rat @ A @ zero_zero_nat )
% 7.75/5.66 = one_one_rat ) ).
% 7.75/5.66
% 7.75/5.66 % power_0
% 7.75/5.66 thf(fact_1402_power__0,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( power_power_nat @ A @ zero_zero_nat )
% 7.75/5.66 = one_one_nat ) ).
% 7.75/5.66
% 7.75/5.66 % power_0
% 7.75/5.66 thf(fact_1403_power__0,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( power_power_real @ A @ zero_zero_nat )
% 7.75/5.66 = one_one_real ) ).
% 7.75/5.66
% 7.75/5.66 % power_0
% 7.75/5.66 thf(fact_1404_power__0,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( power_power_int @ A @ zero_zero_nat )
% 7.75/5.66 = one_one_int ) ).
% 7.75/5.66
% 7.75/5.66 % power_0
% 7.75/5.66 thf(fact_1405_power__0,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( power_power_complex @ A @ zero_zero_nat )
% 7.75/5.66 = one_one_complex ) ).
% 7.75/5.66
% 7.75/5.66 % power_0
% 7.75/5.66 thf(fact_1406_power__0,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 7.75/5.66 = one_one_Code_integer ) ).
% 7.75/5.66
% 7.75/5.66 % power_0
% 7.75/5.66 thf(fact_1407_power__0,axiom,
% 7.75/5.66 ! [A: assn] :
% 7.75/5.66 ( ( power_power_assn @ A @ zero_zero_nat )
% 7.75/5.66 = one_one_assn ) ).
% 7.75/5.66
% 7.75/5.66 % power_0
% 7.75/5.66 thf(fact_1408_less__imp__add__positive,axiom,
% 7.75/5.66 ! [I: nat,J: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J )
% 7.75/5.66 => ? [K2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 7.75/5.66 & ( ( plus_plus_nat @ I @ K2 )
% 7.75/5.66 = J ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_imp_add_positive
% 7.75/5.66 thf(fact_1409_One__nat__def,axiom,
% 7.75/5.66 ( one_one_nat
% 7.75/5.66 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % One_nat_def
% 7.75/5.66 thf(fact_1410_not__is__unit__0,axiom,
% 7.75/5.66 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 7.75/5.66
% 7.75/5.66 % not_is_unit_0
% 7.75/5.66 thf(fact_1411_not__is__unit__0,axiom,
% 7.75/5.66 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 7.75/5.66
% 7.75/5.66 % not_is_unit_0
% 7.75/5.66 thf(fact_1412_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ( divide_divide_nat @ M @ N )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 = ( ( ord_less_nat @ M @ N )
% 7.75/5.66 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % Euclidean_Division.div_eq_0_iff
% 7.75/5.66 thf(fact_1413_nat__mult__eq__cancel1,axiom,
% 7.75/5.66 ! [K: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.66 => ( ( ( times_times_nat @ K @ M )
% 7.75/5.66 = ( times_times_nat @ K @ N ) )
% 7.75/5.66 = ( M = N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_mult_eq_cancel1
% 7.75/5.66 thf(fact_1414_nat__mult__less__cancel1,axiom,
% 7.75/5.66 ! [K: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.66 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.66 = ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_mult_less_cancel1
% 7.75/5.66 thf(fact_1415_mult__less__mono2,axiom,
% 7.75/5.66 ! [I: nat,J: nat,K: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.66 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_mono2
% 7.75/5.66 thf(fact_1416_mult__less__mono1,axiom,
% 7.75/5.66 ! [I: nat,J: nat,K: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.66 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_less_mono1
% 7.75/5.66 thf(fact_1417_nat__power__less__imp__less,axiom,
% 7.75/5.66 ! [I: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ I )
% 7.75/5.66 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 7.75/5.66 => ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_power_less_imp_less
% 7.75/5.66 thf(fact_1418_nat__dvd__not__less,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.66 => ( ( ord_less_nat @ M @ N )
% 7.75/5.66 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_dvd_not_less
% 7.75/5.66 thf(fact_1419_dvd__pos__nat,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( dvd_dvd_nat @ M @ N )
% 7.75/5.66 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_pos_nat
% 7.75/5.66 thf(fact_1420_mult__eq__self__implies__10,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( M
% 7.75/5.66 = ( times_times_nat @ M @ N ) )
% 7.75/5.66 => ( ( N = one_one_nat )
% 7.75/5.66 | ( M = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_eq_self_implies_10
% 7.75/5.66 thf(fact_1421_add__less__imp__less__right,axiom,
% 7.75/5.66 ! [A: real,C: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 7.75/5.66 => ( ord_less_real @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_imp_less_right
% 7.75/5.66 thf(fact_1422_add__less__imp__less__right,axiom,
% 7.75/5.66 ! [A: rat,C: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.66 => ( ord_less_rat @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_imp_less_right
% 7.75/5.66 thf(fact_1423_add__less__imp__less__right,axiom,
% 7.75/5.66 ! [A: nat,C: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 7.75/5.66 => ( ord_less_nat @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_imp_less_right
% 7.75/5.66 thf(fact_1424_add__less__imp__less__right,axiom,
% 7.75/5.66 ! [A: int,C: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 7.75/5.66 => ( ord_less_int @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_imp_less_right
% 7.75/5.66 thf(fact_1425_add__less__imp__less__left,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 7.75/5.66 => ( ord_less_real @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_imp_less_left
% 7.75/5.66 thf(fact_1426_add__less__imp__less__left,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 7.75/5.66 => ( ord_less_rat @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_imp_less_left
% 7.75/5.66 thf(fact_1427_add__less__imp__less__left,axiom,
% 7.75/5.66 ! [C: nat,A: nat,B: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 7.75/5.66 => ( ord_less_nat @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_imp_less_left
% 7.75/5.66 thf(fact_1428_add__less__imp__less__left,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 7.75/5.66 => ( ord_less_int @ A @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_imp_less_left
% 7.75/5.66 thf(fact_1429_add__strict__right__mono,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_right_mono
% 7.75/5.66 thf(fact_1430_add__strict__right__mono,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_right_mono
% 7.75/5.66 thf(fact_1431_add__strict__right__mono,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ B )
% 7.75/5.66 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_right_mono
% 7.75/5.66 thf(fact_1432_add__strict__right__mono,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ B )
% 7.75/5.66 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_right_mono
% 7.75/5.66 thf(fact_1433_add__strict__left__mono,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_left_mono
% 7.75/5.66 thf(fact_1434_add__strict__left__mono,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_left_mono
% 7.75/5.66 thf(fact_1435_add__strict__left__mono,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ B )
% 7.75/5.66 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_left_mono
% 7.75/5.66 thf(fact_1436_add__strict__left__mono,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ B )
% 7.75/5.66 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_left_mono
% 7.75/5.66 thf(fact_1437_add__strict__mono,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ( ord_less_real @ C @ D2 )
% 7.75/5.66 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_mono
% 7.75/5.66 thf(fact_1438_add__strict__mono,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ( ord_less_rat @ C @ D2 )
% 7.75/5.66 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_mono
% 7.75/5.66 thf(fact_1439_add__strict__mono,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ A @ B )
% 7.75/5.66 => ( ( ord_less_nat @ C @ D2 )
% 7.75/5.66 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_mono
% 7.75/5.66 thf(fact_1440_add__strict__mono,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.66 ( ( ord_less_int @ A @ B )
% 7.75/5.66 => ( ( ord_less_int @ C @ D2 )
% 7.75/5.66 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_strict_mono
% 7.75/5.66 thf(fact_1441_add__mono__thms__linordered__field_I1_J,axiom,
% 7.75/5.66 ! [I: real,J: real,K: real,L: real] :
% 7.75/5.66 ( ( ( ord_less_real @ I @ J )
% 7.75/5.66 & ( K = L ) )
% 7.75/5.66 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(1)
% 7.75/5.66 thf(fact_1442_add__mono__thms__linordered__field_I1_J,axiom,
% 7.75/5.66 ! [I: rat,J: rat,K: rat,L: rat] :
% 7.75/5.66 ( ( ( ord_less_rat @ I @ J )
% 7.75/5.66 & ( K = L ) )
% 7.75/5.66 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(1)
% 7.75/5.66 thf(fact_1443_add__mono__thms__linordered__field_I1_J,axiom,
% 7.75/5.66 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.66 ( ( ( ord_less_nat @ I @ J )
% 7.75/5.66 & ( K = L ) )
% 7.75/5.66 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(1)
% 7.75/5.66 thf(fact_1444_add__mono__thms__linordered__field_I1_J,axiom,
% 7.75/5.66 ! [I: int,J: int,K: int,L: int] :
% 7.75/5.66 ( ( ( ord_less_int @ I @ J )
% 7.75/5.66 & ( K = L ) )
% 7.75/5.66 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(1)
% 7.75/5.66 thf(fact_1445_add__mono__thms__linordered__field_I2_J,axiom,
% 7.75/5.66 ! [I: real,J: real,K: real,L: real] :
% 7.75/5.66 ( ( ( I = J )
% 7.75/5.66 & ( ord_less_real @ K @ L ) )
% 7.75/5.66 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(2)
% 7.75/5.66 thf(fact_1446_add__mono__thms__linordered__field_I2_J,axiom,
% 7.75/5.66 ! [I: rat,J: rat,K: rat,L: rat] :
% 7.75/5.66 ( ( ( I = J )
% 7.75/5.66 & ( ord_less_rat @ K @ L ) )
% 7.75/5.66 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(2)
% 7.75/5.66 thf(fact_1447_add__mono__thms__linordered__field_I2_J,axiom,
% 7.75/5.66 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.66 ( ( ( I = J )
% 7.75/5.66 & ( ord_less_nat @ K @ L ) )
% 7.75/5.66 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(2)
% 7.75/5.66 thf(fact_1448_add__mono__thms__linordered__field_I2_J,axiom,
% 7.75/5.66 ! [I: int,J: int,K: int,L: int] :
% 7.75/5.66 ( ( ( I = J )
% 7.75/5.66 & ( ord_less_int @ K @ L ) )
% 7.75/5.66 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(2)
% 7.75/5.66 thf(fact_1449_add__mono__thms__linordered__field_I5_J,axiom,
% 7.75/5.66 ! [I: real,J: real,K: real,L: real] :
% 7.75/5.66 ( ( ( ord_less_real @ I @ J )
% 7.75/5.66 & ( ord_less_real @ K @ L ) )
% 7.75/5.66 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(5)
% 7.75/5.66 thf(fact_1450_add__mono__thms__linordered__field_I5_J,axiom,
% 7.75/5.66 ! [I: rat,J: rat,K: rat,L: rat] :
% 7.75/5.66 ( ( ( ord_less_rat @ I @ J )
% 7.75/5.66 & ( ord_less_rat @ K @ L ) )
% 7.75/5.66 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(5)
% 7.75/5.66 thf(fact_1451_add__mono__thms__linordered__field_I5_J,axiom,
% 7.75/5.66 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.66 ( ( ( ord_less_nat @ I @ J )
% 7.75/5.66 & ( ord_less_nat @ K @ L ) )
% 7.75/5.66 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(5)
% 7.75/5.66 thf(fact_1452_add__mono__thms__linordered__field_I5_J,axiom,
% 7.75/5.66 ! [I: int,J: int,K: int,L: int] :
% 7.75/5.66 ( ( ( ord_less_int @ I @ J )
% 7.75/5.66 & ( ord_less_int @ K @ L ) )
% 7.75/5.66 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_mono_thms_linordered_field(5)
% 7.75/5.66 thf(fact_1453_comm__monoid__mult__class_Omult__1,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( times_times_rat @ one_one_rat @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_mult_class.mult_1
% 7.75/5.66 thf(fact_1454_comm__monoid__mult__class_Omult__1,axiom,
% 7.75/5.66 ! [A: assn] :
% 7.75/5.66 ( ( times_times_assn @ one_one_assn @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_mult_class.mult_1
% 7.75/5.66 thf(fact_1455_comm__monoid__mult__class_Omult__1,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( times_times_real @ one_one_real @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_mult_class.mult_1
% 7.75/5.66 thf(fact_1456_comm__monoid__mult__class_Omult__1,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( times_times_nat @ one_one_nat @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_mult_class.mult_1
% 7.75/5.66 thf(fact_1457_comm__monoid__mult__class_Omult__1,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( times_times_int @ one_one_int @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_mult_class.mult_1
% 7.75/5.66 thf(fact_1458_comm__monoid__mult__class_Omult__1,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_mult_class.mult_1
% 7.75/5.66 thf(fact_1459_comm__monoid__mult__class_Omult__1,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( times_times_complex @ one_one_complex @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_mult_class.mult_1
% 7.75/5.66 thf(fact_1460_mult_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( times_times_rat @ A @ one_one_rat )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % mult.comm_neutral
% 7.75/5.66 thf(fact_1461_mult_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: assn] :
% 7.75/5.66 ( ( times_times_assn @ A @ one_one_assn )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % mult.comm_neutral
% 7.75/5.66 thf(fact_1462_mult_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( times_times_real @ A @ one_one_real )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % mult.comm_neutral
% 7.75/5.66 thf(fact_1463_mult_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( times_times_nat @ A @ one_one_nat )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % mult.comm_neutral
% 7.75/5.66 thf(fact_1464_mult_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( times_times_int @ A @ one_one_int )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % mult.comm_neutral
% 7.75/5.66 thf(fact_1465_mult_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: code_integer] :
% 7.75/5.66 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % mult.comm_neutral
% 7.75/5.66 thf(fact_1466_mult_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( times_times_complex @ A @ one_one_complex )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % mult.comm_neutral
% 7.75/5.66 thf(fact_1467_verit__sum__simplify,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_sum_simplify
% 7.75/5.66 thf(fact_1468_verit__sum__simplify,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( plus_plus_real @ A @ zero_zero_real )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_sum_simplify
% 7.75/5.66 thf(fact_1469_verit__sum__simplify,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_sum_simplify
% 7.75/5.66 thf(fact_1470_verit__sum__simplify,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_sum_simplify
% 7.75/5.66 thf(fact_1471_verit__sum__simplify,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( plus_plus_int @ A @ zero_zero_int )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % verit_sum_simplify
% 7.75/5.66 thf(fact_1472_add_Ogroup__left__neutral,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % add.group_left_neutral
% 7.75/5.66 thf(fact_1473_add_Ogroup__left__neutral,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( plus_plus_real @ zero_zero_real @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % add.group_left_neutral
% 7.75/5.66 thf(fact_1474_add_Ogroup__left__neutral,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % add.group_left_neutral
% 7.75/5.66 thf(fact_1475_add_Ogroup__left__neutral,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( plus_plus_int @ zero_zero_int @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % add.group_left_neutral
% 7.75/5.66 thf(fact_1476_add_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % add.comm_neutral
% 7.75/5.66 thf(fact_1477_add_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( plus_plus_real @ A @ zero_zero_real )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % add.comm_neutral
% 7.75/5.66 thf(fact_1478_add_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % add.comm_neutral
% 7.75/5.66 thf(fact_1479_add_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % add.comm_neutral
% 7.75/5.66 thf(fact_1480_add_Ocomm__neutral,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( plus_plus_int @ A @ zero_zero_int )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % add.comm_neutral
% 7.75/5.66 thf(fact_1481_comm__monoid__add__class_Oadd__0,axiom,
% 7.75/5.66 ! [A: complex] :
% 7.75/5.66 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_add_class.add_0
% 7.75/5.66 thf(fact_1482_comm__monoid__add__class_Oadd__0,axiom,
% 7.75/5.66 ! [A: real] :
% 7.75/5.66 ( ( plus_plus_real @ zero_zero_real @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_add_class.add_0
% 7.75/5.66 thf(fact_1483_comm__monoid__add__class_Oadd__0,axiom,
% 7.75/5.66 ! [A: rat] :
% 7.75/5.66 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_add_class.add_0
% 7.75/5.66 thf(fact_1484_comm__monoid__add__class_Oadd__0,axiom,
% 7.75/5.66 ! [A: nat] :
% 7.75/5.66 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_add_class.add_0
% 7.75/5.66 thf(fact_1485_comm__monoid__add__class_Oadd__0,axiom,
% 7.75/5.66 ! [A: int] :
% 7.75/5.66 ( ( plus_plus_int @ zero_zero_int @ A )
% 7.75/5.66 = A ) ).
% 7.75/5.66
% 7.75/5.66 % comm_monoid_add_class.add_0
% 7.75/5.66 thf(fact_1486_power__Suc__less,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less
% 7.75/5.66 thf(fact_1487_power__Suc__less,axiom,
% 7.75/5.66 ! [A: real,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ A @ one_one_real )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less
% 7.75/5.66 thf(fact_1488_power__Suc__less,axiom,
% 7.75/5.66 ! [A: rat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ A @ one_one_rat )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less
% 7.75/5.66 thf(fact_1489_power__Suc__less,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ A @ one_one_nat )
% 7.75/5.66 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less
% 7.75/5.66 thf(fact_1490_power__Suc__less,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ( ord_less_int @ A @ one_one_int )
% 7.75/5.66 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less
% 7.75/5.66 thf(fact_1491_power__Suc__less__one,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less_one
% 7.75/5.66 thf(fact_1492_power__Suc__less__one,axiom,
% 7.75/5.66 ! [A: real,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.66 => ( ( ord_less_real @ A @ one_one_real )
% 7.75/5.66 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less_one
% 7.75/5.66 thf(fact_1493_power__Suc__less__one,axiom,
% 7.75/5.66 ! [A: rat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.66 => ( ( ord_less_rat @ A @ one_one_rat )
% 7.75/5.66 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less_one
% 7.75/5.66 thf(fact_1494_power__Suc__less__one,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.66 => ( ( ord_less_nat @ A @ one_one_nat )
% 7.75/5.66 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less_one
% 7.75/5.66 thf(fact_1495_power__Suc__less__one,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.66 => ( ( ord_less_int @ A @ one_one_int )
% 7.75/5.66 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_Suc_less_one
% 7.75/5.66 thf(fact_1496_split__mod,axiom,
% 7.75/5.66 ! [P: nat > $o,M: nat,N: nat] :
% 7.75/5.66 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 7.75/5.66 = ( ( ( N = zero_zero_nat )
% 7.75/5.66 => ( P @ M ) )
% 7.75/5.66 & ( ( N != zero_zero_nat )
% 7.75/5.66 => ! [I2: nat,J2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ J2 @ N )
% 7.75/5.66 => ( ( M
% 7.75/5.66 = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J2 ) )
% 7.75/5.66 => ( P @ J2 ) ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % split_mod
% 7.75/5.66 thf(fact_1497_dvd__power,axiom,
% 7.75/5.66 ! [N: nat,X: rat] :
% 7.75/5.66 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 | ( X = one_one_rat ) )
% 7.75/5.66 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_power
% 7.75/5.66 thf(fact_1498_dvd__power,axiom,
% 7.75/5.66 ! [N: nat,X: nat] :
% 7.75/5.66 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 | ( X = one_one_nat ) )
% 7.75/5.66 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_power
% 7.75/5.66 thf(fact_1499_dvd__power,axiom,
% 7.75/5.66 ! [N: nat,X: real] :
% 7.75/5.66 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 | ( X = one_one_real ) )
% 7.75/5.66 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_power
% 7.75/5.66 thf(fact_1500_dvd__power,axiom,
% 7.75/5.66 ! [N: nat,X: int] :
% 7.75/5.66 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 | ( X = one_one_int ) )
% 7.75/5.66 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_power
% 7.75/5.66 thf(fact_1501_dvd__power,axiom,
% 7.75/5.66 ! [N: nat,X: complex] :
% 7.75/5.66 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 | ( X = one_one_complex ) )
% 7.75/5.66 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_power
% 7.75/5.66 thf(fact_1502_dvd__power,axiom,
% 7.75/5.66 ! [N: nat,X: code_integer] :
% 7.75/5.66 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 | ( X = one_one_Code_integer ) )
% 7.75/5.66 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_power
% 7.75/5.66 thf(fact_1503_cong__exp__iff__simps_I2_J,axiom,
% 7.75/5.66 ! [N: num,Q3: num] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 7.75/5.66 = zero_zero_nat ) ) ).
% 7.75/5.66
% 7.75/5.66 % cong_exp_iff_simps(2)
% 7.75/5.66 thf(fact_1504_cong__exp__iff__simps_I2_J,axiom,
% 7.75/5.66 ! [N: num,Q3: num] :
% 7.75/5.66 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.66 = zero_zero_int )
% 7.75/5.66 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 7.75/5.66 = zero_zero_int ) ) ).
% 7.75/5.66
% 7.75/5.66 % cong_exp_iff_simps(2)
% 7.75/5.66 thf(fact_1505_cong__exp__iff__simps_I2_J,axiom,
% 7.75/5.66 ! [N: num,Q3: num] :
% 7.75/5.66 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.66 = zero_z3403309356797280102nteger )
% 7.75/5.66 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.66
% 7.75/5.66 % cong_exp_iff_simps(2)
% 7.75/5.66 thf(fact_1506_cong__exp__iff__simps_I1_J,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 7.75/5.66 = zero_zero_nat ) ).
% 7.75/5.66
% 7.75/5.66 % cong_exp_iff_simps(1)
% 7.75/5.66 thf(fact_1507_cong__exp__iff__simps_I1_J,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 7.75/5.66 = zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % cong_exp_iff_simps(1)
% 7.75/5.66 thf(fact_1508_cong__exp__iff__simps_I1_J,axiom,
% 7.75/5.66 ! [N: num] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 7.75/5.66 = zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % cong_exp_iff_simps(1)
% 7.75/5.66 thf(fact_1509_dvd__mult__cancel2,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.66 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 7.75/5.66 = ( N = one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel2
% 7.75/5.66 thf(fact_1510_dvd__mult__cancel1,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.66 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 7.75/5.66 = ( N = one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel1
% 7.75/5.66 thf(fact_1511_divmod__digit__0_I2_J,axiom,
% 7.75/5.66 ! [B: nat,A: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.66 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 7.75/5.66 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 7.75/5.66 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divmod_digit_0(2)
% 7.75/5.66 thf(fact_1512_divmod__digit__0_I2_J,axiom,
% 7.75/5.66 ! [B: int,A: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.66 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 7.75/5.66 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 7.75/5.66 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divmod_digit_0(2)
% 7.75/5.66 thf(fact_1513_divmod__digit__0_I2_J,axiom,
% 7.75/5.66 ! [B: code_integer,A: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.66 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 7.75/5.66 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 7.75/5.66 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divmod_digit_0(2)
% 7.75/5.66 thf(fact_1514_gt__half__sum,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % gt_half_sum
% 7.75/5.66 thf(fact_1515_gt__half__sum,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % gt_half_sum
% 7.75/5.66 thf(fact_1516_less__half__sum,axiom,
% 7.75/5.66 ! [A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_half_sum
% 7.75/5.66 thf(fact_1517_less__half__sum,axiom,
% 7.75/5.66 ! [A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_half_sum
% 7.75/5.66 thf(fact_1518_power__gt1__lemma,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1_lemma
% 7.75/5.66 thf(fact_1519_power__gt1__lemma,axiom,
% 7.75/5.66 ! [A: real,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.66 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1_lemma
% 7.75/5.66 thf(fact_1520_power__gt1__lemma,axiom,
% 7.75/5.66 ! [A: rat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ A )
% 7.75/5.66 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1_lemma
% 7.75/5.66 thf(fact_1521_power__gt1__lemma,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ A )
% 7.75/5.66 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1_lemma
% 7.75/5.66 thf(fact_1522_power__gt1__lemma,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ one_one_int @ A )
% 7.75/5.66 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1_lemma
% 7.75/5.66 thf(fact_1523_power__less__power__Suc,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_power_Suc
% 7.75/5.66 thf(fact_1524_power__less__power__Suc,axiom,
% 7.75/5.66 ! [A: real,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.66 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_power_Suc
% 7.75/5.66 thf(fact_1525_power__less__power__Suc,axiom,
% 7.75/5.66 ! [A: rat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ A )
% 7.75/5.66 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_power_Suc
% 7.75/5.66 thf(fact_1526_power__less__power__Suc,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ A )
% 7.75/5.66 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_power_Suc
% 7.75/5.66 thf(fact_1527_power__less__power__Suc,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ one_one_int @ A )
% 7.75/5.66 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_less_power_Suc
% 7.75/5.66 thf(fact_1528_not__sum__squares__lt__zero,axiom,
% 7.75/5.66 ! [X: code_integer,Y: code_integer] :
% 7.75/5.66 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 7.75/5.66
% 7.75/5.66 % not_sum_squares_lt_zero
% 7.75/5.66 thf(fact_1529_not__sum__squares__lt__zero,axiom,
% 7.75/5.66 ! [X: real,Y: real] :
% 7.75/5.66 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 7.75/5.66
% 7.75/5.66 % not_sum_squares_lt_zero
% 7.75/5.66 thf(fact_1530_not__sum__squares__lt__zero,axiom,
% 7.75/5.66 ! [X: rat,Y: rat] :
% 7.75/5.66 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 7.75/5.66
% 7.75/5.66 % not_sum_squares_lt_zero
% 7.75/5.66 thf(fact_1531_not__sum__squares__lt__zero,axiom,
% 7.75/5.66 ! [X: int,Y: int] :
% 7.75/5.66 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 7.75/5.66
% 7.75/5.66 % not_sum_squares_lt_zero
% 7.75/5.66 thf(fact_1532_sum__squares__gt__zero__iff,axiom,
% 7.75/5.66 ! [X: code_integer,Y: code_integer] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 7.75/5.66 = ( ( X != zero_z3403309356797280102nteger )
% 7.75/5.66 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % sum_squares_gt_zero_iff
% 7.75/5.66 thf(fact_1533_sum__squares__gt__zero__iff,axiom,
% 7.75/5.66 ! [X: real,Y: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 7.75/5.66 = ( ( X != zero_zero_real )
% 7.75/5.66 | ( Y != zero_zero_real ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % sum_squares_gt_zero_iff
% 7.75/5.66 thf(fact_1534_sum__squares__gt__zero__iff,axiom,
% 7.75/5.66 ! [X: rat,Y: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 7.75/5.66 = ( ( X != zero_zero_rat )
% 7.75/5.66 | ( Y != zero_zero_rat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % sum_squares_gt_zero_iff
% 7.75/5.66 thf(fact_1535_sum__squares__gt__zero__iff,axiom,
% 7.75/5.66 ! [X: int,Y: int] :
% 7.75/5.66 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 7.75/5.66 = ( ( X != zero_zero_int )
% 7.75/5.66 | ( Y != zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % sum_squares_gt_zero_iff
% 7.75/5.66 thf(fact_1536_power__gt1,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 7.75/5.66 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1
% 7.75/5.66 thf(fact_1537_power__gt1,axiom,
% 7.75/5.66 ! [A: real,N: nat] :
% 7.75/5.66 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.66 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1
% 7.75/5.66 thf(fact_1538_power__gt1,axiom,
% 7.75/5.66 ! [A: rat,N: nat] :
% 7.75/5.66 ( ( ord_less_rat @ one_one_rat @ A )
% 7.75/5.66 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1
% 7.75/5.66 thf(fact_1539_power__gt1,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ one_one_nat @ A )
% 7.75/5.66 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1
% 7.75/5.66 thf(fact_1540_power__gt1,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( ord_less_int @ one_one_int @ A )
% 7.75/5.66 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt1
% 7.75/5.66 thf(fact_1541_divide__less__eq,axiom,
% 7.75/5.66 ! [B: real,C: real,A: real] :
% 7.75/5.66 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 7.75/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 7.75/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq
% 7.75/5.66 thf(fact_1542_divide__less__eq,axiom,
% 7.75/5.66 ! [B: rat,C: rat,A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 7.75/5.66 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 7.75/5.66 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_less_eq
% 7.75/5.66 thf(fact_1543_less__divide__eq,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 7.75/5.66 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 7.75/5.66 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 7.75/5.66 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq
% 7.75/5.66 thf(fact_1544_less__divide__eq,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 7.75/5.66 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 7.75/5.66 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_divide_eq
% 7.75/5.66 thf(fact_1545_neg__divide__less__eq,axiom,
% 7.75/5.66 ! [C: real,B: real,A: real] :
% 7.75/5.66 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 7.75/5.66 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % neg_divide_less_eq
% 7.75/5.66 thf(fact_1546_neg__divide__less__eq,axiom,
% 7.75/5.66 ! [C: rat,B: rat,A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 7.75/5.66 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % neg_divide_less_eq
% 7.75/5.66 thf(fact_1547_neg__less__divide__eq,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 7.75/5.66 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % neg_less_divide_eq
% 7.75/5.66 thf(fact_1548_neg__less__divide__eq,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.66 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % neg_less_divide_eq
% 7.75/5.66 thf(fact_1549_pos__divide__less__eq,axiom,
% 7.75/5.66 ! [C: real,B: real,A: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 7.75/5.66 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pos_divide_less_eq
% 7.75/5.66 thf(fact_1550_pos__divide__less__eq,axiom,
% 7.75/5.66 ! [C: rat,B: rat,A: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 7.75/5.66 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pos_divide_less_eq
% 7.75/5.66 thf(fact_1551_pos__less__divide__eq,axiom,
% 7.75/5.66 ! [C: real,A: real,B: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 7.75/5.66 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pos_less_divide_eq
% 7.75/5.66 thf(fact_1552_pos__less__divide__eq,axiom,
% 7.75/5.66 ! [C: rat,A: rat,B: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.66 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % pos_less_divide_eq
% 7.75/5.66 thf(fact_1553_mult__imp__div__pos__less,axiom,
% 7.75/5.66 ! [Y: real,X: real,Z: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.66 => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y ) )
% 7.75/5.66 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_imp_div_pos_less
% 7.75/5.66 thf(fact_1554_mult__imp__div__pos__less,axiom,
% 7.75/5.66 ! [Y: rat,X: rat,Z: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 7.75/5.66 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 7.75/5.66 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_imp_div_pos_less
% 7.75/5.66 thf(fact_1555_mult__imp__less__div__pos,axiom,
% 7.75/5.66 ! [Y: real,Z: real,X: real] :
% 7.75/5.66 ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.66 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X )
% 7.75/5.66 => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_imp_less_div_pos
% 7.75/5.66 thf(fact_1556_mult__imp__less__div__pos,axiom,
% 7.75/5.66 ! [Y: rat,Z: rat,X: rat] :
% 7.75/5.66 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 7.75/5.66 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 7.75/5.66 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_imp_less_div_pos
% 7.75/5.66 thf(fact_1557_divide__strict__left__mono,axiom,
% 7.75/5.66 ! [B: real,A: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ B @ A )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 7.75/5.66 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_strict_left_mono
% 7.75/5.66 thf(fact_1558_divide__strict__left__mono,axiom,
% 7.75/5.66 ! [B: rat,A: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ B @ A )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.66 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_strict_left_mono
% 7.75/5.66 thf(fact_1559_divide__strict__left__mono__neg,axiom,
% 7.75/5.66 ! [A: real,B: real,C: real] :
% 7.75/5.66 ( ( ord_less_real @ A @ B )
% 7.75/5.66 => ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.66 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 7.75/5.66 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_strict_left_mono_neg
% 7.75/5.66 thf(fact_1560_divide__strict__left__mono__neg,axiom,
% 7.75/5.66 ! [A: rat,B: rat,C: rat] :
% 7.75/5.66 ( ( ord_less_rat @ A @ B )
% 7.75/5.66 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.66 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.66 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % divide_strict_left_mono_neg
% 7.75/5.66 thf(fact_1561_div__add__self1,axiom,
% 7.75/5.66 ! [B: nat,A: nat] :
% 7.75/5.66 ( ( B != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 7.75/5.66 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_add_self1
% 7.75/5.66 thf(fact_1562_div__add__self1,axiom,
% 7.75/5.66 ! [B: int,A: int] :
% 7.75/5.66 ( ( B != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 7.75/5.66 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_add_self1
% 7.75/5.66 thf(fact_1563_div__add__self2,axiom,
% 7.75/5.66 ! [B: nat,A: nat] :
% 7.75/5.66 ( ( B != zero_zero_nat )
% 7.75/5.66 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 7.75/5.66 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_add_self2
% 7.75/5.66 thf(fact_1564_div__add__self2,axiom,
% 7.75/5.66 ! [B: int,A: int] :
% 7.75/5.66 ( ( B != zero_zero_int )
% 7.75/5.66 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 7.75/5.66 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_add_self2
% 7.75/5.66 thf(fact_1565_unit__dvdE,axiom,
% 7.75/5.66 ! [A: nat,B: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.66 => ~ ( ( A != zero_zero_nat )
% 7.75/5.66 => ! [C3: nat] :
% 7.75/5.66 ( B
% 7.75/5.66 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_dvdE
% 7.75/5.66 thf(fact_1566_unit__dvdE,axiom,
% 7.75/5.66 ! [A: int,B: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.66 => ~ ( ( A != zero_zero_int )
% 7.75/5.66 => ! [C3: int] :
% 7.75/5.66 ( B
% 7.75/5.66 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_dvdE
% 7.75/5.66 thf(fact_1567_unit__dvdE,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.66 => ~ ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.66 => ! [C3: code_integer] :
% 7.75/5.66 ( B
% 7.75/5.66 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_dvdE
% 7.75/5.66 thf(fact_1568_unit__div__eq__0__iff,axiom,
% 7.75/5.66 ! [B: nat,A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.66 => ( ( ( divide_divide_nat @ A @ B )
% 7.75/5.66 = zero_zero_nat )
% 7.75/5.66 = ( A = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div_eq_0_iff
% 7.75/5.66 thf(fact_1569_unit__div__eq__0__iff,axiom,
% 7.75/5.66 ! [B: int,A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.66 => ( ( ( divide_divide_int @ A @ B )
% 7.75/5.66 = zero_zero_int )
% 7.75/5.66 = ( A = zero_zero_int ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % unit_div_eq_0_iff
% 7.75/5.66 thf(fact_1570_one__less__mult,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.75/5.66 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 7.75/5.66 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % one_less_mult
% 7.75/5.66 thf(fact_1571_n__less__m__mult__n,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 7.75/5.66 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % n_less_m_mult_n
% 7.75/5.66 thf(fact_1572_n__less__n__mult__m,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.66 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 7.75/5.66 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % n_less_n_mult_m
% 7.75/5.66 thf(fact_1573_power__gt__expt,axiom,
% 7.75/5.66 ! [N: nat,K: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.75/5.66 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_gt_expt
% 7.75/5.66 thf(fact_1574_is__unit__power__iff,axiom,
% 7.75/5.66 ! [A: nat,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 7.75/5.66 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.66 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % is_unit_power_iff
% 7.75/5.66 thf(fact_1575_is__unit__power__iff,axiom,
% 7.75/5.66 ! [A: int,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 7.75/5.66 = ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.66 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % is_unit_power_iff
% 7.75/5.66 thf(fact_1576_is__unit__power__iff,axiom,
% 7.75/5.66 ! [A: code_integer,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 7.75/5.66 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.66 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % is_unit_power_iff
% 7.75/5.66 thf(fact_1577_mod__add__eq,axiom,
% 7.75/5.66 ! [A: nat,C: nat,B: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_eq
% 7.75/5.66 thf(fact_1578_mod__add__eq,axiom,
% 7.75/5.66 ! [A: int,C: int,B: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_eq
% 7.75/5.66 thf(fact_1579_mod__add__eq,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_eq
% 7.75/5.66 thf(fact_1580_mod__add__cong,axiom,
% 7.75/5.66 ! [A: nat,C: nat,A4: nat,B: nat,B6: nat] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ A @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ A4 @ C ) )
% 7.75/5.66 => ( ( ( modulo_modulo_nat @ B @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ B6 @ C ) )
% 7.75/5.66 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B6 ) @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_cong
% 7.75/5.66 thf(fact_1581_mod__add__cong,axiom,
% 7.75/5.66 ! [A: int,C: int,A4: int,B: int,B6: int] :
% 7.75/5.66 ( ( ( modulo_modulo_int @ A @ C )
% 7.75/5.66 = ( modulo_modulo_int @ A4 @ C ) )
% 7.75/5.66 => ( ( ( modulo_modulo_int @ B @ C )
% 7.75/5.66 = ( modulo_modulo_int @ B6 @ C ) )
% 7.75/5.66 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B6 ) @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_cong
% 7.75/5.66 thf(fact_1582_mod__add__cong,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B6: code_integer] :
% 7.75/5.66 ( ( ( modulo364778990260209775nteger @ A @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 7.75/5.66 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 7.75/5.66 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B6 ) @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_cong
% 7.75/5.66 thf(fact_1583_mod__add__left__eq,axiom,
% 7.75/5.66 ! [A: nat,C: nat,B: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_left_eq
% 7.75/5.66 thf(fact_1584_mod__add__left__eq,axiom,
% 7.75/5.66 ! [A: int,C: int,B: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_left_eq
% 7.75/5.66 thf(fact_1585_mod__add__left__eq,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_left_eq
% 7.75/5.66 thf(fact_1586_mod__add__right__eq,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_right_eq
% 7.75/5.66 thf(fact_1587_mod__add__right__eq,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_right_eq
% 7.75/5.66 thf(fact_1588_mod__add__right__eq,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_add_right_eq
% 7.75/5.66 thf(fact_1589_mod__mult__eq,axiom,
% 7.75/5.66 ! [A: nat,C: nat,B: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_eq
% 7.75/5.66 thf(fact_1590_mod__mult__eq,axiom,
% 7.75/5.66 ! [A: int,C: int,B: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_eq
% 7.75/5.66 thf(fact_1591_mod__mult__eq,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_eq
% 7.75/5.66 thf(fact_1592_mod__mult__cong,axiom,
% 7.75/5.66 ! [A: nat,C: nat,A4: nat,B: nat,B6: nat] :
% 7.75/5.66 ( ( ( modulo_modulo_nat @ A @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ A4 @ C ) )
% 7.75/5.66 => ( ( ( modulo_modulo_nat @ B @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ B6 @ C ) )
% 7.75/5.66 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B6 ) @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_cong
% 7.75/5.66 thf(fact_1593_mod__mult__cong,axiom,
% 7.75/5.66 ! [A: int,C: int,A4: int,B: int,B6: int] :
% 7.75/5.66 ( ( ( modulo_modulo_int @ A @ C )
% 7.75/5.66 = ( modulo_modulo_int @ A4 @ C ) )
% 7.75/5.66 => ( ( ( modulo_modulo_int @ B @ C )
% 7.75/5.66 = ( modulo_modulo_int @ B6 @ C ) )
% 7.75/5.66 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_int @ ( times_times_int @ A4 @ B6 ) @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_cong
% 7.75/5.66 thf(fact_1594_mod__mult__cong,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B6: code_integer] :
% 7.75/5.66 ( ( ( modulo364778990260209775nteger @ A @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 7.75/5.66 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 7.75/5.66 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B6 ) @ C ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_cong
% 7.75/5.66 thf(fact_1595_mod__mult__mult2,axiom,
% 7.75/5.66 ! [A: nat,C: nat,B: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 7.75/5.66 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_mult2
% 7.75/5.66 thf(fact_1596_mod__mult__mult2,axiom,
% 7.75/5.66 ! [A: int,C: int,B: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 7.75/5.66 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_mult2
% 7.75/5.66 thf(fact_1597_mod__mult__mult2,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.66 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_mult2
% 7.75/5.66 thf(fact_1598_mult__mod__right,axiom,
% 7.75/5.66 ! [C: nat,A: nat,B: nat] :
% 7.75/5.66 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 7.75/5.66 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_mod_right
% 7.75/5.66 thf(fact_1599_mult__mod__right,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 7.75/5.66 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_mod_right
% 7.75/5.66 thf(fact_1600_mult__mod__right,axiom,
% 7.75/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mult_mod_right
% 7.75/5.66 thf(fact_1601_mod__mult__left__eq,axiom,
% 7.75/5.66 ! [A: nat,C: nat,B: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_left_eq
% 7.75/5.66 thf(fact_1602_mod__mult__left__eq,axiom,
% 7.75/5.66 ! [A: int,C: int,B: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_left_eq
% 7.75/5.66 thf(fact_1603_mod__mult__left__eq,axiom,
% 7.75/5.66 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_left_eq
% 7.75/5.66 thf(fact_1604_mod__mult__right__eq,axiom,
% 7.75/5.66 ! [A: nat,B: nat,C: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_right_eq
% 7.75/5.66 thf(fact_1605_mod__mult__right__eq,axiom,
% 7.75/5.66 ! [A: int,B: int,C: int] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_right_eq
% 7.75/5.66 thf(fact_1606_mod__mult__right__eq,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mult_right_eq
% 7.75/5.66 thf(fact_1607_nat__mult__div__cancel1,axiom,
% 7.75/5.66 ! [K: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.66 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.66 = ( divide_divide_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_mult_div_cancel1
% 7.75/5.66 thf(fact_1608_div__less__iff__less__mult,axiom,
% 7.75/5.66 ! [Q3: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 7.75/5.66 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N )
% 7.75/5.66 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q3 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % div_less_iff_less_mult
% 7.75/5.66 thf(fact_1609_power__mod,axiom,
% 7.75/5.66 ! [A: nat,B: nat,N: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 7.75/5.66 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_mod
% 7.75/5.66 thf(fact_1610_power__mod,axiom,
% 7.75/5.66 ! [A: int,B: int,N: nat] :
% 7.75/5.66 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 7.75/5.66 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_mod
% 7.75/5.66 thf(fact_1611_power__mod,axiom,
% 7.75/5.66 ! [A: code_integer,B: code_integer,N: nat] :
% 7.75/5.66 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 7.75/5.66 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 7.75/5.66
% 7.75/5.66 % power_mod
% 7.75/5.66 thf(fact_1612_nat__mult__dvd__cancel1,axiom,
% 7.75/5.66 ! [K: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.66 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.66 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % nat_mult_dvd_cancel1
% 7.75/5.66 thf(fact_1613_dvd__mult__cancel,axiom,
% 7.75/5.66 ! [K: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.66 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.66 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mult_cancel
% 7.75/5.66 thf(fact_1614_dvd__mod__imp__dvd,axiom,
% 7.75/5.66 ! [C: nat,A: nat,B: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 7.75/5.66 => ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.66 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mod_imp_dvd
% 7.75/5.66 thf(fact_1615_dvd__mod__imp__dvd,axiom,
% 7.75/5.66 ! [C: int,A: int,B: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 7.75/5.66 => ( ( dvd_dvd_int @ C @ B )
% 7.75/5.66 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mod_imp_dvd
% 7.75/5.66 thf(fact_1616_dvd__mod__imp__dvd,axiom,
% 7.75/5.66 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 7.75/5.66 => ( ( dvd_dvd_Code_integer @ C @ B )
% 7.75/5.66 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mod_imp_dvd
% 7.75/5.66 thf(fact_1617_dvd__mod__iff,axiom,
% 7.75/5.66 ! [C: nat,B: nat,A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.66 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 7.75/5.66 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mod_iff
% 7.75/5.66 thf(fact_1618_dvd__mod__iff,axiom,
% 7.75/5.66 ! [C: int,B: int,A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ C @ B )
% 7.75/5.66 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 7.75/5.66 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mod_iff
% 7.75/5.66 thf(fact_1619_dvd__mod__iff,axiom,
% 7.75/5.66 ! [C: code_integer,B: code_integer,A: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ C @ B )
% 7.75/5.66 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 7.75/5.66 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mod_iff
% 7.75/5.66 thf(fact_1620_mod__mod__cancel,axiom,
% 7.75/5.66 ! [C: nat,B: nat,A: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.66 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mod_cancel
% 7.75/5.66 thf(fact_1621_mod__mod__cancel,axiom,
% 7.75/5.66 ! [C: int,B: int,A: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ C @ B )
% 7.75/5.66 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 7.75/5.66 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mod_cancel
% 7.75/5.66 thf(fact_1622_mod__mod__cancel,axiom,
% 7.75/5.66 ! [C: code_integer,B: code_integer,A: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ C @ B )
% 7.75/5.66 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 7.75/5.66 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_mod_cancel
% 7.75/5.66 thf(fact_1623_dvd__mod,axiom,
% 7.75/5.66 ! [K: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( dvd_dvd_nat @ K @ M )
% 7.75/5.66 => ( ( dvd_dvd_nat @ K @ N )
% 7.75/5.66 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mod
% 7.75/5.66 thf(fact_1624_dvd__mod,axiom,
% 7.75/5.66 ! [K: int,M: int,N: int] :
% 7.75/5.66 ( ( dvd_dvd_int @ K @ M )
% 7.75/5.66 => ( ( dvd_dvd_int @ K @ N )
% 7.75/5.66 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mod
% 7.75/5.66 thf(fact_1625_dvd__mod,axiom,
% 7.75/5.66 ! [K: code_integer,M: code_integer,N: code_integer] :
% 7.75/5.66 ( ( dvd_dvd_Code_integer @ K @ M )
% 7.75/5.66 => ( ( dvd_dvd_Code_integer @ K @ N )
% 7.75/5.66 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % dvd_mod
% 7.75/5.66 thf(fact_1626_mod__Suc__eq,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 7.75/5.66 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_Suc_eq
% 7.75/5.66 thf(fact_1627_mod__Suc__Suc__eq,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 7.75/5.66 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % mod_Suc_Suc_eq
% 7.75/5.66 thf(fact_1628_Nat_OlessE,axiom,
% 7.75/5.66 ! [I: nat,K: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ K )
% 7.75/5.66 => ( ( K
% 7.75/5.66 != ( suc @ I ) )
% 7.75/5.66 => ~ ! [J3: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J3 )
% 7.75/5.66 => ( K
% 7.75/5.66 != ( suc @ J3 ) ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % Nat.lessE
% 7.75/5.66 thf(fact_1629_Suc__lessD,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 7.75/5.66 => ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_lessD
% 7.75/5.66 thf(fact_1630_Suc__lessE,axiom,
% 7.75/5.66 ! [I: nat,K: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 7.75/5.66 => ~ ! [J3: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J3 )
% 7.75/5.66 => ( K
% 7.75/5.66 != ( suc @ J3 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_lessE
% 7.75/5.66 thf(fact_1631_Suc__lessI,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M @ N )
% 7.75/5.66 => ( ( ( suc @ M )
% 7.75/5.66 != N )
% 7.75/5.66 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_lessI
% 7.75/5.66 thf(fact_1632_less__SucE,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 7.75/5.66 => ( ~ ( ord_less_nat @ M @ N )
% 7.75/5.66 => ( M = N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_SucE
% 7.75/5.66 thf(fact_1633_less__SucI,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M @ N )
% 7.75/5.66 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_SucI
% 7.75/5.66 thf(fact_1634_Ex__less__Suc,axiom,
% 7.75/5.66 ! [N: nat,P: nat > $o] :
% 7.75/5.66 ( ( ? [I2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 7.75/5.66 & ( P @ I2 ) ) )
% 7.75/5.66 = ( ( P @ N )
% 7.75/5.66 | ? [I2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I2 @ N )
% 7.75/5.66 & ( P @ I2 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % Ex_less_Suc
% 7.75/5.66 thf(fact_1635_less__Suc__eq,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 7.75/5.66 = ( ( ord_less_nat @ M @ N )
% 7.75/5.66 | ( M = N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_Suc_eq
% 7.75/5.66 thf(fact_1636_not__less__eq,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ~ ( ord_less_nat @ M @ N ) )
% 7.75/5.66 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_less_eq
% 7.75/5.66 thf(fact_1637_Nat_OAll__less__Suc,axiom,
% 7.75/5.66 ! [N: nat,P: nat > $o] :
% 7.75/5.66 ( ( ! [I2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 7.75/5.66 => ( P @ I2 ) ) )
% 7.75/5.66 = ( ( P @ N )
% 7.75/5.66 & ! [I2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I2 @ N )
% 7.75/5.66 => ( P @ I2 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % Nat.All_less_Suc
% 7.75/5.66 thf(fact_1638_Suc__less__eq2,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.66 = ( ? [M5: nat] :
% 7.75/5.66 ( ( M
% 7.75/5.66 = ( suc @ M5 ) )
% 7.75/5.66 & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_less_eq2
% 7.75/5.66 thf(fact_1639_less__antisym,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ~ ( ord_less_nat @ N @ M )
% 7.75/5.66 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 7.75/5.66 => ( M = N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_antisym
% 7.75/5.66 thf(fact_1640_Suc__less__SucD,axiom,
% 7.75/5.66 ! [M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 7.75/5.66 => ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.66
% 7.75/5.66 % Suc_less_SucD
% 7.75/5.66 thf(fact_1641_less__trans__Suc,axiom,
% 7.75/5.66 ! [I: nat,J: nat,K: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J )
% 7.75/5.66 => ( ( ord_less_nat @ J @ K )
% 7.75/5.66 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_trans_Suc
% 7.75/5.66 thf(fact_1642_less__Suc__induct,axiom,
% 7.75/5.66 ! [I: nat,J: nat,P: nat > nat > $o] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J )
% 7.75/5.66 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 7.75/5.66 => ( ! [I3: nat,J3: nat,K2: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I3 @ J3 )
% 7.75/5.66 => ( ( ord_less_nat @ J3 @ K2 )
% 7.75/5.66 => ( ( P @ I3 @ J3 )
% 7.75/5.66 => ( ( P @ J3 @ K2 )
% 7.75/5.66 => ( P @ I3 @ K2 ) ) ) ) )
% 7.75/5.66 => ( P @ I @ J ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_Suc_induct
% 7.75/5.66 thf(fact_1643_strict__inc__induct,axiom,
% 7.75/5.66 ! [I: nat,J: nat,P: nat > $o] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J )
% 7.75/5.66 => ( ! [I3: nat] :
% 7.75/5.66 ( ( J
% 7.75/5.66 = ( suc @ I3 ) )
% 7.75/5.66 => ( P @ I3 ) )
% 7.75/5.66 => ( ! [I3: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I3 @ J )
% 7.75/5.66 => ( ( P @ ( suc @ I3 ) )
% 7.75/5.66 => ( P @ I3 ) ) )
% 7.75/5.66 => ( P @ I ) ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % strict_inc_induct
% 7.75/5.66 thf(fact_1644_not__less__less__Suc__eq,axiom,
% 7.75/5.66 ! [N: nat,M: nat] :
% 7.75/5.66 ( ~ ( ord_less_nat @ N @ M )
% 7.75/5.66 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 7.75/5.66 = ( N = M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % not_less_less_Suc_eq
% 7.75/5.66 thf(fact_1645_less__add__eq__less,axiom,
% 7.75/5.66 ! [K: nat,L: nat,M: nat,N: nat] :
% 7.75/5.66 ( ( ord_less_nat @ K @ L )
% 7.75/5.66 => ( ( ( plus_plus_nat @ M @ L )
% 7.75/5.66 = ( plus_plus_nat @ K @ N ) )
% 7.75/5.66 => ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % less_add_eq_less
% 7.75/5.66 thf(fact_1646_trans__less__add2,axiom,
% 7.75/5.66 ! [I: nat,J: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J )
% 7.75/5.66 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % trans_less_add2
% 7.75/5.66 thf(fact_1647_trans__less__add1,axiom,
% 7.75/5.66 ! [I: nat,J: nat,M: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J )
% 7.75/5.66 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % trans_less_add1
% 7.75/5.66 thf(fact_1648_add__less__mono1,axiom,
% 7.75/5.66 ! [I: nat,J: nat,K: nat] :
% 7.75/5.66 ( ( ord_less_nat @ I @ J )
% 7.75/5.66 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 7.75/5.66
% 7.75/5.66 % add_less_mono1
% 7.75/5.66 thf(fact_1649_not__add__less2,axiom,
% 7.75/5.66 ! [J: nat,I: nat] :
% 7.75/5.66 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 7.75/5.66
% 7.75/5.66 % not_add_less2
% 7.75/5.66 thf(fact_1650_not__add__less1,axiom,
% 7.75/5.66 ! [I: nat,J: nat] :
% 7.75/5.66 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 7.75/5.66
% 7.75/5.66 % not_add_less1
% 7.75/5.66 thf(fact_1651_add__less__mono,axiom,
% 7.75/5.66 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.67 ( ( ord_less_nat @ I @ J )
% 7.75/5.67 => ( ( ord_less_nat @ K @ L )
% 7.75/5.67 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_less_mono
% 7.75/5.67 thf(fact_1652_add__lessD1,axiom,
% 7.75/5.67 ! [I: nat,J: nat,K: nat] :
% 7.75/5.67 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 7.75/5.67 => ( ord_less_nat @ I @ K ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_lessD1
% 7.75/5.67 thf(fact_1653_cong__exp__iff__simps_I9_J,axiom,
% 7.75/5.67 ! [M: num,Q3: num,N: num] :
% 7.75/5.67 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.67 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 7.75/5.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(9)
% 7.75/5.67 thf(fact_1654_cong__exp__iff__simps_I9_J,axiom,
% 7.75/5.67 ! [M: num,Q3: num,N: num] :
% 7.75/5.67 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.67 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 7.75/5.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(9)
% 7.75/5.67 thf(fact_1655_cong__exp__iff__simps_I9_J,axiom,
% 7.75/5.67 ! [M: num,Q3: num,N: num] :
% 7.75/5.67 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.67 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.67 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 7.75/5.67 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(9)
% 7.75/5.67 thf(fact_1656_cong__exp__iff__simps_I4_J,axiom,
% 7.75/5.67 ! [M: num,N: num] :
% 7.75/5.67 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 7.75/5.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(4)
% 7.75/5.67 thf(fact_1657_cong__exp__iff__simps_I4_J,axiom,
% 7.75/5.67 ! [M: num,N: num] :
% 7.75/5.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 7.75/5.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(4)
% 7.75/5.67 thf(fact_1658_cong__exp__iff__simps_I4_J,axiom,
% 7.75/5.67 ! [M: num,N: num] :
% 7.75/5.67 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 7.75/5.67 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(4)
% 7.75/5.67 thf(fact_1659_zero__neq__numeral,axiom,
% 7.75/5.67 ! [N: num] :
% 7.75/5.67 ( zero_zero_complex
% 7.75/5.67 != ( numera6690914467698888265omplex @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_neq_numeral
% 7.75/5.67 thf(fact_1660_zero__neq__numeral,axiom,
% 7.75/5.67 ! [N: num] :
% 7.75/5.67 ( zero_zero_real
% 7.75/5.67 != ( numeral_numeral_real @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_neq_numeral
% 7.75/5.67 thf(fact_1661_zero__neq__numeral,axiom,
% 7.75/5.67 ! [N: num] :
% 7.75/5.67 ( zero_zero_rat
% 7.75/5.67 != ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_neq_numeral
% 7.75/5.67 thf(fact_1662_zero__neq__numeral,axiom,
% 7.75/5.67 ! [N: num] :
% 7.75/5.67 ( zero_zero_nat
% 7.75/5.67 != ( numeral_numeral_nat @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_neq_numeral
% 7.75/5.67 thf(fact_1663_zero__neq__numeral,axiom,
% 7.75/5.67 ! [N: num] :
% 7.75/5.67 ( zero_zero_int
% 7.75/5.67 != ( numeral_numeral_int @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_neq_numeral
% 7.75/5.67 thf(fact_1664_mult__not__zero,axiom,
% 7.75/5.67 ! [A: rat,B: rat] :
% 7.75/5.67 ( ( ( times_times_rat @ A @ B )
% 7.75/5.67 != zero_zero_rat )
% 7.75/5.67 => ( ( A != zero_zero_rat )
% 7.75/5.67 & ( B != zero_zero_rat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_not_zero
% 7.75/5.67 thf(fact_1665_mult__not__zero,axiom,
% 7.75/5.67 ! [A: real,B: real] :
% 7.75/5.67 ( ( ( times_times_real @ A @ B )
% 7.75/5.67 != zero_zero_real )
% 7.75/5.67 => ( ( A != zero_zero_real )
% 7.75/5.67 & ( B != zero_zero_real ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_not_zero
% 7.75/5.67 thf(fact_1666_mult__not__zero,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( ( times_times_nat @ A @ B )
% 7.75/5.67 != zero_zero_nat )
% 7.75/5.67 => ( ( A != zero_zero_nat )
% 7.75/5.67 & ( B != zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_not_zero
% 7.75/5.67 thf(fact_1667_mult__not__zero,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( ( times_times_int @ A @ B )
% 7.75/5.67 != zero_zero_int )
% 7.75/5.67 => ( ( A != zero_zero_int )
% 7.75/5.67 & ( B != zero_zero_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_not_zero
% 7.75/5.67 thf(fact_1668_mult__not__zero,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( ( times_3573771949741848930nteger @ A @ B )
% 7.75/5.67 != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.67 & ( B != zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_not_zero
% 7.75/5.67 thf(fact_1669_mult__not__zero,axiom,
% 7.75/5.67 ! [A: complex,B: complex] :
% 7.75/5.67 ( ( ( times_times_complex @ A @ B )
% 7.75/5.67 != zero_zero_complex )
% 7.75/5.67 => ( ( A != zero_zero_complex )
% 7.75/5.67 & ( B != zero_zero_complex ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_not_zero
% 7.75/5.67 thf(fact_1670_divisors__zero,axiom,
% 7.75/5.67 ! [A: rat,B: rat] :
% 7.75/5.67 ( ( ( times_times_rat @ A @ B )
% 7.75/5.67 = zero_zero_rat )
% 7.75/5.67 => ( ( A = zero_zero_rat )
% 7.75/5.67 | ( B = zero_zero_rat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divisors_zero
% 7.75/5.67 thf(fact_1671_divisors__zero,axiom,
% 7.75/5.67 ! [A: real,B: real] :
% 7.75/5.67 ( ( ( times_times_real @ A @ B )
% 7.75/5.67 = zero_zero_real )
% 7.75/5.67 => ( ( A = zero_zero_real )
% 7.75/5.67 | ( B = zero_zero_real ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divisors_zero
% 7.75/5.67 thf(fact_1672_divisors__zero,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( ( times_times_nat @ A @ B )
% 7.75/5.67 = zero_zero_nat )
% 7.75/5.67 => ( ( A = zero_zero_nat )
% 7.75/5.67 | ( B = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divisors_zero
% 7.75/5.67 thf(fact_1673_divisors__zero,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( ( times_times_int @ A @ B )
% 7.75/5.67 = zero_zero_int )
% 7.75/5.67 => ( ( A = zero_zero_int )
% 7.75/5.67 | ( B = zero_zero_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divisors_zero
% 7.75/5.67 thf(fact_1674_divisors__zero,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( ( times_3573771949741848930nteger @ A @ B )
% 7.75/5.67 = zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( A = zero_z3403309356797280102nteger )
% 7.75/5.67 | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divisors_zero
% 7.75/5.67 thf(fact_1675_divisors__zero,axiom,
% 7.75/5.67 ! [A: complex,B: complex] :
% 7.75/5.67 ( ( ( times_times_complex @ A @ B )
% 7.75/5.67 = zero_zero_complex )
% 7.75/5.67 => ( ( A = zero_zero_complex )
% 7.75/5.67 | ( B = zero_zero_complex ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divisors_zero
% 7.75/5.67 thf(fact_1676_no__zero__divisors,axiom,
% 7.75/5.67 ! [A: rat,B: rat] :
% 7.75/5.67 ( ( A != zero_zero_rat )
% 7.75/5.67 => ( ( B != zero_zero_rat )
% 7.75/5.67 => ( ( times_times_rat @ A @ B )
% 7.75/5.67 != zero_zero_rat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % no_zero_divisors
% 7.75/5.67 thf(fact_1677_no__zero__divisors,axiom,
% 7.75/5.67 ! [A: real,B: real] :
% 7.75/5.67 ( ( A != zero_zero_real )
% 7.75/5.67 => ( ( B != zero_zero_real )
% 7.75/5.67 => ( ( times_times_real @ A @ B )
% 7.75/5.67 != zero_zero_real ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % no_zero_divisors
% 7.75/5.67 thf(fact_1678_no__zero__divisors,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( A != zero_zero_nat )
% 7.75/5.67 => ( ( B != zero_zero_nat )
% 7.75/5.67 => ( ( times_times_nat @ A @ B )
% 7.75/5.67 != zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % no_zero_divisors
% 7.75/5.67 thf(fact_1679_no__zero__divisors,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( A != zero_zero_int )
% 7.75/5.67 => ( ( B != zero_zero_int )
% 7.75/5.67 => ( ( times_times_int @ A @ B )
% 7.75/5.67 != zero_zero_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % no_zero_divisors
% 7.75/5.67 thf(fact_1680_no__zero__divisors,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( B != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( times_3573771949741848930nteger @ A @ B )
% 7.75/5.67 != zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % no_zero_divisors
% 7.75/5.67 thf(fact_1681_no__zero__divisors,axiom,
% 7.75/5.67 ! [A: complex,B: complex] :
% 7.75/5.67 ( ( A != zero_zero_complex )
% 7.75/5.67 => ( ( B != zero_zero_complex )
% 7.75/5.67 => ( ( times_times_complex @ A @ B )
% 7.75/5.67 != zero_zero_complex ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % no_zero_divisors
% 7.75/5.67 thf(fact_1682_mult__left__cancel,axiom,
% 7.75/5.67 ! [C: rat,A: rat,B: rat] :
% 7.75/5.67 ( ( C != zero_zero_rat )
% 7.75/5.67 => ( ( ( times_times_rat @ C @ A )
% 7.75/5.67 = ( times_times_rat @ C @ B ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_left_cancel
% 7.75/5.67 thf(fact_1683_mult__left__cancel,axiom,
% 7.75/5.67 ! [C: real,A: real,B: real] :
% 7.75/5.67 ( ( C != zero_zero_real )
% 7.75/5.67 => ( ( ( times_times_real @ C @ A )
% 7.75/5.67 = ( times_times_real @ C @ B ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_left_cancel
% 7.75/5.67 thf(fact_1684_mult__left__cancel,axiom,
% 7.75/5.67 ! [C: nat,A: nat,B: nat] :
% 7.75/5.67 ( ( C != zero_zero_nat )
% 7.75/5.67 => ( ( ( times_times_nat @ C @ A )
% 7.75/5.67 = ( times_times_nat @ C @ B ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_left_cancel
% 7.75/5.67 thf(fact_1685_mult__left__cancel,axiom,
% 7.75/5.67 ! [C: int,A: int,B: int] :
% 7.75/5.67 ( ( C != zero_zero_int )
% 7.75/5.67 => ( ( ( times_times_int @ C @ A )
% 7.75/5.67 = ( times_times_int @ C @ B ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_left_cancel
% 7.75/5.67 thf(fact_1686_mult__left__cancel,axiom,
% 7.75/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( C != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( ( times_3573771949741848930nteger @ C @ A )
% 7.75/5.67 = ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_left_cancel
% 7.75/5.67 thf(fact_1687_mult__left__cancel,axiom,
% 7.75/5.67 ! [C: complex,A: complex,B: complex] :
% 7.75/5.67 ( ( C != zero_zero_complex )
% 7.75/5.67 => ( ( ( times_times_complex @ C @ A )
% 7.75/5.67 = ( times_times_complex @ C @ B ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_left_cancel
% 7.75/5.67 thf(fact_1688_mult__right__cancel,axiom,
% 7.75/5.67 ! [C: rat,A: rat,B: rat] :
% 7.75/5.67 ( ( C != zero_zero_rat )
% 7.75/5.67 => ( ( ( times_times_rat @ A @ C )
% 7.75/5.67 = ( times_times_rat @ B @ C ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_right_cancel
% 7.75/5.67 thf(fact_1689_mult__right__cancel,axiom,
% 7.75/5.67 ! [C: real,A: real,B: real] :
% 7.75/5.67 ( ( C != zero_zero_real )
% 7.75/5.67 => ( ( ( times_times_real @ A @ C )
% 7.75/5.67 = ( times_times_real @ B @ C ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_right_cancel
% 7.75/5.67 thf(fact_1690_mult__right__cancel,axiom,
% 7.75/5.67 ! [C: nat,A: nat,B: nat] :
% 7.75/5.67 ( ( C != zero_zero_nat )
% 7.75/5.67 => ( ( ( times_times_nat @ A @ C )
% 7.75/5.67 = ( times_times_nat @ B @ C ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_right_cancel
% 7.75/5.67 thf(fact_1691_mult__right__cancel,axiom,
% 7.75/5.67 ! [C: int,A: int,B: int] :
% 7.75/5.67 ( ( C != zero_zero_int )
% 7.75/5.67 => ( ( ( times_times_int @ A @ C )
% 7.75/5.67 = ( times_times_int @ B @ C ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_right_cancel
% 7.75/5.67 thf(fact_1692_mult__right__cancel,axiom,
% 7.75/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( C != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( ( times_3573771949741848930nteger @ A @ C )
% 7.75/5.67 = ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_right_cancel
% 7.75/5.67 thf(fact_1693_mult__right__cancel,axiom,
% 7.75/5.67 ! [C: complex,A: complex,B: complex] :
% 7.75/5.67 ( ( C != zero_zero_complex )
% 7.75/5.67 => ( ( ( times_times_complex @ A @ C )
% 7.75/5.67 = ( times_times_complex @ B @ C ) )
% 7.75/5.67 = ( A = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_right_cancel
% 7.75/5.67 thf(fact_1694_mod2__eq__if,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_nat ) )
% 7.75/5.67 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod2_eq_if
% 7.75/5.67 thf(fact_1695_mod2__eq__if,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_int ) )
% 7.75/5.67 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod2_eq_if
% 7.75/5.67 thf(fact_1696_mod2__eq__if,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_z3403309356797280102nteger ) )
% 7.75/5.67 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_Code_integer ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod2_eq_if
% 7.75/5.67 thf(fact_1697_parity__cases,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 != zero_zero_nat ) )
% 7.75/5.67 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 != one_one_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % parity_cases
% 7.75/5.67 thf(fact_1698_parity__cases,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 != zero_zero_int ) )
% 7.75/5.67 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 != one_one_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % parity_cases
% 7.75/5.67 thf(fact_1699_parity__cases,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 != zero_z3403309356797280102nteger ) )
% 7.75/5.67 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 != one_one_Code_integer ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % parity_cases
% 7.75/5.67 thf(fact_1700_dvd__unit__imp__unit,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.67 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_unit_imp_unit
% 7.75/5.67 thf(fact_1701_dvd__unit__imp__unit,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ A @ B )
% 7.75/5.67 => ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_unit_imp_unit
% 7.75/5.67 thf(fact_1702_unit__imp__dvd,axiom,
% 7.75/5.67 ! [B: nat,A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( dvd_dvd_nat @ B @ A ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_imp_dvd
% 7.75/5.67 thf(fact_1703_unit__imp__dvd,axiom,
% 7.75/5.67 ! [B: int,A: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( dvd_dvd_int @ B @ A ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_imp_dvd
% 7.75/5.67 thf(fact_1704_one__dvd,axiom,
% 7.75/5.67 ! [A: assn] : ( dvd_dvd_assn @ one_one_assn @ A ) ).
% 7.75/5.67
% 7.75/5.67 % one_dvd
% 7.75/5.67 thf(fact_1705_one__dvd,axiom,
% 7.75/5.67 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 7.75/5.67
% 7.75/5.67 % one_dvd
% 7.75/5.67 thf(fact_1706_one__dvd,axiom,
% 7.75/5.67 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 7.75/5.67
% 7.75/5.67 % one_dvd
% 7.75/5.67 thf(fact_1707_one__dvd,axiom,
% 7.75/5.67 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 7.75/5.67
% 7.75/5.67 % one_dvd
% 7.75/5.67 thf(fact_1708_one__dvd,axiom,
% 7.75/5.67 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 7.75/5.67
% 7.75/5.67 % one_dvd
% 7.75/5.67 thf(fact_1709_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 7.75/5.67 ! [A: rat,N: nat] :
% 7.75/5.67 ( ( A != zero_zero_rat )
% 7.75/5.67 => ( ( power_power_rat @ A @ N )
% 7.75/5.67 != zero_zero_rat ) ) ).
% 7.75/5.67
% 7.75/5.67 % semiring_1_no_zero_divisors_class.power_not_zero
% 7.75/5.67 thf(fact_1710_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 7.75/5.67 ! [A: nat,N: nat] :
% 7.75/5.67 ( ( A != zero_zero_nat )
% 7.75/5.67 => ( ( power_power_nat @ A @ N )
% 7.75/5.67 != zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % semiring_1_no_zero_divisors_class.power_not_zero
% 7.75/5.67 thf(fact_1711_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 7.75/5.67 ! [A: real,N: nat] :
% 7.75/5.67 ( ( A != zero_zero_real )
% 7.75/5.67 => ( ( power_power_real @ A @ N )
% 7.75/5.67 != zero_zero_real ) ) ).
% 7.75/5.67
% 7.75/5.67 % semiring_1_no_zero_divisors_class.power_not_zero
% 7.75/5.67 thf(fact_1712_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 7.75/5.67 ! [A: int,N: nat] :
% 7.75/5.67 ( ( A != zero_zero_int )
% 7.75/5.67 => ( ( power_power_int @ A @ N )
% 7.75/5.67 != zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % semiring_1_no_zero_divisors_class.power_not_zero
% 7.75/5.67 thf(fact_1713_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 7.75/5.67 ! [A: complex,N: nat] :
% 7.75/5.67 ( ( A != zero_zero_complex )
% 7.75/5.67 => ( ( power_power_complex @ A @ N )
% 7.75/5.67 != zero_zero_complex ) ) ).
% 7.75/5.67
% 7.75/5.67 % semiring_1_no_zero_divisors_class.power_not_zero
% 7.75/5.67 thf(fact_1714_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 7.75/5.67 ! [A: code_integer,N: nat] :
% 7.75/5.67 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( power_8256067586552552935nteger @ A @ N )
% 7.75/5.67 != zero_z3403309356797280102nteger ) ) ).
% 7.75/5.67
% 7.75/5.67 % semiring_1_no_zero_divisors_class.power_not_zero
% 7.75/5.67 thf(fact_1715_divmod__digit__0_I1_J,axiom,
% 7.75/5.67 ! [B: nat,A: nat] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.67 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 7.75/5.67 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 7.75/5.67 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divmod_digit_0(1)
% 7.75/5.67 thf(fact_1716_divmod__digit__0_I1_J,axiom,
% 7.75/5.67 ! [B: int,A: int] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.67 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 7.75/5.67 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 7.75/5.67 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divmod_digit_0(1)
% 7.75/5.67 thf(fact_1717_divmod__digit__0_I1_J,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer] :
% 7.75/5.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.67 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 7.75/5.67 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 7.75/5.67 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divmod_digit_0(1)
% 7.75/5.67 thf(fact_1718_list__decode_Ocases,axiom,
% 7.75/5.67 ! [X: nat] :
% 7.75/5.67 ( ( X != zero_zero_nat )
% 7.75/5.67 => ~ ! [N2: nat] :
% 7.75/5.67 ( X
% 7.75/5.67 != ( suc @ N2 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % list_decode.cases
% 7.75/5.67 thf(fact_1719_nat_Odistinct_I1_J,axiom,
% 7.75/5.67 ! [X22: nat] :
% 7.75/5.67 ( zero_zero_nat
% 7.75/5.67 != ( suc @ X22 ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat.distinct(1)
% 7.75/5.67 thf(fact_1720_old_Onat_Odistinct_I2_J,axiom,
% 7.75/5.67 ! [Nat2: nat] :
% 7.75/5.67 ( ( suc @ Nat2 )
% 7.75/5.67 != zero_zero_nat ) ).
% 7.75/5.67
% 7.75/5.67 % old.nat.distinct(2)
% 7.75/5.67 thf(fact_1721_old_Onat_Odistinct_I1_J,axiom,
% 7.75/5.67 ! [Nat2: nat] :
% 7.75/5.67 ( zero_zero_nat
% 7.75/5.67 != ( suc @ Nat2 ) ) ).
% 7.75/5.67
% 7.75/5.67 % old.nat.distinct(1)
% 7.75/5.67 thf(fact_1722_nat_OdiscI,axiom,
% 7.75/5.67 ! [Nat: nat,X22: nat] :
% 7.75/5.67 ( ( Nat
% 7.75/5.67 = ( suc @ X22 ) )
% 7.75/5.67 => ( Nat != zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat.discI
% 7.75/5.67 thf(fact_1723_old_Onat_Oexhaust,axiom,
% 7.75/5.67 ! [Y: nat] :
% 7.75/5.67 ( ( Y != zero_zero_nat )
% 7.75/5.67 => ~ ! [Nat3: nat] :
% 7.75/5.67 ( Y
% 7.75/5.67 != ( suc @ Nat3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % old.nat.exhaust
% 7.75/5.67 thf(fact_1724_nat__induct,axiom,
% 7.75/5.67 ! [P: nat > $o,N: nat] :
% 7.75/5.67 ( ( P @ zero_zero_nat )
% 7.75/5.67 => ( ! [N2: nat] :
% 7.75/5.67 ( ( P @ N2 )
% 7.75/5.67 => ( P @ ( suc @ N2 ) ) )
% 7.75/5.67 => ( P @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_induct
% 7.75/5.67 thf(fact_1725_diff__induct,axiom,
% 7.75/5.67 ! [P: nat > nat > $o,M: nat,N: nat] :
% 7.75/5.67 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 7.75/5.67 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 7.75/5.67 => ( ! [X3: nat,Y3: nat] :
% 7.75/5.67 ( ( P @ X3 @ Y3 )
% 7.75/5.67 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 7.75/5.67 => ( P @ M @ N ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % diff_induct
% 7.75/5.67 thf(fact_1726_zero__induct,axiom,
% 7.75/5.67 ! [P: nat > $o,K: nat] :
% 7.75/5.67 ( ( P @ K )
% 7.75/5.67 => ( ! [N2: nat] :
% 7.75/5.67 ( ( P @ ( suc @ N2 ) )
% 7.75/5.67 => ( P @ N2 ) )
% 7.75/5.67 => ( P @ zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_induct
% 7.75/5.67 thf(fact_1727_Suc__neq__Zero,axiom,
% 7.75/5.67 ! [M: nat] :
% 7.75/5.67 ( ( suc @ M )
% 7.75/5.67 != zero_zero_nat ) ).
% 7.75/5.67
% 7.75/5.67 % Suc_neq_Zero
% 7.75/5.67 thf(fact_1728_Zero__neq__Suc,axiom,
% 7.75/5.67 ! [M: nat] :
% 7.75/5.67 ( zero_zero_nat
% 7.75/5.67 != ( suc @ M ) ) ).
% 7.75/5.67
% 7.75/5.67 % Zero_neq_Suc
% 7.75/5.67 thf(fact_1729_Zero__not__Suc,axiom,
% 7.75/5.67 ! [M: nat] :
% 7.75/5.67 ( zero_zero_nat
% 7.75/5.67 != ( suc @ M ) ) ).
% 7.75/5.67
% 7.75/5.67 % Zero_not_Suc
% 7.75/5.67 thf(fact_1730_not0__implies__Suc,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( N != zero_zero_nat )
% 7.75/5.67 => ? [M2: nat] :
% 7.75/5.67 ( N
% 7.75/5.67 = ( suc @ M2 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % not0_implies_Suc
% 7.75/5.67 thf(fact_1731_dvd__0__left,axiom,
% 7.75/5.67 ! [A: complex] :
% 7.75/5.67 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 7.75/5.67 => ( A = zero_zero_complex ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_0_left
% 7.75/5.67 thf(fact_1732_dvd__0__left,axiom,
% 7.75/5.67 ! [A: real] :
% 7.75/5.67 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 7.75/5.67 => ( A = zero_zero_real ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_0_left
% 7.75/5.67 thf(fact_1733_dvd__0__left,axiom,
% 7.75/5.67 ! [A: rat] :
% 7.75/5.67 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 7.75/5.67 => ( A = zero_zero_rat ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_0_left
% 7.75/5.67 thf(fact_1734_dvd__0__left,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 7.75/5.67 => ( A = zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_0_left
% 7.75/5.67 thf(fact_1735_dvd__0__left,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 7.75/5.67 => ( A = zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_0_left
% 7.75/5.67 thf(fact_1736_dvd__field__iff,axiom,
% 7.75/5.67 ( dvd_dvd_complex
% 7.75/5.67 = ( ^ [A3: complex,B4: complex] :
% 7.75/5.67 ( ( A3 = zero_zero_complex )
% 7.75/5.67 => ( B4 = zero_zero_complex ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_field_iff
% 7.75/5.67 thf(fact_1737_dvd__field__iff,axiom,
% 7.75/5.67 ( dvd_dvd_real
% 7.75/5.67 = ( ^ [A3: real,B4: real] :
% 7.75/5.67 ( ( A3 = zero_zero_real )
% 7.75/5.67 => ( B4 = zero_zero_real ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_field_iff
% 7.75/5.67 thf(fact_1738_dvd__field__iff,axiom,
% 7.75/5.67 ( dvd_dvd_rat
% 7.75/5.67 = ( ^ [A3: rat,B4: rat] :
% 7.75/5.67 ( ( A3 = zero_zero_rat )
% 7.75/5.67 => ( B4 = zero_zero_rat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_field_iff
% 7.75/5.67 thf(fact_1739_nat__mult__1,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( times_times_nat @ one_one_nat @ N )
% 7.75/5.67 = N ) ).
% 7.75/5.67
% 7.75/5.67 % nat_mult_1
% 7.75/5.67 thf(fact_1740_nat__mult__1__right,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( times_times_nat @ N @ one_one_nat )
% 7.75/5.67 = N ) ).
% 7.75/5.67
% 7.75/5.67 % nat_mult_1_right
% 7.75/5.67 thf(fact_1741_add__eq__self__zero,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ( plus_plus_nat @ M @ N )
% 7.75/5.67 = M )
% 7.75/5.67 => ( N = zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_eq_self_zero
% 7.75/5.67 thf(fact_1742_Euclid__induct,axiom,
% 7.75/5.67 ! [P: nat > nat > $o,A: nat,B: nat] :
% 7.75/5.67 ( ! [A5: nat,B2: nat] :
% 7.75/5.67 ( ( P @ A5 @ B2 )
% 7.75/5.67 = ( P @ B2 @ A5 ) )
% 7.75/5.67 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 7.75/5.67 => ( ! [A5: nat,B2: nat] :
% 7.75/5.67 ( ( P @ A5 @ B2 )
% 7.75/5.67 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B2 ) ) )
% 7.75/5.67 => ( P @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % Euclid_induct
% 7.75/5.67 thf(fact_1743_plus__nat_Oadd__0,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 7.75/5.67 = N ) ).
% 7.75/5.67
% 7.75/5.67 % plus_nat.add_0
% 7.75/5.67 thf(fact_1744_assn__one__left,axiom,
% 7.75/5.67 ! [P: assn] :
% 7.75/5.67 ( ( times_times_assn @ one_one_assn @ P )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % assn_one_left
% 7.75/5.67 thf(fact_1745_nat__mult__eq__cancel__disj,axiom,
% 7.75/5.67 ! [K: nat,M: nat,N: nat] :
% 7.75/5.67 ( ( ( times_times_nat @ K @ M )
% 7.75/5.67 = ( times_times_nat @ K @ N ) )
% 7.75/5.67 = ( ( K = zero_zero_nat )
% 7.75/5.67 | ( M = N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_mult_eq_cancel_disj
% 7.75/5.67 thf(fact_1746_mult__0,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( times_times_nat @ zero_zero_nat @ N )
% 7.75/5.67 = zero_zero_nat ) ).
% 7.75/5.67
% 7.75/5.67 % mult_0
% 7.75/5.67 thf(fact_1747_nat__mod__eq__iff,axiom,
% 7.75/5.67 ! [X: nat,N: nat,Y: nat] :
% 7.75/5.67 ( ( ( modulo_modulo_nat @ X @ N )
% 7.75/5.67 = ( modulo_modulo_nat @ Y @ N ) )
% 7.75/5.67 = ( ? [Q1: nat,Q22: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 7.75/5.67 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_mod_eq_iff
% 7.75/5.67 thf(fact_1748_gcd__nat_Oextremum__uniqueI,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 7.75/5.67 => ( A = zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % gcd_nat.extremum_uniqueI
% 7.75/5.67 thf(fact_1749_gcd__nat_Onot__eq__extremum,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( A != zero_zero_nat )
% 7.75/5.67 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 7.75/5.67 & ( A != zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % gcd_nat.not_eq_extremum
% 7.75/5.67 thf(fact_1750_gcd__nat_Oextremum__unique,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 7.75/5.67 = ( A = zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % gcd_nat.extremum_unique
% 7.75/5.67 thf(fact_1751_gcd__nat_Oextremum__strict,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 7.75/5.67 & ( zero_zero_nat != A ) ) ).
% 7.75/5.67
% 7.75/5.67 % gcd_nat.extremum_strict
% 7.75/5.67 thf(fact_1752_gcd__nat_Oextremum,axiom,
% 7.75/5.67 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 7.75/5.67
% 7.75/5.67 % gcd_nat.extremum
% 7.75/5.67 thf(fact_1753_divide__less__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [B: real,C: real,W: num] :
% 7.75/5.67 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 7.75/5.67 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.67 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 7.75/5.67 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.67 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.67 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 7.75/5.67 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.67 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_less_eq_numeral(1)
% 7.75/5.67 thf(fact_1754_divide__less__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [B: rat,C: rat,W: num] :
% 7.75/5.67 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 7.75/5.67 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.67 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 7.75/5.67 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.67 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.67 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 7.75/5.67 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.67 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_less_eq_numeral(1)
% 7.75/5.67 thf(fact_1755_less__divide__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [W: num,B: real,C: real] :
% 7.75/5.67 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 7.75/5.67 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.67 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 7.75/5.67 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.67 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.67 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 7.75/5.67 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.67 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_divide_eq_numeral(1)
% 7.75/5.67 thf(fact_1756_less__divide__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [W: num,B: rat,C: rat] :
% 7.75/5.67 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.67 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.67 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 7.75/5.67 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.67 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.67 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 7.75/5.67 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.67 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_divide_eq_numeral(1)
% 7.75/5.67 thf(fact_1757_pos2,axiom,
% 7.75/5.67 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 7.75/5.67
% 7.75/5.67 % pos2
% 7.75/5.67 thf(fact_1758_is__unitE,axiom,
% 7.75/5.67 ! [A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.67 => ~ ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.67 => ! [B2: code_integer] :
% 7.75/5.67 ( ( B2 != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ B2 @ one_one_Code_integer )
% 7.75/5.67 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 7.75/5.67 = B2 )
% 7.75/5.67 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B2 )
% 7.75/5.67 = A )
% 7.75/5.67 => ( ( ( times_3573771949741848930nteger @ A @ B2 )
% 7.75/5.67 = one_one_Code_integer )
% 7.75/5.67 => ( ( divide6298287555418463151nteger @ C @ A )
% 7.75/5.67 != ( times_3573771949741848930nteger @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unitE
% 7.75/5.67 thf(fact_1759_is__unitE,axiom,
% 7.75/5.67 ! [A: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.67 => ~ ( ( A != zero_zero_nat )
% 7.75/5.67 => ! [B2: nat] :
% 7.75/5.67 ( ( B2 != zero_zero_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ B2 @ one_one_nat )
% 7.75/5.67 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 7.75/5.67 = B2 )
% 7.75/5.67 => ( ( ( divide_divide_nat @ one_one_nat @ B2 )
% 7.75/5.67 = A )
% 7.75/5.67 => ( ( ( times_times_nat @ A @ B2 )
% 7.75/5.67 = one_one_nat )
% 7.75/5.67 => ( ( divide_divide_nat @ C @ A )
% 7.75/5.67 != ( times_times_nat @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unitE
% 7.75/5.67 thf(fact_1760_is__unitE,axiom,
% 7.75/5.67 ! [A: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.67 => ~ ( ( A != zero_zero_int )
% 7.75/5.67 => ! [B2: int] :
% 7.75/5.67 ( ( B2 != zero_zero_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ B2 @ one_one_int )
% 7.75/5.67 => ( ( ( divide_divide_int @ one_one_int @ A )
% 7.75/5.67 = B2 )
% 7.75/5.67 => ( ( ( divide_divide_int @ one_one_int @ B2 )
% 7.75/5.67 = A )
% 7.75/5.67 => ( ( ( times_times_int @ A @ B2 )
% 7.75/5.67 = one_one_int )
% 7.75/5.67 => ( ( divide_divide_int @ C @ A )
% 7.75/5.67 != ( times_times_int @ C @ B2 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unitE
% 7.75/5.67 thf(fact_1761_is__unit__div__mult__cancel__left,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 7.75/5.67 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_div_mult_cancel_left
% 7.75/5.67 thf(fact_1762_is__unit__div__mult__cancel__left,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( A != zero_zero_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 7.75/5.67 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_div_mult_cancel_left
% 7.75/5.67 thf(fact_1763_is__unit__div__mult__cancel__left,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( A != zero_zero_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 7.75/5.67 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_div_mult_cancel_left
% 7.75/5.67 thf(fact_1764_is__unit__div__mult__cancel__right,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 7.75/5.67 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_div_mult_cancel_right
% 7.75/5.67 thf(fact_1765_is__unit__div__mult__cancel__right,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( A != zero_zero_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 7.75/5.67 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_div_mult_cancel_right
% 7.75/5.67 thf(fact_1766_is__unit__div__mult__cancel__right,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( A != zero_zero_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 7.75/5.67 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_div_mult_cancel_right
% 7.75/5.67 thf(fact_1767_split__div,axiom,
% 7.75/5.67 ! [P: nat > $o,M: nat,N: nat] :
% 7.75/5.67 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 7.75/5.67 = ( ( ( N = zero_zero_nat )
% 7.75/5.67 => ( P @ zero_zero_nat ) )
% 7.75/5.67 & ( ( N != zero_zero_nat )
% 7.75/5.67 => ! [I2: nat,J2: nat] :
% 7.75/5.67 ( ( ord_less_nat @ J2 @ N )
% 7.75/5.67 => ( ( M
% 7.75/5.67 = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J2 ) )
% 7.75/5.67 => ( P @ I2 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_div
% 7.75/5.67 thf(fact_1768_dividend__less__div__times,axiom,
% 7.75/5.67 ! [N: nat,M: nat] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.67 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dividend_less_div_times
% 7.75/5.67 thf(fact_1769_dividend__less__times__div,axiom,
% 7.75/5.67 ! [N: nat,M: nat] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.67 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dividend_less_times_div
% 7.75/5.67 thf(fact_1770_zero__less__power__eq,axiom,
% 7.75/5.67 ! [A: code_integer,N: nat] :
% 7.75/5.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.67 = ( ( N = zero_zero_nat )
% 7.75/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 & ( A != zero_z3403309356797280102nteger ) )
% 7.75/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_less_power_eq
% 7.75/5.67 thf(fact_1771_zero__less__power__eq,axiom,
% 7.75/5.67 ! [A: real,N: nat] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 7.75/5.67 = ( ( N = zero_zero_nat )
% 7.75/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 & ( A != zero_zero_real ) )
% 7.75/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_less_power_eq
% 7.75/5.67 thf(fact_1772_zero__less__power__eq,axiom,
% 7.75/5.67 ! [A: rat,N: nat] :
% 7.75/5.67 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 7.75/5.67 = ( ( N = zero_zero_nat )
% 7.75/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 & ( A != zero_zero_rat ) )
% 7.75/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_less_power_eq
% 7.75/5.67 thf(fact_1773_zero__less__power__eq,axiom,
% 7.75/5.67 ! [A: int,N: nat] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 7.75/5.67 = ( ( N = zero_zero_nat )
% 7.75/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 & ( A != zero_zero_int ) )
% 7.75/5.67 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zero_less_power_eq
% 7.75/5.67 thf(fact_1774_odd__iff__mod__2__eq__one,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 7.75/5.67 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % odd_iff_mod_2_eq_one
% 7.75/5.67 thf(fact_1775_odd__iff__mod__2__eq__one,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 7.75/5.67 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % odd_iff_mod_2_eq_one
% 7.75/5.67 thf(fact_1776_odd__iff__mod__2__eq__one,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 7.75/5.67 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_Code_integer ) ) ).
% 7.75/5.67
% 7.75/5.67 % odd_iff_mod_2_eq_one
% 7.75/5.67 thf(fact_1777_even__iff__mod__2__eq__zero,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_iff_mod_2_eq_zero
% 7.75/5.67 thf(fact_1778_even__iff__mod__2__eq__zero,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_iff_mod_2_eq_zero
% 7.75/5.67 thf(fact_1779_even__iff__mod__2__eq__zero,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_iff_mod_2_eq_zero
% 7.75/5.67 thf(fact_1780_cong__exp__iff__simps_I8_J,axiom,
% 7.75/5.67 ! [M: num,Q3: num] :
% 7.75/5.67 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.67 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(8)
% 7.75/5.67 thf(fact_1781_cong__exp__iff__simps_I8_J,axiom,
% 7.75/5.67 ! [M: num,Q3: num] :
% 7.75/5.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.67 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(8)
% 7.75/5.67 thf(fact_1782_cong__exp__iff__simps_I8_J,axiom,
% 7.75/5.67 ! [M: num,Q3: num] :
% 7.75/5.67 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.67 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(8)
% 7.75/5.67 thf(fact_1783_cong__exp__iff__simps_I6_J,axiom,
% 7.75/5.67 ! [Q3: num,N: num] :
% 7.75/5.67 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.67 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(6)
% 7.75/5.67 thf(fact_1784_cong__exp__iff__simps_I6_J,axiom,
% 7.75/5.67 ! [Q3: num,N: num] :
% 7.75/5.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.67 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(6)
% 7.75/5.67 thf(fact_1785_cong__exp__iff__simps_I6_J,axiom,
% 7.75/5.67 ! [Q3: num,N: num] :
% 7.75/5.67 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.67 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % cong_exp_iff_simps(6)
% 7.75/5.67 thf(fact_1786_mod__eqE,axiom,
% 7.75/5.67 ! [A: int,C: int,B: int] :
% 7.75/5.67 ( ( ( modulo_modulo_int @ A @ C )
% 7.75/5.67 = ( modulo_modulo_int @ B @ C ) )
% 7.75/5.67 => ~ ! [D3: int] :
% 7.75/5.67 ( B
% 7.75/5.67 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_eqE
% 7.75/5.67 thf(fact_1787_mod__eqE,axiom,
% 7.75/5.67 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.67 ( ( ( modulo364778990260209775nteger @ A @ C )
% 7.75/5.67 = ( modulo364778990260209775nteger @ B @ C ) )
% 7.75/5.67 => ~ ! [D3: code_integer] :
% 7.75/5.67 ( B
% 7.75/5.67 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_eqE
% 7.75/5.67 thf(fact_1788_div__add1__eq,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 7.75/5.67 = ( 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 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_add1_eq
% 7.75/5.67 thf(fact_1789_div__add1__eq,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.67 = ( 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 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_add1_eq
% 7.75/5.67 thf(fact_1790_div__add1__eq,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.67 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_add1_eq
% 7.75/5.67 thf(fact_1791_half__gt__zero,axiom,
% 7.75/5.67 ! [A: real] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.67 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % half_gt_zero
% 7.75/5.67 thf(fact_1792_half__gt__zero,axiom,
% 7.75/5.67 ! [A: rat] :
% 7.75/5.67 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.67 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % half_gt_zero
% 7.75/5.67 thf(fact_1793_half__gt__zero__iff,axiom,
% 7.75/5.67 ! [A: real] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.67 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 7.75/5.67
% 7.75/5.67 % half_gt_zero_iff
% 7.75/5.67 thf(fact_1794_half__gt__zero__iff,axiom,
% 7.75/5.67 ! [A: rat] :
% 7.75/5.67 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 7.75/5.67 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.67
% 7.75/5.67 % half_gt_zero_iff
% 7.75/5.67 thf(fact_1795_power2__less__0,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ~ ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_z3403309356797280102nteger ) ).
% 7.75/5.67
% 7.75/5.67 % power2_less_0
% 7.75/5.67 thf(fact_1796_power2__less__0,axiom,
% 7.75/5.67 ! [A: real] :
% 7.75/5.67 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 7.75/5.67
% 7.75/5.67 % power2_less_0
% 7.75/5.67 thf(fact_1797_power2__less__0,axiom,
% 7.75/5.67 ! [A: rat] :
% 7.75/5.67 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 7.75/5.67
% 7.75/5.67 % power2_less_0
% 7.75/5.67 thf(fact_1798_power2__less__0,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 7.75/5.67
% 7.75/5.67 % power2_less_0
% 7.75/5.67 thf(fact_1799_less__2__cases,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 => ( ( N = zero_zero_nat )
% 7.75/5.67 | ( N
% 7.75/5.67 = ( suc @ zero_zero_nat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_2_cases
% 7.75/5.67 thf(fact_1800_less__2__cases__iff,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = ( ( N = zero_zero_nat )
% 7.75/5.67 | ( N
% 7.75/5.67 = ( suc @ zero_zero_nat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_2_cases_iff
% 7.75/5.67 thf(fact_1801_odd__pos,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % odd_pos
% 7.75/5.67 thf(fact_1802_nat__induct2,axiom,
% 7.75/5.67 ! [P: nat > $o,N: nat] :
% 7.75/5.67 ( ( P @ zero_zero_nat )
% 7.75/5.67 => ( ( P @ one_one_nat )
% 7.75/5.67 => ( ! [N2: nat] :
% 7.75/5.67 ( ( P @ N2 )
% 7.75/5.67 => ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.67 => ( P @ N ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_induct2
% 7.75/5.67 thf(fact_1803_div__mod__decomp,axiom,
% 7.75/5.67 ! [A2: nat,N: nat] :
% 7.75/5.67 ( A2
% 7.75/5.67 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_mod_decomp
% 7.75/5.67 thf(fact_1804_one__plus__numeral__commute,axiom,
% 7.75/5.67 ! [X: num] :
% 7.75/5.67 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 7.75/5.67 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_plus_numeral_commute
% 7.75/5.67 thf(fact_1805_one__plus__numeral__commute,axiom,
% 7.75/5.67 ! [X: num] :
% 7.75/5.67 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 7.75/5.67 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_plus_numeral_commute
% 7.75/5.67 thf(fact_1806_one__plus__numeral__commute,axiom,
% 7.75/5.67 ! [X: num] :
% 7.75/5.67 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 7.75/5.67 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_plus_numeral_commute
% 7.75/5.67 thf(fact_1807_one__plus__numeral__commute,axiom,
% 7.75/5.67 ! [X: num] :
% 7.75/5.67 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 7.75/5.67 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_plus_numeral_commute
% 7.75/5.67 thf(fact_1808_one__plus__numeral__commute,axiom,
% 7.75/5.67 ! [X: num] :
% 7.75/5.67 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 7.75/5.67 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_plus_numeral_commute
% 7.75/5.67 thf(fact_1809_numeral__One,axiom,
% 7.75/5.67 ( ( numera6690914467698888265omplex @ one )
% 7.75/5.67 = one_one_complex ) ).
% 7.75/5.67
% 7.75/5.67 % numeral_One
% 7.75/5.67 thf(fact_1810_numeral__One,axiom,
% 7.75/5.67 ( ( numeral_numeral_real @ one )
% 7.75/5.67 = one_one_real ) ).
% 7.75/5.67
% 7.75/5.67 % numeral_One
% 7.75/5.67 thf(fact_1811_numeral__One,axiom,
% 7.75/5.67 ( ( numeral_numeral_rat @ one )
% 7.75/5.67 = one_one_rat ) ).
% 7.75/5.67
% 7.75/5.67 % numeral_One
% 7.75/5.67 thf(fact_1812_numeral__One,axiom,
% 7.75/5.67 ( ( numeral_numeral_nat @ one )
% 7.75/5.67 = one_one_nat ) ).
% 7.75/5.67
% 7.75/5.67 % numeral_One
% 7.75/5.67 thf(fact_1813_numeral__One,axiom,
% 7.75/5.67 ( ( numeral_numeral_int @ one )
% 7.75/5.67 = one_one_int ) ).
% 7.75/5.67
% 7.75/5.67 % numeral_One
% 7.75/5.67 thf(fact_1814_less__imp__Suc__add,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ord_less_nat @ M @ N )
% 7.75/5.67 => ? [K2: nat] :
% 7.75/5.67 ( N
% 7.75/5.67 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_imp_Suc_add
% 7.75/5.67 thf(fact_1815_less__iff__Suc__add,axiom,
% 7.75/5.67 ( ord_less_nat
% 7.75/5.67 = ( ^ [M4: nat,N3: nat] :
% 7.75/5.67 ? [K3: nat] :
% 7.75/5.67 ( N3
% 7.75/5.67 = ( suc @ ( plus_plus_nat @ M4 @ K3 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_iff_Suc_add
% 7.75/5.67 thf(fact_1816_less__add__Suc2,axiom,
% 7.75/5.67 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_add_Suc2
% 7.75/5.67 thf(fact_1817_less__add__Suc1,axiom,
% 7.75/5.67 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_add_Suc1
% 7.75/5.67 thf(fact_1818_less__natE,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ord_less_nat @ M @ N )
% 7.75/5.67 => ~ ! [Q5: nat] :
% 7.75/5.67 ( N
% 7.75/5.67 != ( suc @ ( plus_plus_nat @ M @ Q5 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_natE
% 7.75/5.67 thf(fact_1819_left__right__inverse__power,axiom,
% 7.75/5.67 ! [X: rat,Y: rat,N: nat] :
% 7.75/5.67 ( ( ( times_times_rat @ X @ Y )
% 7.75/5.67 = one_one_rat )
% 7.75/5.67 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 7.75/5.67 = one_one_rat ) ) ).
% 7.75/5.67
% 7.75/5.67 % left_right_inverse_power
% 7.75/5.67 thf(fact_1820_left__right__inverse__power,axiom,
% 7.75/5.67 ! [X: assn,Y: assn,N: nat] :
% 7.75/5.67 ( ( ( times_times_assn @ X @ Y )
% 7.75/5.67 = one_one_assn )
% 7.75/5.67 => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ ( power_power_assn @ Y @ N ) )
% 7.75/5.67 = one_one_assn ) ) ).
% 7.75/5.67
% 7.75/5.67 % left_right_inverse_power
% 7.75/5.67 thf(fact_1821_left__right__inverse__power,axiom,
% 7.75/5.67 ! [X: real,Y: real,N: nat] :
% 7.75/5.67 ( ( ( times_times_real @ X @ Y )
% 7.75/5.67 = one_one_real )
% 7.75/5.67 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 7.75/5.67 = one_one_real ) ) ).
% 7.75/5.67
% 7.75/5.67 % left_right_inverse_power
% 7.75/5.67 thf(fact_1822_left__right__inverse__power,axiom,
% 7.75/5.67 ! [X: nat,Y: nat,N: nat] :
% 7.75/5.67 ( ( ( times_times_nat @ X @ Y )
% 7.75/5.67 = one_one_nat )
% 7.75/5.67 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 7.75/5.67 = one_one_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % left_right_inverse_power
% 7.75/5.67 thf(fact_1823_left__right__inverse__power,axiom,
% 7.75/5.67 ! [X: int,Y: int,N: nat] :
% 7.75/5.67 ( ( ( times_times_int @ X @ Y )
% 7.75/5.67 = one_one_int )
% 7.75/5.67 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 7.75/5.67 = one_one_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % left_right_inverse_power
% 7.75/5.67 thf(fact_1824_left__right__inverse__power,axiom,
% 7.75/5.67 ! [X: code_integer,Y: code_integer,N: nat] :
% 7.75/5.67 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 7.75/5.67 = one_one_Code_integer )
% 7.75/5.67 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 7.75/5.67 = one_one_Code_integer ) ) ).
% 7.75/5.67
% 7.75/5.67 % left_right_inverse_power
% 7.75/5.67 thf(fact_1825_left__right__inverse__power,axiom,
% 7.75/5.67 ! [X: complex,Y: complex,N: nat] :
% 7.75/5.67 ( ( ( times_times_complex @ X @ Y )
% 7.75/5.67 = one_one_complex )
% 7.75/5.67 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 7.75/5.67 = one_one_complex ) ) ).
% 7.75/5.67
% 7.75/5.67 % left_right_inverse_power
% 7.75/5.67 thf(fact_1826_Suc__mult__less__cancel1,axiom,
% 7.75/5.67 ! [K: nat,M: nat,N: nat] :
% 7.75/5.67 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 7.75/5.67 = ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % Suc_mult_less_cancel1
% 7.75/5.67 thf(fact_1827_power__one__over,axiom,
% 7.75/5.67 ! [A: complex,N: nat] :
% 7.75/5.67 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 7.75/5.67 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % power_one_over
% 7.75/5.67 thf(fact_1828_power__one__over,axiom,
% 7.75/5.67 ! [A: real,N: nat] :
% 7.75/5.67 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 7.75/5.67 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % power_one_over
% 7.75/5.67 thf(fact_1829_power__one__over,axiom,
% 7.75/5.67 ! [A: rat,N: nat] :
% 7.75/5.67 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 7.75/5.67 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % power_one_over
% 7.75/5.67 thf(fact_1830_unit__mult__right__cancel,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.67 => ( ( ( times_times_nat @ B @ A )
% 7.75/5.67 = ( times_times_nat @ C @ A ) )
% 7.75/5.67 = ( B = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_mult_right_cancel
% 7.75/5.67 thf(fact_1831_unit__mult__right__cancel,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.67 => ( ( ( times_times_int @ B @ A )
% 7.75/5.67 = ( times_times_int @ C @ A ) )
% 7.75/5.67 = ( B = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_mult_right_cancel
% 7.75/5.67 thf(fact_1832_unit__mult__right__cancel,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.67 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 7.75/5.67 = ( times_3573771949741848930nteger @ C @ A ) )
% 7.75/5.67 = ( B = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_mult_right_cancel
% 7.75/5.67 thf(fact_1833_unit__mult__left__cancel,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.67 => ( ( ( times_times_nat @ A @ B )
% 7.75/5.67 = ( times_times_nat @ A @ C ) )
% 7.75/5.67 = ( B = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_mult_left_cancel
% 7.75/5.67 thf(fact_1834_unit__mult__left__cancel,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.67 => ( ( ( times_times_int @ A @ B )
% 7.75/5.67 = ( times_times_int @ A @ C ) )
% 7.75/5.67 = ( B = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_mult_left_cancel
% 7.75/5.67 thf(fact_1835_unit__mult__left__cancel,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.67 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 7.75/5.67 = ( times_3573771949741848930nteger @ A @ C ) )
% 7.75/5.67 = ( B = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_mult_left_cancel
% 7.75/5.67 thf(fact_1836_mult__unit__dvd__iff_H,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_unit_dvd_iff'
% 7.75/5.67 thf(fact_1837_mult__unit__dvd__iff_H,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_unit_dvd_iff'
% 7.75/5.67 thf(fact_1838_mult__unit__dvd__iff_H,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_unit_dvd_iff'
% 7.75/5.67 thf(fact_1839_dvd__mult__unit__iff_H,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 7.75/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_mult_unit_iff'
% 7.75/5.67 thf(fact_1840_dvd__mult__unit__iff_H,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 7.75/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_mult_unit_iff'
% 7.75/5.67 thf(fact_1841_dvd__mult__unit__iff_H,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_mult_unit_iff'
% 7.75/5.67 thf(fact_1842_mult__unit__dvd__iff,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_unit_dvd_iff
% 7.75/5.67 thf(fact_1843_mult__unit__dvd__iff,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_unit_dvd_iff
% 7.75/5.67 thf(fact_1844_mult__unit__dvd__iff,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_unit_dvd_iff
% 7.75/5.67 thf(fact_1845_dvd__mult__unit__iff,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 7.75/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_mult_unit_iff
% 7.75/5.67 thf(fact_1846_dvd__mult__unit__iff,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 7.75/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_mult_unit_iff
% 7.75/5.67 thf(fact_1847_dvd__mult__unit__iff,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.67 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_mult_unit_iff
% 7.75/5.67 thf(fact_1848_is__unit__mult__iff,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 7.75/5.67 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.67 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_mult_iff
% 7.75/5.67 thf(fact_1849_is__unit__mult__iff,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 7.75/5.67 = ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.67 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_mult_iff
% 7.75/5.67 thf(fact_1850_is__unit__mult__iff,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 7.75/5.67 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 7.75/5.67 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_mult_iff
% 7.75/5.67 thf(fact_1851_dvd__div__unit__iff,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 7.75/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_unit_iff
% 7.75/5.67 thf(fact_1852_dvd__div__unit__iff,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 7.75/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_unit_iff
% 7.75/5.67 thf(fact_1853_div__unit__dvd__iff,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_unit_dvd_iff
% 7.75/5.67 thf(fact_1854_div__unit__dvd__iff,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_unit_dvd_iff
% 7.75/5.67 thf(fact_1855_unit__div__cancel,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 7.75/5.67 => ( ( ( divide_divide_nat @ B @ A )
% 7.75/5.67 = ( divide_divide_nat @ C @ A ) )
% 7.75/5.67 = ( B = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_div_cancel
% 7.75/5.67 thf(fact_1856_unit__div__cancel,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ A @ one_one_int )
% 7.75/5.67 => ( ( ( divide_divide_int @ B @ A )
% 7.75/5.67 = ( divide_divide_int @ C @ A ) )
% 7.75/5.67 = ( B = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_div_cancel
% 7.75/5.67 thf(fact_1857_frac__eq__eq,axiom,
% 7.75/5.67 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 7.75/5.67 ( ( Y != zero_zero_complex )
% 7.75/5.67 => ( ( Z != zero_zero_complex )
% 7.75/5.67 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 7.75/5.67 = ( divide1717551699836669952omplex @ W @ Z ) )
% 7.75/5.67 = ( ( times_times_complex @ X @ Z )
% 7.75/5.67 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % frac_eq_eq
% 7.75/5.67 thf(fact_1858_frac__eq__eq,axiom,
% 7.75/5.67 ! [Y: real,Z: real,X: real,W: real] :
% 7.75/5.67 ( ( Y != zero_zero_real )
% 7.75/5.67 => ( ( Z != zero_zero_real )
% 7.75/5.67 => ( ( ( divide_divide_real @ X @ Y )
% 7.75/5.67 = ( divide_divide_real @ W @ Z ) )
% 7.75/5.67 = ( ( times_times_real @ X @ Z )
% 7.75/5.67 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % frac_eq_eq
% 7.75/5.67 thf(fact_1859_frac__eq__eq,axiom,
% 7.75/5.67 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 7.75/5.67 ( ( Y != zero_zero_rat )
% 7.75/5.67 => ( ( Z != zero_zero_rat )
% 7.75/5.67 => ( ( ( divide_divide_rat @ X @ Y )
% 7.75/5.67 = ( divide_divide_rat @ W @ Z ) )
% 7.75/5.67 = ( ( times_times_rat @ X @ Z )
% 7.75/5.67 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % frac_eq_eq
% 7.75/5.67 thf(fact_1860_divide__eq__eq,axiom,
% 7.75/5.67 ! [B: complex,C: complex,A: complex] :
% 7.75/5.67 ( ( ( divide1717551699836669952omplex @ B @ C )
% 7.75/5.67 = A )
% 7.75/5.67 = ( ( ( C != zero_zero_complex )
% 7.75/5.67 => ( B
% 7.75/5.67 = ( times_times_complex @ A @ C ) ) )
% 7.75/5.67 & ( ( C = zero_zero_complex )
% 7.75/5.67 => ( A = zero_zero_complex ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_eq_eq
% 7.75/5.67 thf(fact_1861_divide__eq__eq,axiom,
% 7.75/5.67 ! [B: real,C: real,A: real] :
% 7.75/5.67 ( ( ( divide_divide_real @ B @ C )
% 7.75/5.67 = A )
% 7.75/5.67 = ( ( ( C != zero_zero_real )
% 7.75/5.67 => ( B
% 7.75/5.67 = ( times_times_real @ A @ C ) ) )
% 7.75/5.67 & ( ( C = zero_zero_real )
% 7.75/5.67 => ( A = zero_zero_real ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_eq_eq
% 7.75/5.67 thf(fact_1862_divide__eq__eq,axiom,
% 7.75/5.67 ! [B: rat,C: rat,A: rat] :
% 7.75/5.67 ( ( ( divide_divide_rat @ B @ C )
% 7.75/5.67 = A )
% 7.75/5.67 = ( ( ( C != zero_zero_rat )
% 7.75/5.67 => ( B
% 7.75/5.67 = ( times_times_rat @ A @ C ) ) )
% 7.75/5.67 & ( ( C = zero_zero_rat )
% 7.75/5.67 => ( A = zero_zero_rat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_eq_eq
% 7.75/5.67 thf(fact_1863_eq__divide__eq,axiom,
% 7.75/5.67 ! [A: complex,B: complex,C: complex] :
% 7.75/5.67 ( ( A
% 7.75/5.67 = ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.67 = ( ( ( C != zero_zero_complex )
% 7.75/5.67 => ( ( times_times_complex @ A @ C )
% 7.75/5.67 = B ) )
% 7.75/5.67 & ( ( C = zero_zero_complex )
% 7.75/5.67 => ( A = zero_zero_complex ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % eq_divide_eq
% 7.75/5.67 thf(fact_1864_eq__divide__eq,axiom,
% 7.75/5.67 ! [A: real,B: real,C: real] :
% 7.75/5.67 ( ( A
% 7.75/5.67 = ( divide_divide_real @ B @ C ) )
% 7.75/5.67 = ( ( ( C != zero_zero_real )
% 7.75/5.67 => ( ( times_times_real @ A @ C )
% 7.75/5.67 = B ) )
% 7.75/5.67 & ( ( C = zero_zero_real )
% 7.75/5.67 => ( A = zero_zero_real ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % eq_divide_eq
% 7.75/5.67 thf(fact_1865_eq__divide__eq,axiom,
% 7.75/5.67 ! [A: rat,B: rat,C: rat] :
% 7.75/5.67 ( ( A
% 7.75/5.67 = ( divide_divide_rat @ B @ C ) )
% 7.75/5.67 = ( ( ( C != zero_zero_rat )
% 7.75/5.67 => ( ( times_times_rat @ A @ C )
% 7.75/5.67 = B ) )
% 7.75/5.67 & ( ( C = zero_zero_rat )
% 7.75/5.67 => ( A = zero_zero_rat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % eq_divide_eq
% 7.75/5.67 thf(fact_1866_divide__eq__imp,axiom,
% 7.75/5.67 ! [C: complex,B: complex,A: complex] :
% 7.75/5.67 ( ( C != zero_zero_complex )
% 7.75/5.67 => ( ( B
% 7.75/5.67 = ( times_times_complex @ A @ C ) )
% 7.75/5.67 => ( ( divide1717551699836669952omplex @ B @ C )
% 7.75/5.67 = A ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_eq_imp
% 7.75/5.67 thf(fact_1867_divide__eq__imp,axiom,
% 7.75/5.67 ! [C: real,B: real,A: real] :
% 7.75/5.67 ( ( C != zero_zero_real )
% 7.75/5.67 => ( ( B
% 7.75/5.67 = ( times_times_real @ A @ C ) )
% 7.75/5.67 => ( ( divide_divide_real @ B @ C )
% 7.75/5.67 = A ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_eq_imp
% 7.75/5.67 thf(fact_1868_divide__eq__imp,axiom,
% 7.75/5.67 ! [C: rat,B: rat,A: rat] :
% 7.75/5.67 ( ( C != zero_zero_rat )
% 7.75/5.67 => ( ( B
% 7.75/5.67 = ( times_times_rat @ A @ C ) )
% 7.75/5.67 => ( ( divide_divide_rat @ B @ C )
% 7.75/5.67 = A ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_eq_imp
% 7.75/5.67 thf(fact_1869_eq__divide__imp,axiom,
% 7.75/5.67 ! [C: complex,A: complex,B: complex] :
% 7.75/5.67 ( ( C != zero_zero_complex )
% 7.75/5.67 => ( ( ( times_times_complex @ A @ C )
% 7.75/5.67 = B )
% 7.75/5.67 => ( A
% 7.75/5.67 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % eq_divide_imp
% 7.75/5.67 thf(fact_1870_eq__divide__imp,axiom,
% 7.75/5.67 ! [C: real,A: real,B: real] :
% 7.75/5.67 ( ( C != zero_zero_real )
% 7.75/5.67 => ( ( ( times_times_real @ A @ C )
% 7.75/5.67 = B )
% 7.75/5.67 => ( A
% 7.75/5.67 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % eq_divide_imp
% 7.75/5.67 thf(fact_1871_eq__divide__imp,axiom,
% 7.75/5.67 ! [C: rat,A: rat,B: rat] :
% 7.75/5.67 ( ( C != zero_zero_rat )
% 7.75/5.67 => ( ( ( times_times_rat @ A @ C )
% 7.75/5.67 = B )
% 7.75/5.67 => ( A
% 7.75/5.67 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % eq_divide_imp
% 7.75/5.67 thf(fact_1872_nonzero__divide__eq__eq,axiom,
% 7.75/5.67 ! [C: complex,B: complex,A: complex] :
% 7.75/5.67 ( ( C != zero_zero_complex )
% 7.75/5.67 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 7.75/5.67 = A )
% 7.75/5.67 = ( B
% 7.75/5.67 = ( times_times_complex @ A @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nonzero_divide_eq_eq
% 7.75/5.67 thf(fact_1873_nonzero__divide__eq__eq,axiom,
% 7.75/5.67 ! [C: real,B: real,A: real] :
% 7.75/5.67 ( ( C != zero_zero_real )
% 7.75/5.67 => ( ( ( divide_divide_real @ B @ C )
% 7.75/5.67 = A )
% 7.75/5.67 = ( B
% 7.75/5.67 = ( times_times_real @ A @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nonzero_divide_eq_eq
% 7.75/5.67 thf(fact_1874_nonzero__divide__eq__eq,axiom,
% 7.75/5.67 ! [C: rat,B: rat,A: rat] :
% 7.75/5.67 ( ( C != zero_zero_rat )
% 7.75/5.67 => ( ( ( divide_divide_rat @ B @ C )
% 7.75/5.67 = A )
% 7.75/5.67 = ( B
% 7.75/5.67 = ( times_times_rat @ A @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nonzero_divide_eq_eq
% 7.75/5.67 thf(fact_1875_nonzero__eq__divide__eq,axiom,
% 7.75/5.67 ! [C: complex,A: complex,B: complex] :
% 7.75/5.67 ( ( C != zero_zero_complex )
% 7.75/5.67 => ( ( A
% 7.75/5.67 = ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.67 = ( ( times_times_complex @ A @ C )
% 7.75/5.67 = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nonzero_eq_divide_eq
% 7.75/5.67 thf(fact_1876_nonzero__eq__divide__eq,axiom,
% 7.75/5.67 ! [C: real,A: real,B: real] :
% 7.75/5.67 ( ( C != zero_zero_real )
% 7.75/5.67 => ( ( A
% 7.75/5.67 = ( divide_divide_real @ B @ C ) )
% 7.75/5.67 = ( ( times_times_real @ A @ C )
% 7.75/5.67 = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nonzero_eq_divide_eq
% 7.75/5.67 thf(fact_1877_nonzero__eq__divide__eq,axiom,
% 7.75/5.67 ! [C: rat,A: rat,B: rat] :
% 7.75/5.67 ( ( C != zero_zero_rat )
% 7.75/5.67 => ( ( A
% 7.75/5.67 = ( divide_divide_rat @ B @ C ) )
% 7.75/5.67 = ( ( times_times_rat @ A @ C )
% 7.75/5.67 = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nonzero_eq_divide_eq
% 7.75/5.67 thf(fact_1878_numerals_I1_J,axiom,
% 7.75/5.67 ( ( numeral_numeral_nat @ one )
% 7.75/5.67 = one_one_nat ) ).
% 7.75/5.67
% 7.75/5.67 % numerals(1)
% 7.75/5.67 thf(fact_1879_less__mult__imp__div__less,axiom,
% 7.75/5.67 ! [M: nat,I: nat,N: nat] :
% 7.75/5.67 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 7.75/5.67 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 7.75/5.67
% 7.75/5.67 % less_mult_imp_div_less
% 7.75/5.67 thf(fact_1880_Suc__eq__plus1__left,axiom,
% 7.75/5.67 ( suc
% 7.75/5.67 = ( plus_plus_nat @ one_one_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % Suc_eq_plus1_left
% 7.75/5.67 thf(fact_1881_plus__1__eq__Suc,axiom,
% 7.75/5.67 ( ( plus_plus_nat @ one_one_nat )
% 7.75/5.67 = suc ) ).
% 7.75/5.67
% 7.75/5.67 % plus_1_eq_Suc
% 7.75/5.67 thf(fact_1882_Suc__eq__plus1,axiom,
% 7.75/5.67 ( suc
% 7.75/5.67 = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % Suc_eq_plus1
% 7.75/5.67 thf(fact_1883_dvd__div__eq__0__iff,axiom,
% 7.75/5.67 ! [B: complex,A: complex] :
% 7.75/5.67 ( ( dvd_dvd_complex @ B @ A )
% 7.75/5.67 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 7.75/5.67 = zero_zero_complex )
% 7.75/5.67 = ( A = zero_zero_complex ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_eq_0_iff
% 7.75/5.67 thf(fact_1884_dvd__div__eq__0__iff,axiom,
% 7.75/5.67 ! [B: real,A: real] :
% 7.75/5.67 ( ( dvd_dvd_real @ B @ A )
% 7.75/5.67 => ( ( ( divide_divide_real @ A @ B )
% 7.75/5.67 = zero_zero_real )
% 7.75/5.67 = ( A = zero_zero_real ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_eq_0_iff
% 7.75/5.67 thf(fact_1885_dvd__div__eq__0__iff,axiom,
% 7.75/5.67 ! [B: rat,A: rat] :
% 7.75/5.67 ( ( dvd_dvd_rat @ B @ A )
% 7.75/5.67 => ( ( ( divide_divide_rat @ A @ B )
% 7.75/5.67 = zero_zero_rat )
% 7.75/5.67 = ( A = zero_zero_rat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_eq_0_iff
% 7.75/5.67 thf(fact_1886_dvd__div__eq__0__iff,axiom,
% 7.75/5.67 ! [B: nat,A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.67 => ( ( ( divide_divide_nat @ A @ B )
% 7.75/5.67 = zero_zero_nat )
% 7.75/5.67 = ( A = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_eq_0_iff
% 7.75/5.67 thf(fact_1887_dvd__div__eq__0__iff,axiom,
% 7.75/5.67 ! [B: int,A: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ A )
% 7.75/5.67 => ( ( ( divide_divide_int @ A @ B )
% 7.75/5.67 = zero_zero_int )
% 7.75/5.67 = ( A = zero_zero_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_eq_0_iff
% 7.75/5.67 thf(fact_1888_one__is__add,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ( suc @ zero_zero_nat )
% 7.75/5.67 = ( plus_plus_nat @ M @ N ) )
% 7.75/5.67 = ( ( ( M
% 7.75/5.67 = ( suc @ zero_zero_nat ) )
% 7.75/5.67 & ( N = zero_zero_nat ) )
% 7.75/5.67 | ( ( M = zero_zero_nat )
% 7.75/5.67 & ( N
% 7.75/5.67 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_is_add
% 7.75/5.67 thf(fact_1889_add__is__1,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ( plus_plus_nat @ M @ N )
% 7.75/5.67 = ( suc @ zero_zero_nat ) )
% 7.75/5.67 = ( ( ( M
% 7.75/5.67 = ( suc @ zero_zero_nat ) )
% 7.75/5.67 & ( N = zero_zero_nat ) )
% 7.75/5.67 | ( ( M = zero_zero_nat )
% 7.75/5.67 & ( N
% 7.75/5.67 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_is_1
% 7.75/5.67 thf(fact_1890_bits__stable__imp__add__self,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = A )
% 7.75/5.67 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.67 = zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % bits_stable_imp_add_self
% 7.75/5.67 thf(fact_1891_bits__stable__imp__add__self,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = A )
% 7.75/5.67 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 7.75/5.67 = zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % bits_stable_imp_add_self
% 7.75/5.67 thf(fact_1892_bits__stable__imp__add__self,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 = A )
% 7.75/5.67 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 7.75/5.67 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.67
% 7.75/5.67 % bits_stable_imp_add_self
% 7.75/5.67 thf(fact_1893_pow_Osimps_I1_J,axiom,
% 7.75/5.67 ! [X: num] :
% 7.75/5.67 ( ( pow @ X @ one )
% 7.75/5.67 = X ) ).
% 7.75/5.67
% 7.75/5.67 % pow.simps(1)
% 7.75/5.67 thf(fact_1894_not__sum__power2__lt__zero,axiom,
% 7.75/5.67 ! [X: code_integer,Y: code_integer] :
% 7.75/5.67 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger ) ).
% 7.75/5.67
% 7.75/5.67 % not_sum_power2_lt_zero
% 7.75/5.67 thf(fact_1895_not__sum__power2__lt__zero,axiom,
% 7.75/5.67 ! [X: real,Y: real] :
% 7.75/5.67 ~ ( 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 ) ).
% 7.75/5.67
% 7.75/5.67 % not_sum_power2_lt_zero
% 7.75/5.67 thf(fact_1896_not__sum__power2__lt__zero,axiom,
% 7.75/5.67 ! [X: rat,Y: rat] :
% 7.75/5.67 ~ ( 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 ) ).
% 7.75/5.67
% 7.75/5.67 % not_sum_power2_lt_zero
% 7.75/5.67 thf(fact_1897_not__sum__power2__lt__zero,axiom,
% 7.75/5.67 ! [X: int,Y: int] :
% 7.75/5.67 ~ ( 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 ) ).
% 7.75/5.67
% 7.75/5.67 % not_sum_power2_lt_zero
% 7.75/5.67 thf(fact_1898_sum__power2__gt__zero__iff,axiom,
% 7.75/5.67 ! [X: code_integer,Y: code_integer] :
% 7.75/5.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.67 = ( ( X != zero_z3403309356797280102nteger )
% 7.75/5.67 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % sum_power2_gt_zero_iff
% 7.75/5.67 thf(fact_1899_sum__power2__gt__zero__iff,axiom,
% 7.75/5.67 ! [X: real,Y: real] :
% 7.75/5.67 ( ( 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 ) ) ) ) )
% 7.75/5.67 = ( ( X != zero_zero_real )
% 7.75/5.67 | ( Y != zero_zero_real ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % sum_power2_gt_zero_iff
% 7.75/5.67 thf(fact_1900_sum__power2__gt__zero__iff,axiom,
% 7.75/5.67 ! [X: rat,Y: rat] :
% 7.75/5.67 ( ( 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 ) ) ) ) )
% 7.75/5.67 = ( ( X != zero_zero_rat )
% 7.75/5.67 | ( Y != zero_zero_rat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % sum_power2_gt_zero_iff
% 7.75/5.67 thf(fact_1901_sum__power2__gt__zero__iff,axiom,
% 7.75/5.67 ! [X: int,Y: int] :
% 7.75/5.67 ( ( 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 ) ) ) ) )
% 7.75/5.67 = ( ( X != zero_zero_int )
% 7.75/5.67 | ( Y != zero_zero_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % sum_power2_gt_zero_iff
% 7.75/5.67 thf(fact_1902_div__2__gt__zero,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.75/5.67 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_2_gt_zero
% 7.75/5.67 thf(fact_1903_Suc__n__div__2__gt__zero,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.67 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % Suc_n_div_2_gt_zero
% 7.75/5.67 thf(fact_1904_nat__bit__induct,axiom,
% 7.75/5.67 ! [P: nat > $o,N: nat] :
% 7.75/5.67 ( ( P @ zero_zero_nat )
% 7.75/5.67 => ( ! [N2: nat] :
% 7.75/5.67 ( ( P @ N2 )
% 7.75/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 7.75/5.67 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 7.75/5.67 => ( ! [N2: nat] :
% 7.75/5.67 ( ( P @ N2 )
% 7.75/5.67 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 7.75/5.67 => ( P @ N ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_bit_induct
% 7.75/5.67 thf(fact_1905_VEBT__internal_OT__vebt__buildupi_Osimps_I2_J,axiom,
% 7.75/5.67 ( ( vEBT_V441764108873111860ildupi @ ( suc @ zero_zero_nat ) )
% 7.75/5.67 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % VEBT_internal.T_vebt_buildupi.simps(2)
% 7.75/5.67 thf(fact_1906_VEBT__internal_OT__vebt__buildupi_Osimps_I1_J,axiom,
% 7.75/5.67 ( ( vEBT_V441764108873111860ildupi @ zero_zero_nat )
% 7.75/5.67 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % VEBT_internal.T_vebt_buildupi.simps(1)
% 7.75/5.67 thf(fact_1907_cancel__div__mod__rules_I2_J,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 7.75/5.67 = ( plus_plus_nat @ A @ C ) ) ).
% 7.75/5.67
% 7.75/5.67 % cancel_div_mod_rules(2)
% 7.75/5.67 thf(fact_1908_cancel__div__mod__rules_I2_J,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 7.75/5.67 = ( plus_plus_int @ A @ C ) ) ).
% 7.75/5.67
% 7.75/5.67 % cancel_div_mod_rules(2)
% 7.75/5.67 thf(fact_1909_cancel__div__mod__rules_I2_J,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 7.75/5.67
% 7.75/5.67 % cancel_div_mod_rules(2)
% 7.75/5.67 thf(fact_1910_cancel__div__mod__rules_I1_J,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 7.75/5.67 = ( plus_plus_nat @ A @ C ) ) ).
% 7.75/5.67
% 7.75/5.67 % cancel_div_mod_rules(1)
% 7.75/5.67 thf(fact_1911_cancel__div__mod__rules_I1_J,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 7.75/5.67 = ( plus_plus_int @ A @ C ) ) ).
% 7.75/5.67
% 7.75/5.67 % cancel_div_mod_rules(1)
% 7.75/5.67 thf(fact_1912_cancel__div__mod__rules_I1_J,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.67 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 7.75/5.67
% 7.75/5.67 % cancel_div_mod_rules(1)
% 7.75/5.67 thf(fact_1913_mod__div__decomp,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( A
% 7.75/5.67 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_div_decomp
% 7.75/5.67 thf(fact_1914_mod__div__decomp,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( A
% 7.75/5.67 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_div_decomp
% 7.75/5.67 thf(fact_1915_mod__div__decomp,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( A
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_div_decomp
% 7.75/5.67 thf(fact_1916_div__mult__mod__eq,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % div_mult_mod_eq
% 7.75/5.67 thf(fact_1917_div__mult__mod__eq,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % div_mult_mod_eq
% 7.75/5.67 thf(fact_1918_div__mult__mod__eq,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % div_mult_mod_eq
% 7.75/5.67 thf(fact_1919_mod__div__mult__eq,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % mod_div_mult_eq
% 7.75/5.67 thf(fact_1920_mod__div__mult__eq,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % mod_div_mult_eq
% 7.75/5.67 thf(fact_1921_mod__div__mult__eq,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % mod_div_mult_eq
% 7.75/5.67 thf(fact_1922_mod__mult__div__eq,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % mod_mult_div_eq
% 7.75/5.67 thf(fact_1923_mod__mult__div__eq,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % mod_mult_div_eq
% 7.75/5.67 thf(fact_1924_mod__mult__div__eq,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % mod_mult_div_eq
% 7.75/5.67 thf(fact_1925_mult__div__mod__eq,axiom,
% 7.75/5.67 ! [B: nat,A: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % mult_div_mod_eq
% 7.75/5.67 thf(fact_1926_mult__div__mod__eq,axiom,
% 7.75/5.67 ! [B: int,A: int] :
% 7.75/5.67 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % mult_div_mod_eq
% 7.75/5.67 thf(fact_1927_mult__div__mod__eq,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer] :
% 7.75/5.67 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 7.75/5.67 = A ) ).
% 7.75/5.67
% 7.75/5.67 % mult_div_mod_eq
% 7.75/5.67 thf(fact_1928_div__mult1__eq,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 7.75/5.67 = ( 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 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_mult1_eq
% 7.75/5.67 thf(fact_1929_div__mult1__eq,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 7.75/5.67 = ( 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 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_mult1_eq
% 7.75/5.67 thf(fact_1930_div__mult1__eq,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.67 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_mult1_eq
% 7.75/5.67 thf(fact_1931_odd__power__less__zero,axiom,
% 7.75/5.67 ! [A: code_integer,N: nat] :
% 7.75/5.67 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_z3403309356797280102nteger ) ) ).
% 7.75/5.67
% 7.75/5.67 % odd_power_less_zero
% 7.75/5.67 thf(fact_1932_odd__power__less__zero,axiom,
% 7.75/5.67 ! [A: real,N: nat] :
% 7.75/5.67 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.67 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 7.75/5.67
% 7.75/5.67 % odd_power_less_zero
% 7.75/5.67 thf(fact_1933_odd__power__less__zero,axiom,
% 7.75/5.67 ! [A: rat,N: nat] :
% 7.75/5.67 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.67 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 7.75/5.67
% 7.75/5.67 % odd_power_less_zero
% 7.75/5.67 thf(fact_1934_odd__power__less__zero,axiom,
% 7.75/5.67 ! [A: int,N: nat] :
% 7.75/5.67 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.67 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % odd_power_less_zero
% 7.75/5.67 thf(fact_1935_mod__mult2__eq,axiom,
% 7.75/5.67 ! [M: nat,N: nat,Q3: nat] :
% 7.75/5.67 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q3 ) )
% 7.75/5.67 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q3 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_mult2_eq
% 7.75/5.67 thf(fact_1936_add__right__imp__eq,axiom,
% 7.75/5.67 ! [B: real,A: real,C: real] :
% 7.75/5.67 ( ( ( plus_plus_real @ B @ A )
% 7.75/5.67 = ( plus_plus_real @ C @ A ) )
% 7.75/5.67 => ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_right_imp_eq
% 7.75/5.67 thf(fact_1937_add__right__imp__eq,axiom,
% 7.75/5.67 ! [B: rat,A: rat,C: rat] :
% 7.75/5.67 ( ( ( plus_plus_rat @ B @ A )
% 7.75/5.67 = ( plus_plus_rat @ C @ A ) )
% 7.75/5.67 => ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_right_imp_eq
% 7.75/5.67 thf(fact_1938_add__right__imp__eq,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( ( plus_plus_nat @ B @ A )
% 7.75/5.67 = ( plus_plus_nat @ C @ A ) )
% 7.75/5.67 => ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_right_imp_eq
% 7.75/5.67 thf(fact_1939_add__right__imp__eq,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( ( plus_plus_int @ B @ A )
% 7.75/5.67 = ( plus_plus_int @ C @ A ) )
% 7.75/5.67 => ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_right_imp_eq
% 7.75/5.67 thf(fact_1940_add__left__imp__eq,axiom,
% 7.75/5.67 ! [A: real,B: real,C: real] :
% 7.75/5.67 ( ( ( plus_plus_real @ A @ B )
% 7.75/5.67 = ( plus_plus_real @ A @ C ) )
% 7.75/5.67 => ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_left_imp_eq
% 7.75/5.67 thf(fact_1941_add__left__imp__eq,axiom,
% 7.75/5.67 ! [A: rat,B: rat,C: rat] :
% 7.75/5.67 ( ( ( plus_plus_rat @ A @ B )
% 7.75/5.67 = ( plus_plus_rat @ A @ C ) )
% 7.75/5.67 => ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_left_imp_eq
% 7.75/5.67 thf(fact_1942_add__left__imp__eq,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( ( plus_plus_nat @ A @ B )
% 7.75/5.67 = ( plus_plus_nat @ A @ C ) )
% 7.75/5.67 => ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_left_imp_eq
% 7.75/5.67 thf(fact_1943_add__left__imp__eq,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( ( plus_plus_int @ A @ B )
% 7.75/5.67 = ( plus_plus_int @ A @ C ) )
% 7.75/5.67 => ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_left_imp_eq
% 7.75/5.67 thf(fact_1944_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 7.75/5.67 ! [B: real,A: real,C: real] :
% 7.75/5.67 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 7.75/5.67 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_add_class.add.left_commute
% 7.75/5.67 thf(fact_1945_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 7.75/5.67 ! [B: rat,A: rat,C: rat] :
% 7.75/5.67 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 7.75/5.67 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_add_class.add.left_commute
% 7.75/5.67 thf(fact_1946_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 7.75/5.67 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_add_class.add.left_commute
% 7.75/5.67 thf(fact_1947_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 7.75/5.67 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_add_class.add.left_commute
% 7.75/5.67 thf(fact_1948_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 7.75/5.67 ( plus_plus_real
% 7.75/5.67 = ( ^ [A3: real,B4: real] : ( plus_plus_real @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_add_class.add.commute
% 7.75/5.67 thf(fact_1949_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 7.75/5.67 ( plus_plus_rat
% 7.75/5.67 = ( ^ [A3: rat,B4: rat] : ( plus_plus_rat @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_add_class.add.commute
% 7.75/5.67 thf(fact_1950_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 7.75/5.67 ( plus_plus_nat
% 7.75/5.67 = ( ^ [A3: nat,B4: nat] : ( plus_plus_nat @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_add_class.add.commute
% 7.75/5.67 thf(fact_1951_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 7.75/5.67 ( plus_plus_int
% 7.75/5.67 = ( ^ [A3: int,B4: int] : ( plus_plus_int @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_add_class.add.commute
% 7.75/5.67 thf(fact_1952_add_Oright__cancel,axiom,
% 7.75/5.67 ! [B: real,A: real,C: real] :
% 7.75/5.67 ( ( ( plus_plus_real @ B @ A )
% 7.75/5.67 = ( plus_plus_real @ C @ A ) )
% 7.75/5.67 = ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.right_cancel
% 7.75/5.67 thf(fact_1953_add_Oright__cancel,axiom,
% 7.75/5.67 ! [B: rat,A: rat,C: rat] :
% 7.75/5.67 ( ( ( plus_plus_rat @ B @ A )
% 7.75/5.67 = ( plus_plus_rat @ C @ A ) )
% 7.75/5.67 = ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.right_cancel
% 7.75/5.67 thf(fact_1954_add_Oright__cancel,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( ( plus_plus_int @ B @ A )
% 7.75/5.67 = ( plus_plus_int @ C @ A ) )
% 7.75/5.67 = ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.right_cancel
% 7.75/5.67 thf(fact_1955_add_Oleft__cancel,axiom,
% 7.75/5.67 ! [A: real,B: real,C: real] :
% 7.75/5.67 ( ( ( plus_plus_real @ A @ B )
% 7.75/5.67 = ( plus_plus_real @ A @ C ) )
% 7.75/5.67 = ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.left_cancel
% 7.75/5.67 thf(fact_1956_add_Oleft__cancel,axiom,
% 7.75/5.67 ! [A: rat,B: rat,C: rat] :
% 7.75/5.67 ( ( ( plus_plus_rat @ A @ B )
% 7.75/5.67 = ( plus_plus_rat @ A @ C ) )
% 7.75/5.67 = ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.left_cancel
% 7.75/5.67 thf(fact_1957_add_Oleft__cancel,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( ( plus_plus_int @ A @ B )
% 7.75/5.67 = ( plus_plus_int @ A @ C ) )
% 7.75/5.67 = ( B = C ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.left_cancel
% 7.75/5.67 thf(fact_1958_add_Oassoc,axiom,
% 7.75/5.67 ! [A: real,B: real,C: real] :
% 7.75/5.67 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 7.75/5.67 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.assoc
% 7.75/5.67 thf(fact_1959_add_Oassoc,axiom,
% 7.75/5.67 ! [A: rat,B: rat,C: rat] :
% 7.75/5.67 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 7.75/5.67 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.assoc
% 7.75/5.67 thf(fact_1960_add_Oassoc,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 7.75/5.67 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.assoc
% 7.75/5.67 thf(fact_1961_add_Oassoc,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 7.75/5.67 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add.assoc
% 7.75/5.67 thf(fact_1962_group__cancel_Oadd2,axiom,
% 7.75/5.67 ! [B3: real,K: real,B: real,A: real] :
% 7.75/5.67 ( ( B3
% 7.75/5.67 = ( plus_plus_real @ K @ B ) )
% 7.75/5.67 => ( ( plus_plus_real @ A @ B3 )
% 7.75/5.67 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % group_cancel.add2
% 7.75/5.67 thf(fact_1963_group__cancel_Oadd2,axiom,
% 7.75/5.67 ! [B3: rat,K: rat,B: rat,A: rat] :
% 7.75/5.67 ( ( B3
% 7.75/5.67 = ( plus_plus_rat @ K @ B ) )
% 7.75/5.67 => ( ( plus_plus_rat @ A @ B3 )
% 7.75/5.67 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % group_cancel.add2
% 7.75/5.67 thf(fact_1964_group__cancel_Oadd2,axiom,
% 7.75/5.67 ! [B3: nat,K: nat,B: nat,A: nat] :
% 7.75/5.67 ( ( B3
% 7.75/5.67 = ( plus_plus_nat @ K @ B ) )
% 7.75/5.67 => ( ( plus_plus_nat @ A @ B3 )
% 7.75/5.67 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % group_cancel.add2
% 7.75/5.67 thf(fact_1965_group__cancel_Oadd2,axiom,
% 7.75/5.67 ! [B3: int,K: int,B: int,A: int] :
% 7.75/5.67 ( ( B3
% 7.75/5.67 = ( plus_plus_int @ K @ B ) )
% 7.75/5.67 => ( ( plus_plus_int @ A @ B3 )
% 7.75/5.67 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % group_cancel.add2
% 7.75/5.67 thf(fact_1966_group__cancel_Oadd1,axiom,
% 7.75/5.67 ! [A2: real,K: real,A: real,B: real] :
% 7.75/5.67 ( ( A2
% 7.75/5.67 = ( plus_plus_real @ K @ A ) )
% 7.75/5.67 => ( ( plus_plus_real @ A2 @ B )
% 7.75/5.67 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % group_cancel.add1
% 7.75/5.67 thf(fact_1967_group__cancel_Oadd1,axiom,
% 7.75/5.67 ! [A2: rat,K: rat,A: rat,B: rat] :
% 7.75/5.67 ( ( A2
% 7.75/5.67 = ( plus_plus_rat @ K @ A ) )
% 7.75/5.67 => ( ( plus_plus_rat @ A2 @ B )
% 7.75/5.67 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % group_cancel.add1
% 7.75/5.67 thf(fact_1968_group__cancel_Oadd1,axiom,
% 7.75/5.67 ! [A2: nat,K: nat,A: nat,B: nat] :
% 7.75/5.67 ( ( A2
% 7.75/5.67 = ( plus_plus_nat @ K @ A ) )
% 7.75/5.67 => ( ( plus_plus_nat @ A2 @ B )
% 7.75/5.67 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % group_cancel.add1
% 7.75/5.67 thf(fact_1969_group__cancel_Oadd1,axiom,
% 7.75/5.67 ! [A2: int,K: int,A: int,B: int] :
% 7.75/5.67 ( ( A2
% 7.75/5.67 = ( plus_plus_int @ K @ A ) )
% 7.75/5.67 => ( ( plus_plus_int @ A2 @ B )
% 7.75/5.67 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % group_cancel.add1
% 7.75/5.67 thf(fact_1970_add__mono__thms__linordered__semiring_I4_J,axiom,
% 7.75/5.67 ! [I: real,J: real,K: real,L: real] :
% 7.75/5.67 ( ( ( I = J )
% 7.75/5.67 & ( K = L ) )
% 7.75/5.67 => ( ( plus_plus_real @ I @ K )
% 7.75/5.67 = ( plus_plus_real @ J @ L ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_mono_thms_linordered_semiring(4)
% 7.75/5.67 thf(fact_1971_add__mono__thms__linordered__semiring_I4_J,axiom,
% 7.75/5.67 ! [I: rat,J: rat,K: rat,L: rat] :
% 7.75/5.67 ( ( ( I = J )
% 7.75/5.67 & ( K = L ) )
% 7.75/5.67 => ( ( plus_plus_rat @ I @ K )
% 7.75/5.67 = ( plus_plus_rat @ J @ L ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_mono_thms_linordered_semiring(4)
% 7.75/5.67 thf(fact_1972_add__mono__thms__linordered__semiring_I4_J,axiom,
% 7.75/5.67 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.67 ( ( ( I = J )
% 7.75/5.67 & ( K = L ) )
% 7.75/5.67 => ( ( plus_plus_nat @ I @ K )
% 7.75/5.67 = ( plus_plus_nat @ J @ L ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_mono_thms_linordered_semiring(4)
% 7.75/5.67 thf(fact_1973_add__mono__thms__linordered__semiring_I4_J,axiom,
% 7.75/5.67 ! [I: int,J: int,K: int,L: int] :
% 7.75/5.67 ( ( ( I = J )
% 7.75/5.67 & ( K = L ) )
% 7.75/5.67 => ( ( plus_plus_int @ I @ K )
% 7.75/5.67 = ( plus_plus_int @ J @ L ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_mono_thms_linordered_semiring(4)
% 7.75/5.67 thf(fact_1974_mult_Oassoc,axiom,
% 7.75/5.67 ! [A: assn,B: assn,C: assn] :
% 7.75/5.67 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 7.75/5.67 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult.assoc
% 7.75/5.67 thf(fact_1975_mult_Oassoc,axiom,
% 7.75/5.67 ! [A: real,B: real,C: real] :
% 7.75/5.67 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 7.75/5.67 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult.assoc
% 7.75/5.67 thf(fact_1976_mult_Oassoc,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 7.75/5.67 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult.assoc
% 7.75/5.67 thf(fact_1977_mult_Oassoc,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 7.75/5.67 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult.assoc
% 7.75/5.67 thf(fact_1978_mult_Oassoc,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.67 ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 7.75/5.67 = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult.assoc
% 7.75/5.67 thf(fact_1979_mult_Oassoc,axiom,
% 7.75/5.67 ! [A: complex,B: complex,C: complex] :
% 7.75/5.67 ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 7.75/5.67 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult.assoc
% 7.75/5.67 thf(fact_1980_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 7.75/5.67 ( times_times_assn
% 7.75/5.67 = ( ^ [A3: assn,B4: assn] : ( times_times_assn @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.commute
% 7.75/5.67 thf(fact_1981_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 7.75/5.67 ( times_times_real
% 7.75/5.67 = ( ^ [A3: real,B4: real] : ( times_times_real @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.commute
% 7.75/5.67 thf(fact_1982_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 7.75/5.67 ( times_times_nat
% 7.75/5.67 = ( ^ [A3: nat,B4: nat] : ( times_times_nat @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.commute
% 7.75/5.67 thf(fact_1983_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 7.75/5.67 ( times_times_int
% 7.75/5.67 = ( ^ [A3: int,B4: int] : ( times_times_int @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.commute
% 7.75/5.67 thf(fact_1984_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 7.75/5.67 ( times_3573771949741848930nteger
% 7.75/5.67 = ( ^ [A3: code_integer,B4: code_integer] : ( times_3573771949741848930nteger @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.commute
% 7.75/5.67 thf(fact_1985_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 7.75/5.67 ( times_times_complex
% 7.75/5.67 = ( ^ [A3: complex,B4: complex] : ( times_times_complex @ B4 @ A3 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.commute
% 7.75/5.67 thf(fact_1986_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 7.75/5.67 ! [B: assn,A: assn,C: assn] :
% 7.75/5.67 ( ( times_times_assn @ B @ ( times_times_assn @ A @ C ) )
% 7.75/5.67 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.left_commute
% 7.75/5.67 thf(fact_1987_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 7.75/5.67 ! [B: real,A: real,C: real] :
% 7.75/5.67 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 7.75/5.67 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.left_commute
% 7.75/5.67 thf(fact_1988_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 7.75/5.67 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.left_commute
% 7.75/5.67 thf(fact_1989_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 7.75/5.67 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.left_commute
% 7.75/5.67 thf(fact_1990_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( times_3573771949741848930nteger @ B @ ( times_3573771949741848930nteger @ A @ C ) )
% 7.75/5.67 = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.left_commute
% 7.75/5.67 thf(fact_1991_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 7.75/5.67 ! [B: complex,A: complex,C: complex] :
% 7.75/5.67 ( ( times_times_complex @ B @ ( times_times_complex @ A @ C ) )
% 7.75/5.67 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % ab_semigroup_mult_class.mult.left_commute
% 7.75/5.67 thf(fact_1992_unit__eq__div1,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.67 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 7.75/5.67 = C )
% 7.75/5.67 = ( A
% 7.75/5.67 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_eq_div1
% 7.75/5.67 thf(fact_1993_unit__eq__div1,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( ( divide_divide_nat @ A @ B )
% 7.75/5.67 = C )
% 7.75/5.67 = ( A
% 7.75/5.67 = ( times_times_nat @ C @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_eq_div1
% 7.75/5.67 thf(fact_1994_unit__eq__div1,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( ( divide_divide_int @ A @ B )
% 7.75/5.67 = C )
% 7.75/5.67 = ( A
% 7.75/5.67 = ( times_times_int @ C @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_eq_div1
% 7.75/5.67 thf(fact_1995_unit__eq__div2,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.67 => ( ( A
% 7.75/5.67 = ( divide6298287555418463151nteger @ C @ B ) )
% 7.75/5.67 = ( ( times_3573771949741848930nteger @ A @ B )
% 7.75/5.67 = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_eq_div2
% 7.75/5.67 thf(fact_1996_unit__eq__div2,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( A
% 7.75/5.67 = ( divide_divide_nat @ C @ B ) )
% 7.75/5.67 = ( ( times_times_nat @ A @ B )
% 7.75/5.67 = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_eq_div2
% 7.75/5.67 thf(fact_1997_unit__eq__div2,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( A
% 7.75/5.67 = ( divide_divide_int @ C @ B ) )
% 7.75/5.67 = ( ( times_times_int @ A @ B )
% 7.75/5.67 = C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_eq_div2
% 7.75/5.67 thf(fact_1998_div__mult__unit2,axiom,
% 7.75/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ B @ A )
% 7.75/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.67 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_mult_unit2
% 7.75/5.67 thf(fact_1999_div__mult__unit2,axiom,
% 7.75/5.67 ! [C: nat,B: nat,A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 7.75/5.67 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_mult_unit2
% 7.75/5.67 thf(fact_2000_div__mult__unit2,axiom,
% 7.75/5.67 ! [C: int,B: int,A: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ C @ one_one_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ B @ A )
% 7.75/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 7.75/5.67 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_mult_unit2
% 7.75/5.67 thf(fact_2001_unit__div__commute,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.67 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 7.75/5.67 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_div_commute
% 7.75/5.67 thf(fact_2002_unit__div__commute,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 7.75/5.67 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_div_commute
% 7.75/5.67 thf(fact_2003_unit__div__commute,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 7.75/5.67 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_div_commute
% 7.75/5.67 thf(fact_2004_unit__div__mult__swap,axiom,
% 7.75/5.67 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 7.75/5.67 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 7.75/5.67 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_div_mult_swap
% 7.75/5.67 thf(fact_2005_unit__div__mult__swap,axiom,
% 7.75/5.67 ! [C: nat,A: nat,B: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 7.75/5.67 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 7.75/5.67 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_div_mult_swap
% 7.75/5.67 thf(fact_2006_unit__div__mult__swap,axiom,
% 7.75/5.67 ! [C: int,A: int,B: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ C @ one_one_int )
% 7.75/5.67 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 7.75/5.67 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unit_div_mult_swap
% 7.75/5.67 thf(fact_2007_is__unit__div__mult2__eq,axiom,
% 7.75/5.67 ! [B: code_integer,C: code_integer,A: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 7.75/5.67 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.67 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_div_mult2_eq
% 7.75/5.67 thf(fact_2008_is__unit__div__mult2__eq,axiom,
% 7.75/5.67 ! [B: nat,C: nat,A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 7.75/5.67 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 7.75/5.67 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_div_mult2_eq
% 7.75/5.67 thf(fact_2009_is__unit__div__mult2__eq,axiom,
% 7.75/5.67 ! [B: int,C: int,A: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ B @ one_one_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ C @ one_one_int )
% 7.75/5.67 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 7.75/5.67 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % is_unit_div_mult2_eq
% 7.75/5.67 thf(fact_2010_divide__eq__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [B: complex,C: complex,W: num] :
% 7.75/5.67 ( ( ( divide1717551699836669952omplex @ B @ C )
% 7.75/5.67 = ( numera6690914467698888265omplex @ W ) )
% 7.75/5.67 = ( ( ( C != zero_zero_complex )
% 7.75/5.67 => ( B
% 7.75/5.67 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 7.75/5.67 & ( ( C = zero_zero_complex )
% 7.75/5.67 => ( ( numera6690914467698888265omplex @ W )
% 7.75/5.67 = zero_zero_complex ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_eq_eq_numeral(1)
% 7.75/5.67 thf(fact_2011_divide__eq__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [B: real,C: real,W: num] :
% 7.75/5.67 ( ( ( divide_divide_real @ B @ C )
% 7.75/5.67 = ( numeral_numeral_real @ W ) )
% 7.75/5.67 = ( ( ( C != zero_zero_real )
% 7.75/5.67 => ( B
% 7.75/5.67 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 7.75/5.67 & ( ( C = zero_zero_real )
% 7.75/5.67 => ( ( numeral_numeral_real @ W )
% 7.75/5.67 = zero_zero_real ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_eq_eq_numeral(1)
% 7.75/5.67 thf(fact_2012_divide__eq__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [B: rat,C: rat,W: num] :
% 7.75/5.67 ( ( ( divide_divide_rat @ B @ C )
% 7.75/5.67 = ( numeral_numeral_rat @ W ) )
% 7.75/5.67 = ( ( ( C != zero_zero_rat )
% 7.75/5.67 => ( B
% 7.75/5.67 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 7.75/5.67 & ( ( C = zero_zero_rat )
% 7.75/5.67 => ( ( numeral_numeral_rat @ W )
% 7.75/5.67 = zero_zero_rat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_eq_eq_numeral(1)
% 7.75/5.67 thf(fact_2013_eq__divide__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [W: num,B: complex,C: complex] :
% 7.75/5.67 ( ( ( numera6690914467698888265omplex @ W )
% 7.75/5.67 = ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.67 = ( ( ( C != zero_zero_complex )
% 7.75/5.67 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 7.75/5.67 = B ) )
% 7.75/5.67 & ( ( C = zero_zero_complex )
% 7.75/5.67 => ( ( numera6690914467698888265omplex @ W )
% 7.75/5.67 = zero_zero_complex ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % eq_divide_eq_numeral(1)
% 7.75/5.67 thf(fact_2014_eq__divide__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [W: num,B: real,C: real] :
% 7.75/5.67 ( ( ( numeral_numeral_real @ W )
% 7.75/5.67 = ( divide_divide_real @ B @ C ) )
% 7.75/5.67 = ( ( ( C != zero_zero_real )
% 7.75/5.67 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 7.75/5.67 = B ) )
% 7.75/5.67 & ( ( C = zero_zero_real )
% 7.75/5.67 => ( ( numeral_numeral_real @ W )
% 7.75/5.67 = zero_zero_real ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % eq_divide_eq_numeral(1)
% 7.75/5.67 thf(fact_2015_eq__divide__eq__numeral_I1_J,axiom,
% 7.75/5.67 ! [W: num,B: rat,C: rat] :
% 7.75/5.67 ( ( ( numeral_numeral_rat @ W )
% 7.75/5.67 = ( divide_divide_rat @ B @ C ) )
% 7.75/5.67 = ( ( ( C != zero_zero_rat )
% 7.75/5.67 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 7.75/5.67 = B ) )
% 7.75/5.67 & ( ( C = zero_zero_rat )
% 7.75/5.67 => ( ( numeral_numeral_rat @ W )
% 7.75/5.67 = zero_zero_rat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % eq_divide_eq_numeral(1)
% 7.75/5.67 thf(fact_2016_add__divide__eq__if__simps_I2_J,axiom,
% 7.75/5.67 ! [Z: complex,A: complex,B: complex] :
% 7.75/5.67 ( ( ( Z = zero_zero_complex )
% 7.75/5.67 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 7.75/5.67 = B ) )
% 7.75/5.67 & ( ( Z != zero_zero_complex )
% 7.75/5.67 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 7.75/5.67 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_divide_eq_if_simps(2)
% 7.75/5.67 thf(fact_2017_add__divide__eq__if__simps_I2_J,axiom,
% 7.75/5.67 ! [Z: real,A: real,B: real] :
% 7.75/5.67 ( ( ( Z = zero_zero_real )
% 7.75/5.67 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 7.75/5.67 = B ) )
% 7.75/5.67 & ( ( Z != zero_zero_real )
% 7.75/5.67 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 7.75/5.67 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_divide_eq_if_simps(2)
% 7.75/5.67 thf(fact_2018_add__divide__eq__if__simps_I2_J,axiom,
% 7.75/5.67 ! [Z: rat,A: rat,B: rat] :
% 7.75/5.67 ( ( ( Z = zero_zero_rat )
% 7.75/5.67 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 7.75/5.67 = B ) )
% 7.75/5.67 & ( ( Z != zero_zero_rat )
% 7.75/5.67 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 7.75/5.67 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_divide_eq_if_simps(2)
% 7.75/5.67 thf(fact_2019_add__divide__eq__if__simps_I1_J,axiom,
% 7.75/5.67 ! [Z: complex,A: complex,B: complex] :
% 7.75/5.67 ( ( ( Z = zero_zero_complex )
% 7.75/5.67 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 7.75/5.67 = A ) )
% 7.75/5.67 & ( ( Z != zero_zero_complex )
% 7.75/5.67 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 7.75/5.67 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_divide_eq_if_simps(1)
% 7.75/5.67 thf(fact_2020_add__divide__eq__if__simps_I1_J,axiom,
% 7.75/5.67 ! [Z: real,A: real,B: real] :
% 7.75/5.67 ( ( ( Z = zero_zero_real )
% 7.75/5.67 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 7.75/5.67 = A ) )
% 7.75/5.67 & ( ( Z != zero_zero_real )
% 7.75/5.67 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 7.75/5.67 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_divide_eq_if_simps(1)
% 7.75/5.67 thf(fact_2021_add__divide__eq__if__simps_I1_J,axiom,
% 7.75/5.67 ! [Z: rat,A: rat,B: rat] :
% 7.75/5.67 ( ( ( Z = zero_zero_rat )
% 7.75/5.67 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 7.75/5.67 = A ) )
% 7.75/5.67 & ( ( Z != zero_zero_rat )
% 7.75/5.67 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 7.75/5.67 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_divide_eq_if_simps(1)
% 7.75/5.67 thf(fact_2022_add__frac__eq,axiom,
% 7.75/5.67 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 7.75/5.67 ( ( Y != zero_zero_complex )
% 7.75/5.67 => ( ( Z != zero_zero_complex )
% 7.75/5.67 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 7.75/5.67 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_frac_eq
% 7.75/5.67 thf(fact_2023_add__frac__eq,axiom,
% 7.75/5.67 ! [Y: real,Z: real,X: real,W: real] :
% 7.75/5.67 ( ( Y != zero_zero_real )
% 7.75/5.67 => ( ( Z != zero_zero_real )
% 7.75/5.67 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 7.75/5.67 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_frac_eq
% 7.75/5.67 thf(fact_2024_add__frac__eq,axiom,
% 7.75/5.67 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 7.75/5.67 ( ( Y != zero_zero_rat )
% 7.75/5.67 => ( ( Z != zero_zero_rat )
% 7.75/5.67 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 7.75/5.67 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_frac_eq
% 7.75/5.67 thf(fact_2025_add__frac__num,axiom,
% 7.75/5.67 ! [Y: complex,X: complex,Z: complex] :
% 7.75/5.67 ( ( Y != zero_zero_complex )
% 7.75/5.67 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z )
% 7.75/5.67 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_frac_num
% 7.75/5.67 thf(fact_2026_add__frac__num,axiom,
% 7.75/5.67 ! [Y: real,X: real,Z: real] :
% 7.75/5.67 ( ( Y != zero_zero_real )
% 7.75/5.67 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z )
% 7.75/5.67 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_frac_num
% 7.75/5.67 thf(fact_2027_add__frac__num,axiom,
% 7.75/5.67 ! [Y: rat,X: rat,Z: rat] :
% 7.75/5.67 ( ( Y != zero_zero_rat )
% 7.75/5.67 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 7.75/5.67 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_frac_num
% 7.75/5.67 thf(fact_2028_add__num__frac,axiom,
% 7.75/5.67 ! [Y: complex,Z: complex,X: complex] :
% 7.75/5.67 ( ( Y != zero_zero_complex )
% 7.75/5.67 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y ) )
% 7.75/5.67 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_num_frac
% 7.75/5.67 thf(fact_2029_add__num__frac,axiom,
% 7.75/5.67 ! [Y: real,Z: real,X: real] :
% 7.75/5.67 ( ( Y != zero_zero_real )
% 7.75/5.67 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y ) )
% 7.75/5.67 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_num_frac
% 7.75/5.67 thf(fact_2030_add__num__frac,axiom,
% 7.75/5.67 ! [Y: rat,Z: rat,X: rat] :
% 7.75/5.67 ( ( Y != zero_zero_rat )
% 7.75/5.67 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 7.75/5.67 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_num_frac
% 7.75/5.67 thf(fact_2031_add__divide__eq__iff,axiom,
% 7.75/5.67 ! [Z: complex,X: complex,Y: complex] :
% 7.75/5.67 ( ( Z != zero_zero_complex )
% 7.75/5.67 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 7.75/5.67 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_divide_eq_iff
% 7.75/5.67 thf(fact_2032_add__divide__eq__iff,axiom,
% 7.75/5.67 ! [Z: real,X: real,Y: real] :
% 7.75/5.67 ( ( Z != zero_zero_real )
% 7.75/5.67 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 7.75/5.67 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_divide_eq_iff
% 7.75/5.67 thf(fact_2033_add__divide__eq__iff,axiom,
% 7.75/5.67 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.67 ( ( Z != zero_zero_rat )
% 7.75/5.67 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 7.75/5.67 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_divide_eq_iff
% 7.75/5.67 thf(fact_2034_divide__add__eq__iff,axiom,
% 7.75/5.67 ! [Z: complex,X: complex,Y: complex] :
% 7.75/5.67 ( ( Z != zero_zero_complex )
% 7.75/5.67 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 7.75/5.67 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_add_eq_iff
% 7.75/5.67 thf(fact_2035_divide__add__eq__iff,axiom,
% 7.75/5.67 ! [Z: real,X: real,Y: real] :
% 7.75/5.67 ( ( Z != zero_zero_real )
% 7.75/5.67 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 7.75/5.67 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_add_eq_iff
% 7.75/5.67 thf(fact_2036_divide__add__eq__iff,axiom,
% 7.75/5.67 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.67 ( ( Z != zero_zero_rat )
% 7.75/5.67 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 7.75/5.67 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divide_add_eq_iff
% 7.75/5.67 thf(fact_2037_dvd__div__eq__mult,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.67 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ A @ B )
% 7.75/5.67 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 7.75/5.67 = C )
% 7.75/5.67 = ( B
% 7.75/5.67 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_eq_mult
% 7.75/5.67 thf(fact_2038_dvd__div__eq__mult,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat] :
% 7.75/5.67 ( ( A != zero_zero_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.67 => ( ( ( divide_divide_nat @ B @ A )
% 7.75/5.67 = C )
% 7.75/5.67 = ( B
% 7.75/5.67 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_eq_mult
% 7.75/5.67 thf(fact_2039_dvd__div__eq__mult,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int] :
% 7.75/5.67 ( ( A != zero_zero_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ A @ B )
% 7.75/5.67 => ( ( ( divide_divide_int @ B @ A )
% 7.75/5.67 = C )
% 7.75/5.67 = ( B
% 7.75/5.67 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_eq_mult
% 7.75/5.67 thf(fact_2040_div__dvd__iff__mult,axiom,
% 7.75/5.67 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.67 ( ( B != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ B @ A )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_dvd_iff_mult
% 7.75/5.67 thf(fact_2041_div__dvd__iff__mult,axiom,
% 7.75/5.67 ! [B: nat,A: nat,C: nat] :
% 7.75/5.67 ( ( B != zero_zero_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ B @ A )
% 7.75/5.67 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_dvd_iff_mult
% 7.75/5.67 thf(fact_2042_div__dvd__iff__mult,axiom,
% 7.75/5.67 ! [B: int,A: int,C: int] :
% 7.75/5.67 ( ( B != zero_zero_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ B @ A )
% 7.75/5.67 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 7.75/5.67 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_dvd_iff_mult
% 7.75/5.67 thf(fact_2043_dvd__div__iff__mult,axiom,
% 7.75/5.67 ! [C: code_integer,B: code_integer,A: code_integer] :
% 7.75/5.67 ( ( C != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ C @ B )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 7.75/5.67 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_iff_mult
% 7.75/5.67 thf(fact_2044_dvd__div__iff__mult,axiom,
% 7.75/5.67 ! [C: nat,B: nat,A: nat] :
% 7.75/5.67 ( ( C != zero_zero_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ C @ B )
% 7.75/5.67 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 7.75/5.67 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_iff_mult
% 7.75/5.67 thf(fact_2045_dvd__div__iff__mult,axiom,
% 7.75/5.67 ! [C: int,B: int,A: int] :
% 7.75/5.67 ( ( C != zero_zero_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ C @ B )
% 7.75/5.67 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 7.75/5.67 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_iff_mult
% 7.75/5.67 thf(fact_2046_dvd__div__div__eq__mult,axiom,
% 7.75/5.67 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 7.75/5.67 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( C != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ A @ B )
% 7.75/5.67 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 7.75/5.67 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 7.75/5.67 = ( divide6298287555418463151nteger @ D2 @ C ) )
% 7.75/5.67 = ( ( times_3573771949741848930nteger @ B @ C )
% 7.75/5.67 = ( times_3573771949741848930nteger @ A @ D2 ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_div_eq_mult
% 7.75/5.67 thf(fact_2047_dvd__div__div__eq__mult,axiom,
% 7.75/5.67 ! [A: nat,C: nat,B: nat,D2: nat] :
% 7.75/5.67 ( ( A != zero_zero_nat )
% 7.75/5.67 => ( ( C != zero_zero_nat )
% 7.75/5.67 => ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.67 => ( ( dvd_dvd_nat @ C @ D2 )
% 7.75/5.67 => ( ( ( divide_divide_nat @ B @ A )
% 7.75/5.67 = ( divide_divide_nat @ D2 @ C ) )
% 7.75/5.67 = ( ( times_times_nat @ B @ C )
% 7.75/5.67 = ( times_times_nat @ A @ D2 ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_div_eq_mult
% 7.75/5.67 thf(fact_2048_dvd__div__div__eq__mult,axiom,
% 7.75/5.67 ! [A: int,C: int,B: int,D2: int] :
% 7.75/5.67 ( ( A != zero_zero_int )
% 7.75/5.67 => ( ( C != zero_zero_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ A @ B )
% 7.75/5.67 => ( ( dvd_dvd_int @ C @ D2 )
% 7.75/5.67 => ( ( ( divide_divide_int @ B @ A )
% 7.75/5.67 = ( divide_divide_int @ D2 @ C ) )
% 7.75/5.67 = ( ( times_times_int @ B @ C )
% 7.75/5.67 = ( times_times_int @ A @ D2 ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dvd_div_div_eq_mult
% 7.75/5.67 thf(fact_2049_numeral__1__eq__Suc__0,axiom,
% 7.75/5.67 ( ( numeral_numeral_nat @ one )
% 7.75/5.67 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % numeral_1_eq_Suc_0
% 7.75/5.67 thf(fact_2050_bezout__add__strong__nat,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( A != zero_zero_nat )
% 7.75/5.67 => ? [D3: nat,X3: nat,Y3: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ D3 @ A )
% 7.75/5.67 & ( dvd_dvd_nat @ D3 @ B )
% 7.75/5.67 & ( ( times_times_nat @ A @ X3 )
% 7.75/5.67 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % bezout_add_strong_nat
% 7.75/5.67 thf(fact_2051_odd__one,axiom,
% 7.75/5.67 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 7.75/5.67
% 7.75/5.67 % odd_one
% 7.75/5.67 thf(fact_2052_odd__one,axiom,
% 7.75/5.67 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 7.75/5.67
% 7.75/5.67 % odd_one
% 7.75/5.67 thf(fact_2053_one__power2,axiom,
% 7.75/5.67 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_rat ) ).
% 7.75/5.67
% 7.75/5.67 % one_power2
% 7.75/5.67 thf(fact_2054_one__power2,axiom,
% 7.75/5.67 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_nat ) ).
% 7.75/5.67
% 7.75/5.67 % one_power2
% 7.75/5.67 thf(fact_2055_one__power2,axiom,
% 7.75/5.67 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_real ) ).
% 7.75/5.67
% 7.75/5.67 % one_power2
% 7.75/5.67 thf(fact_2056_one__power2,axiom,
% 7.75/5.67 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_int ) ).
% 7.75/5.67
% 7.75/5.67 % one_power2
% 7.75/5.67 thf(fact_2057_one__power2,axiom,
% 7.75/5.67 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_complex ) ).
% 7.75/5.67
% 7.75/5.67 % one_power2
% 7.75/5.67 thf(fact_2058_one__power2,axiom,
% 7.75/5.67 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_Code_integer ) ).
% 7.75/5.67
% 7.75/5.67 % one_power2
% 7.75/5.67 thf(fact_2059_even__zero,axiom,
% 7.75/5.67 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 7.75/5.67
% 7.75/5.67 % even_zero
% 7.75/5.67 thf(fact_2060_even__zero,axiom,
% 7.75/5.67 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 7.75/5.67
% 7.75/5.67 % even_zero
% 7.75/5.67 thf(fact_2061_zero__power2,axiom,
% 7.75/5.67 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_rat ) ).
% 7.75/5.67
% 7.75/5.67 % zero_power2
% 7.75/5.67 thf(fact_2062_zero__power2,axiom,
% 7.75/5.67 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_nat ) ).
% 7.75/5.67
% 7.75/5.67 % zero_power2
% 7.75/5.67 thf(fact_2063_zero__power2,axiom,
% 7.75/5.67 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_real ) ).
% 7.75/5.67
% 7.75/5.67 % zero_power2
% 7.75/5.67 thf(fact_2064_zero__power2,axiom,
% 7.75/5.67 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_int ) ).
% 7.75/5.67
% 7.75/5.67 % zero_power2
% 7.75/5.67 thf(fact_2065_zero__power2,axiom,
% 7.75/5.67 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_complex ) ).
% 7.75/5.67
% 7.75/5.67 % zero_power2
% 7.75/5.67 thf(fact_2066_zero__power2,axiom,
% 7.75/5.67 ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_z3403309356797280102nteger ) ).
% 7.75/5.67
% 7.75/5.67 % zero_power2
% 7.75/5.67 thf(fact_2067_nat__1__add__1,axiom,
% 7.75/5.67 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 7.75/5.67 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_1_add_1
% 7.75/5.67 thf(fact_2068_numeral__2__eq__2,axiom,
% 7.75/5.67 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 7.75/5.67 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % numeral_2_eq_2
% 7.75/5.67 thf(fact_2069_field__less__half__sum,axiom,
% 7.75/5.67 ! [X: real,Y: real] :
% 7.75/5.67 ( ( ord_less_real @ X @ Y )
% 7.75/5.67 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % field_less_half_sum
% 7.75/5.67 thf(fact_2070_field__less__half__sum,axiom,
% 7.75/5.67 ! [X: rat,Y: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X @ Y )
% 7.75/5.67 => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % field_less_half_sum
% 7.75/5.67 thf(fact_2071_exp__add__not__zero__imp__left,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.67 != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 7.75/5.67 != zero_z3403309356797280102nteger ) ) ).
% 7.75/5.67
% 7.75/5.67 % exp_add_not_zero_imp_left
% 7.75/5.67 thf(fact_2072_exp__add__not__zero__imp__left,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.67 != zero_zero_nat )
% 7.75/5.67 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 7.75/5.67 != zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % exp_add_not_zero_imp_left
% 7.75/5.67 thf(fact_2073_exp__add__not__zero__imp__left,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.67 != zero_zero_int )
% 7.75/5.67 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 7.75/5.67 != zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % exp_add_not_zero_imp_left
% 7.75/5.67 thf(fact_2074_exp__add__not__zero__imp__right,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.67 != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 != zero_z3403309356797280102nteger ) ) ).
% 7.75/5.67
% 7.75/5.67 % exp_add_not_zero_imp_right
% 7.75/5.67 thf(fact_2075_exp__add__not__zero__imp__right,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.67 != zero_zero_nat )
% 7.75/5.67 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 != zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % exp_add_not_zero_imp_right
% 7.75/5.67 thf(fact_2076_exp__add__not__zero__imp__right,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.67 != zero_zero_int )
% 7.75/5.67 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 != zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % exp_add_not_zero_imp_right
% 7.75/5.67 thf(fact_2077_div__exp__mod__exp__eq,axiom,
% 7.75/5.67 ! [A: nat,N: nat,M: nat] :
% 7.75/5.67 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.67 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_exp_mod_exp_eq
% 7.75/5.67 thf(fact_2078_div__exp__mod__exp__eq,axiom,
% 7.75/5.67 ! [A: int,N: nat,M: nat] :
% 7.75/5.67 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.67 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_exp_mod_exp_eq
% 7.75/5.67 thf(fact_2079_div__exp__mod__exp__eq,axiom,
% 7.75/5.67 ! [A: code_integer,N: nat,M: nat] :
% 7.75/5.67 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.67 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_exp_mod_exp_eq
% 7.75/5.67 thf(fact_2080_oddE,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ~ ! [B2: code_integer] :
% 7.75/5.67 ( A
% 7.75/5.67 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) @ one_one_Code_integer ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % oddE
% 7.75/5.67 thf(fact_2081_oddE,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ~ ! [B2: nat] :
% 7.75/5.67 ( A
% 7.75/5.67 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) @ one_one_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % oddE
% 7.75/5.67 thf(fact_2082_oddE,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 => ~ ! [B2: int] :
% 7.75/5.67 ( A
% 7.75/5.67 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) @ one_one_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % oddE
% 7.75/5.67 thf(fact_2083_verit__eq__simplify_I10_J,axiom,
% 7.75/5.67 ! [X22: num] :
% 7.75/5.67 ( one
% 7.75/5.67 != ( bit0 @ X22 ) ) ).
% 7.75/5.67
% 7.75/5.67 % verit_eq_simplify(10)
% 7.75/5.67 thf(fact_2084_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 7.75/5.67 ! [X: nat,N: nat,M: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 7.75/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.67 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.67 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % VEBT_internal.exp_split_high_low(1)
% 7.75/5.67 thf(fact_2085_nat__add__offset__less,axiom,
% 7.75/5.67 ! [Y: nat,N: nat,X: nat,M: nat,Sz: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.67 => ( ( Sz
% 7.75/5.67 = ( plus_plus_nat @ M @ N ) )
% 7.75/5.67 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ Y ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Sz ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_add_offset_less
% 7.75/5.67 thf(fact_2086_replicate__eq__replicate,axiom,
% 7.75/5.67 ! [M: nat,X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 7.75/5.67 ( ( ( replicate_VEBT_VEBT @ M @ X )
% 7.75/5.67 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 7.75/5.67 = ( ( M = N )
% 7.75/5.67 & ( ( M != zero_zero_nat )
% 7.75/5.67 => ( X = Y ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % replicate_eq_replicate
% 7.75/5.67 thf(fact_2087_nat__mod__eq_H,axiom,
% 7.75/5.67 ! [A: nat,N: nat] :
% 7.75/5.67 ( ( ord_less_nat @ A @ N )
% 7.75/5.67 => ( ( modulo_modulo_nat @ A @ N )
% 7.75/5.67 = A ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_mod_eq'
% 7.75/5.67 thf(fact_2088_mod__lemma,axiom,
% 7.75/5.67 ! [C: nat,R2: nat,B: nat,Q3: nat] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ C )
% 7.75/5.67 => ( ( ord_less_nat @ R2 @ B )
% 7.75/5.67 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ Q3 @ C ) ) @ R2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_lemma
% 7.75/5.67 thf(fact_2089_even__even__mod__4__iff,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.67 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_even_mod_4_iff
% 7.75/5.67 thf(fact_2090_msrevs_I1_J,axiom,
% 7.75/5.67 ! [N: nat,K: nat,M: nat] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.67 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) @ N )
% 7.75/5.67 = ( plus_plus_nat @ ( divide_divide_nat @ M @ N ) @ K ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % msrevs(1)
% 7.75/5.67 thf(fact_2091_n__less__equal__power__2,axiom,
% 7.75/5.67 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % n_less_equal_power_2
% 7.75/5.67 thf(fact_2092_set__bit__0,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 7.75/5.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % set_bit_0
% 7.75/5.67 thf(fact_2093_set__bit__0,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % set_bit_0
% 7.75/5.67 thf(fact_2094_set__bit__0,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 7.75/5.67 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % set_bit_0
% 7.75/5.67 thf(fact_2095_not__real__square__gt__zero,axiom,
% 7.75/5.67 ! [X: real] :
% 7.75/5.67 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 7.75/5.67 = ( X = zero_zero_real ) ) ).
% 7.75/5.67
% 7.75/5.67 % not_real_square_gt_zero
% 7.75/5.67 thf(fact_2096_int__div__same__is__1,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.67 => ( ( ( divide_divide_int @ A @ B )
% 7.75/5.67 = A )
% 7.75/5.67 = ( B = one_one_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % int_div_same_is_1
% 7.75/5.67 thf(fact_2097_semiring__norm_I78_J,axiom,
% 7.75/5.67 ! [M: num,N: num] :
% 7.75/5.67 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 7.75/5.67 = ( ord_less_num @ M @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % semiring_norm(78)
% 7.75/5.67 thf(fact_2098_semiring__norm_I75_J,axiom,
% 7.75/5.67 ! [M: num] :
% 7.75/5.67 ~ ( ord_less_num @ M @ one ) ).
% 7.75/5.67
% 7.75/5.67 % semiring_norm(75)
% 7.75/5.67 thf(fact_2099_one__mod__exp__eq__one,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( modulo_modulo_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.67 = one_one_int ) ).
% 7.75/5.67
% 7.75/5.67 % one_mod_exp_eq_one
% 7.75/5.67 thf(fact_2100_zmod__numeral__Bit0,axiom,
% 7.75/5.67 ! [V: num,W: num] :
% 7.75/5.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 7.75/5.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zmod_numeral_Bit0
% 7.75/5.67 thf(fact_2101_semiring__norm_I76_J,axiom,
% 7.75/5.67 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % semiring_norm(76)
% 7.75/5.67 thf(fact_2102_half__negative__int__iff,axiom,
% 7.75/5.67 ! [K: int] :
% 7.75/5.67 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 7.75/5.67 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % half_negative_int_iff
% 7.75/5.67 thf(fact_2103_zdiv__mono__strict,axiom,
% 7.75/5.67 ! [A2: int,B3: int,N: int] :
% 7.75/5.67 ( ( ord_less_int @ A2 @ B3 )
% 7.75/5.67 => ( ( ord_less_int @ zero_zero_int @ N )
% 7.75/5.67 => ( ( ( modulo_modulo_int @ A2 @ N )
% 7.75/5.67 = zero_zero_int )
% 7.75/5.67 => ( ( ( modulo_modulo_int @ B3 @ N )
% 7.75/5.67 = zero_zero_int )
% 7.75/5.67 => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B3 @ N ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zdiv_mono_strict
% 7.75/5.67 thf(fact_2104_real__arch__pow__inv,axiom,
% 7.75/5.67 ! [Y: real,X: real] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.67 => ( ( ord_less_real @ X @ one_one_real )
% 7.75/5.67 => ? [N2: nat] : ( ord_less_real @ ( power_power_real @ X @ N2 ) @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % real_arch_pow_inv
% 7.75/5.67 thf(fact_2105_pos__imp__zdiv__neg__iff,axiom,
% 7.75/5.67 ! [B: int,A: int] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.67 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 7.75/5.67 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pos_imp_zdiv_neg_iff
% 7.75/5.67 thf(fact_2106_neg__imp__zdiv__neg__iff,axiom,
% 7.75/5.67 ! [B: int,A: int] :
% 7.75/5.67 ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.67 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 7.75/5.67 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % neg_imp_zdiv_neg_iff
% 7.75/5.67 thf(fact_2107_int__div__less__self,axiom,
% 7.75/5.67 ! [X: int,K: int] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ X )
% 7.75/5.67 => ( ( ord_less_int @ one_one_int @ K )
% 7.75/5.67 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % int_div_less_self
% 7.75/5.67 thf(fact_2108_div__neg__pos__less0,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.67 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.67 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_neg_pos_less0
% 7.75/5.67 thf(fact_2109_zdiv__mult__self,axiom,
% 7.75/5.67 ! [M: int,A: int,N: int] :
% 7.75/5.67 ( ( M != zero_zero_int )
% 7.75/5.67 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ M @ N ) ) @ M )
% 7.75/5.67 = ( plus_plus_int @ ( divide_divide_int @ A @ M ) @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zdiv_mult_self
% 7.75/5.67 thf(fact_2110_realpow__pos__nth2,axiom,
% 7.75/5.67 ! [A: real,N: nat] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.67 => ? [R3: real] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ R3 )
% 7.75/5.67 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 7.75/5.67 = A ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % realpow_pos_nth2
% 7.75/5.67 thf(fact_2111_mod__exp__less__eq__exp,axiom,
% 7.75/5.67 ! [A: int,N: nat] : ( ord_less_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_exp_less_eq_exp
% 7.75/5.67 thf(fact_2112_pos__mod__bound2,axiom,
% 7.75/5.67 ! [A: int] : ( ord_less_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pos_mod_bound2
% 7.75/5.67 thf(fact_2113_axxmod2,axiom,
% 7.75/5.67 ! [X: int] :
% 7.75/5.67 ( ( ( modulo_modulo_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ X ) @ X ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_int )
% 7.75/5.67 & ( ( modulo_modulo_int @ ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ X ) @ X ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % axxmod2
% 7.75/5.67 thf(fact_2114_nmod2,axiom,
% 7.75/5.67 ! [N: int] :
% 7.75/5.67 ( ( ( modulo_modulo_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_int )
% 7.75/5.67 | ( ( modulo_modulo_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % nmod2
% 7.75/5.67 thf(fact_2115_mod__2__neq__1__eq__eq__0,axiom,
% 7.75/5.67 ! [K: int] :
% 7.75/5.67 ( ( ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 != one_one_int )
% 7.75/5.67 = ( ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_2_neq_1_eq_eq_0
% 7.75/5.67 thf(fact_2116_div__mod__decomp__int,axiom,
% 7.75/5.67 ! [A2: int,N: int] :
% 7.75/5.67 ( A2
% 7.75/5.67 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % div_mod_decomp_int
% 7.75/5.67 thf(fact_2117_real__arch__pow,axiom,
% 7.75/5.67 ! [X: real,Y: real] :
% 7.75/5.67 ( ( ord_less_real @ one_one_real @ X )
% 7.75/5.67 => ? [N2: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N2 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % real_arch_pow
% 7.75/5.67 thf(fact_2118_realpow__pos__nth,axiom,
% 7.75/5.67 ! [N: nat,A: real] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.67 => ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.67 => ? [R3: real] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ R3 )
% 7.75/5.67 & ( ( power_power_real @ R3 @ N )
% 7.75/5.67 = A ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % realpow_pos_nth
% 7.75/5.67 thf(fact_2119_realpow__pos__nth__unique,axiom,
% 7.75/5.67 ! [N: nat,A: real] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.67 => ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.67 => ? [X3: real] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ X3 )
% 7.75/5.67 & ( ( power_power_real @ X3 @ N )
% 7.75/5.67 = A )
% 7.75/5.67 & ! [Y4: real] :
% 7.75/5.67 ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 7.75/5.67 & ( ( power_power_real @ Y4 @ N )
% 7.75/5.67 = A ) )
% 7.75/5.67 => ( Y4 = X3 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % realpow_pos_nth_unique
% 7.75/5.67 thf(fact_2120_p1mod22k_H,axiom,
% 7.75/5.67 ! [B: int,N: nat] :
% 7.75/5.67 ( ( 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 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % p1mod22k'
% 7.75/5.67 thf(fact_2121_p1mod22k,axiom,
% 7.75/5.67 ! [B: int,N: nat] :
% 7.75/5.67 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ one_one_int ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.67 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) @ one_one_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % p1mod22k
% 7.75/5.67 thf(fact_2122_z1pmod2,axiom,
% 7.75/5.67 ! [B: int] :
% 7.75/5.67 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = one_one_int ) ).
% 7.75/5.67
% 7.75/5.67 % z1pmod2
% 7.75/5.67 thf(fact_2123_axxdiv2,axiom,
% 7.75/5.67 ! [X: int] :
% 7.75/5.67 ( ( ( divide_divide_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ X ) @ X ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = X )
% 7.75/5.67 & ( ( divide_divide_int @ ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ X ) @ X ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = X ) ) ).
% 7.75/5.67
% 7.75/5.67 % axxdiv2
% 7.75/5.67 thf(fact_2124_minf_I7_J,axiom,
% 7.75/5.67 ! [T: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.67 => ~ ( ord_less_real @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(7)
% 7.75/5.67 thf(fact_2125_minf_I7_J,axiom,
% 7.75/5.67 ! [T: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.67 => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(7)
% 7.75/5.67 thf(fact_2126_minf_I7_J,axiom,
% 7.75/5.67 ! [T: num] :
% 7.75/5.67 ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ X5 @ Z3 )
% 7.75/5.67 => ~ ( ord_less_num @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(7)
% 7.75/5.67 thf(fact_2127_minf_I7_J,axiom,
% 7.75/5.67 ! [T: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.67 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(7)
% 7.75/5.67 thf(fact_2128_minf_I7_J,axiom,
% 7.75/5.67 ! [T: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.67 => ~ ( ord_less_int @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(7)
% 7.75/5.67 thf(fact_2129_minf_I5_J,axiom,
% 7.75/5.67 ! [T: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.67 => ( ord_less_real @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(5)
% 7.75/5.67 thf(fact_2130_minf_I5_J,axiom,
% 7.75/5.67 ! [T: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.67 => ( ord_less_rat @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(5)
% 7.75/5.67 thf(fact_2131_minf_I5_J,axiom,
% 7.75/5.67 ! [T: num] :
% 7.75/5.67 ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ X5 @ Z3 )
% 7.75/5.67 => ( ord_less_num @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(5)
% 7.75/5.67 thf(fact_2132_minf_I5_J,axiom,
% 7.75/5.67 ! [T: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.67 => ( ord_less_nat @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(5)
% 7.75/5.67 thf(fact_2133_minf_I5_J,axiom,
% 7.75/5.67 ! [T: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.67 => ( ord_less_int @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(5)
% 7.75/5.67 thf(fact_2134_minf_I4_J,axiom,
% 7.75/5.67 ! [T: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(4)
% 7.75/5.67 thf(fact_2135_minf_I4_J,axiom,
% 7.75/5.67 ! [T: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(4)
% 7.75/5.67 thf(fact_2136_minf_I4_J,axiom,
% 7.75/5.67 ! [T: num] :
% 7.75/5.67 ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(4)
% 7.75/5.67 thf(fact_2137_minf_I4_J,axiom,
% 7.75/5.67 ! [T: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(4)
% 7.75/5.67 thf(fact_2138_minf_I4_J,axiom,
% 7.75/5.67 ! [T: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(4)
% 7.75/5.67 thf(fact_2139_minf_I3_J,axiom,
% 7.75/5.67 ! [T: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(3)
% 7.75/5.67 thf(fact_2140_minf_I3_J,axiom,
% 7.75/5.67 ! [T: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(3)
% 7.75/5.67 thf(fact_2141_minf_I3_J,axiom,
% 7.75/5.67 ! [T: num] :
% 7.75/5.67 ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(3)
% 7.75/5.67 thf(fact_2142_minf_I3_J,axiom,
% 7.75/5.67 ! [T: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(3)
% 7.75/5.67 thf(fact_2143_minf_I3_J,axiom,
% 7.75/5.67 ! [T: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(3)
% 7.75/5.67 thf(fact_2144_minf_I2_J,axiom,
% 7.75/5.67 ! [P: real > $o,P3: real > $o,Q: real > $o,Q4: real > $o] :
% 7.75/5.67 ( ? [Z4: real] :
% 7.75/5.67 ! [X3: real] :
% 7.75/5.67 ( ( ord_less_real @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: real] :
% 7.75/5.67 ! [X3: real] :
% 7.75/5.67 ( ( ord_less_real @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(2)
% 7.75/5.67 thf(fact_2145_minf_I2_J,axiom,
% 7.75/5.67 ! [P: rat > $o,P3: rat > $o,Q: rat > $o,Q4: rat > $o] :
% 7.75/5.67 ( ? [Z4: rat] :
% 7.75/5.67 ! [X3: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: rat] :
% 7.75/5.67 ! [X3: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(2)
% 7.75/5.67 thf(fact_2146_minf_I2_J,axiom,
% 7.75/5.67 ! [P: num > $o,P3: num > $o,Q: num > $o,Q4: num > $o] :
% 7.75/5.67 ( ? [Z4: num] :
% 7.75/5.67 ! [X3: num] :
% 7.75/5.67 ( ( ord_less_num @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: num] :
% 7.75/5.67 ! [X3: num] :
% 7.75/5.67 ( ( ord_less_num @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(2)
% 7.75/5.67 thf(fact_2147_minf_I2_J,axiom,
% 7.75/5.67 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 7.75/5.67 ( ? [Z4: nat] :
% 7.75/5.67 ! [X3: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: nat] :
% 7.75/5.67 ! [X3: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(2)
% 7.75/5.67 thf(fact_2148_minf_I2_J,axiom,
% 7.75/5.67 ! [P: int > $o,P3: int > $o,Q: int > $o,Q4: int > $o] :
% 7.75/5.67 ( ? [Z4: int] :
% 7.75/5.67 ! [X3: int] :
% 7.75/5.67 ( ( ord_less_int @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: int] :
% 7.75/5.67 ! [X3: int] :
% 7.75/5.67 ( ( ord_less_int @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(2)
% 7.75/5.67 thf(fact_2149_minf_I1_J,axiom,
% 7.75/5.67 ! [P: real > $o,P3: real > $o,Q: real > $o,Q4: real > $o] :
% 7.75/5.67 ( ? [Z4: real] :
% 7.75/5.67 ! [X3: real] :
% 7.75/5.67 ( ( ord_less_real @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: real] :
% 7.75/5.67 ! [X3: real] :
% 7.75/5.67 ( ( ord_less_real @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(1)
% 7.75/5.67 thf(fact_2150_minf_I1_J,axiom,
% 7.75/5.67 ! [P: rat > $o,P3: rat > $o,Q: rat > $o,Q4: rat > $o] :
% 7.75/5.67 ( ? [Z4: rat] :
% 7.75/5.67 ! [X3: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: rat] :
% 7.75/5.67 ! [X3: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(1)
% 7.75/5.67 thf(fact_2151_minf_I1_J,axiom,
% 7.75/5.67 ! [P: num > $o,P3: num > $o,Q: num > $o,Q4: num > $o] :
% 7.75/5.67 ( ? [Z4: num] :
% 7.75/5.67 ! [X3: num] :
% 7.75/5.67 ( ( ord_less_num @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: num] :
% 7.75/5.67 ! [X3: num] :
% 7.75/5.67 ( ( ord_less_num @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(1)
% 7.75/5.67 thf(fact_2152_minf_I1_J,axiom,
% 7.75/5.67 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 7.75/5.67 ( ? [Z4: nat] :
% 7.75/5.67 ! [X3: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: nat] :
% 7.75/5.67 ! [X3: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(1)
% 7.75/5.67 thf(fact_2153_minf_I1_J,axiom,
% 7.75/5.67 ! [P: int > $o,P3: int > $o,Q: int > $o,Q4: int > $o] :
% 7.75/5.67 ( ? [Z4: int] :
% 7.75/5.67 ! [X3: int] :
% 7.75/5.67 ( ( ord_less_int @ X3 @ Z4 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: int] :
% 7.75/5.67 ! [X3: int] :
% 7.75/5.67 ( ( ord_less_int @ X3 @ Z4 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(1)
% 7.75/5.67 thf(fact_2154_pinf_I7_J,axiom,
% 7.75/5.67 ! [T: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.67 => ( ord_less_real @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(7)
% 7.75/5.67 thf(fact_2155_pinf_I7_J,axiom,
% 7.75/5.67 ! [T: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.67 => ( ord_less_rat @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(7)
% 7.75/5.67 thf(fact_2156_pinf_I7_J,axiom,
% 7.75/5.67 ! [T: num] :
% 7.75/5.67 ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ Z3 @ X5 )
% 7.75/5.67 => ( ord_less_num @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(7)
% 7.75/5.67 thf(fact_2157_pinf_I7_J,axiom,
% 7.75/5.67 ! [T: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.67 => ( ord_less_nat @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(7)
% 7.75/5.67 thf(fact_2158_pinf_I7_J,axiom,
% 7.75/5.67 ! [T: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.67 => ( ord_less_int @ T @ X5 ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(7)
% 7.75/5.67 thf(fact_2159_pinf_I5_J,axiom,
% 7.75/5.67 ! [T: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.67 => ~ ( ord_less_real @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(5)
% 7.75/5.67 thf(fact_2160_pinf_I5_J,axiom,
% 7.75/5.67 ! [T: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.67 => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(5)
% 7.75/5.67 thf(fact_2161_pinf_I5_J,axiom,
% 7.75/5.67 ! [T: num] :
% 7.75/5.67 ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ Z3 @ X5 )
% 7.75/5.67 => ~ ( ord_less_num @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(5)
% 7.75/5.67 thf(fact_2162_pinf_I5_J,axiom,
% 7.75/5.67 ! [T: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.67 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(5)
% 7.75/5.67 thf(fact_2163_pinf_I5_J,axiom,
% 7.75/5.67 ! [T: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.67 => ~ ( ord_less_int @ X5 @ T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(5)
% 7.75/5.67 thf(fact_2164_pinf_I4_J,axiom,
% 7.75/5.67 ! [T: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(4)
% 7.75/5.67 thf(fact_2165_pinf_I4_J,axiom,
% 7.75/5.67 ! [T: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(4)
% 7.75/5.67 thf(fact_2166_pinf_I4_J,axiom,
% 7.75/5.67 ! [T: num] :
% 7.75/5.67 ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(4)
% 7.75/5.67 thf(fact_2167_pinf_I4_J,axiom,
% 7.75/5.67 ! [T: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(4)
% 7.75/5.67 thf(fact_2168_pinf_I4_J,axiom,
% 7.75/5.67 ! [T: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(4)
% 7.75/5.67 thf(fact_2169_pinf_I3_J,axiom,
% 7.75/5.67 ! [T: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(3)
% 7.75/5.67 thf(fact_2170_pinf_I3_J,axiom,
% 7.75/5.67 ! [T: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(3)
% 7.75/5.67 thf(fact_2171_pinf_I3_J,axiom,
% 7.75/5.67 ! [T: num] :
% 7.75/5.67 ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(3)
% 7.75/5.67 thf(fact_2172_pinf_I3_J,axiom,
% 7.75/5.67 ! [T: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(3)
% 7.75/5.67 thf(fact_2173_pinf_I3_J,axiom,
% 7.75/5.67 ! [T: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.67 => ( X5 != T ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(3)
% 7.75/5.67 thf(fact_2174_pinf_I2_J,axiom,
% 7.75/5.67 ! [P: real > $o,P3: real > $o,Q: real > $o,Q4: real > $o] :
% 7.75/5.67 ( ? [Z4: real] :
% 7.75/5.67 ! [X3: real] :
% 7.75/5.67 ( ( ord_less_real @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: real] :
% 7.75/5.67 ! [X3: real] :
% 7.75/5.67 ( ( ord_less_real @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(2)
% 7.75/5.67 thf(fact_2175_pinf_I2_J,axiom,
% 7.75/5.67 ! [P: rat > $o,P3: rat > $o,Q: rat > $o,Q4: rat > $o] :
% 7.75/5.67 ( ? [Z4: rat] :
% 7.75/5.67 ! [X3: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: rat] :
% 7.75/5.67 ! [X3: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(2)
% 7.75/5.67 thf(fact_2176_pinf_I2_J,axiom,
% 7.75/5.67 ! [P: num > $o,P3: num > $o,Q: num > $o,Q4: num > $o] :
% 7.75/5.67 ( ? [Z4: num] :
% 7.75/5.67 ! [X3: num] :
% 7.75/5.67 ( ( ord_less_num @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: num] :
% 7.75/5.67 ! [X3: num] :
% 7.75/5.67 ( ( ord_less_num @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(2)
% 7.75/5.67 thf(fact_2177_pinf_I2_J,axiom,
% 7.75/5.67 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 7.75/5.67 ( ? [Z4: nat] :
% 7.75/5.67 ! [X3: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: nat] :
% 7.75/5.67 ! [X3: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(2)
% 7.75/5.67 thf(fact_2178_pinf_I2_J,axiom,
% 7.75/5.67 ! [P: int > $o,P3: int > $o,Q: int > $o,Q4: int > $o] :
% 7.75/5.67 ( ? [Z4: int] :
% 7.75/5.67 ! [X3: int] :
% 7.75/5.67 ( ( ord_less_int @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: int] :
% 7.75/5.67 ! [X3: int] :
% 7.75/5.67 ( ( ord_less_int @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 | ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(2)
% 7.75/5.67 thf(fact_2179_pinf_I1_J,axiom,
% 7.75/5.67 ! [P: real > $o,P3: real > $o,Q: real > $o,Q4: real > $o] :
% 7.75/5.67 ( ? [Z4: real] :
% 7.75/5.67 ! [X3: real] :
% 7.75/5.67 ( ( ord_less_real @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: real] :
% 7.75/5.67 ! [X3: real] :
% 7.75/5.67 ( ( ord_less_real @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(1)
% 7.75/5.67 thf(fact_2180_pinf_I1_J,axiom,
% 7.75/5.67 ! [P: rat > $o,P3: rat > $o,Q: rat > $o,Q4: rat > $o] :
% 7.75/5.67 ( ? [Z4: rat] :
% 7.75/5.67 ! [X3: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: rat] :
% 7.75/5.67 ! [X3: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(1)
% 7.75/5.67 thf(fact_2181_pinf_I1_J,axiom,
% 7.75/5.67 ! [P: num > $o,P3: num > $o,Q: num > $o,Q4: num > $o] :
% 7.75/5.67 ( ? [Z4: num] :
% 7.75/5.67 ! [X3: num] :
% 7.75/5.67 ( ( ord_less_num @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: num] :
% 7.75/5.67 ! [X3: num] :
% 7.75/5.67 ( ( ord_less_num @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: num] :
% 7.75/5.67 ! [X5: num] :
% 7.75/5.67 ( ( ord_less_num @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(1)
% 7.75/5.67 thf(fact_2182_pinf_I1_J,axiom,
% 7.75/5.67 ! [P: nat > $o,P3: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 7.75/5.67 ( ? [Z4: nat] :
% 7.75/5.67 ! [X3: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: nat] :
% 7.75/5.67 ! [X3: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(1)
% 7.75/5.67 thf(fact_2183_pinf_I1_J,axiom,
% 7.75/5.67 ! [P: int > $o,P3: int > $o,Q: int > $o,Q4: int > $o] :
% 7.75/5.67 ( ? [Z4: int] :
% 7.75/5.67 ! [X3: int] :
% 7.75/5.67 ( ( ord_less_int @ Z4 @ X3 )
% 7.75/5.67 => ( ( P @ X3 )
% 7.75/5.67 = ( P3 @ X3 ) ) )
% 7.75/5.67 => ( ? [Z4: int] :
% 7.75/5.67 ! [X3: int] :
% 7.75/5.67 ( ( ord_less_int @ Z4 @ X3 )
% 7.75/5.67 => ( ( Q @ X3 )
% 7.75/5.67 = ( Q4 @ X3 ) ) )
% 7.75/5.67 => ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.67 => ( ( ( P @ X5 )
% 7.75/5.67 & ( Q @ X5 ) )
% 7.75/5.67 = ( ( P3 @ X5 )
% 7.75/5.67 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(1)
% 7.75/5.67 thf(fact_2184_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Ocases,axiom,
% 7.75/5.67 ! [X: nat] :
% 7.75/5.67 ( ( X != zero_zero_nat )
% 7.75/5.67 => ( ( X
% 7.75/5.67 != ( suc @ zero_zero_nat ) )
% 7.75/5.67 => ~ ! [Va: nat] :
% 7.75/5.67 ( X
% 7.75/5.67 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.cases
% 7.75/5.67 thf(fact_2185_nat__mod__eq,axiom,
% 7.75/5.67 ! [B: nat,N: nat,A: nat] :
% 7.75/5.67 ( ( ord_less_nat @ B @ N )
% 7.75/5.67 => ( ( ( modulo_modulo_nat @ A @ N )
% 7.75/5.67 = ( modulo_modulo_nat @ B @ N ) )
% 7.75/5.67 => ( ( modulo_modulo_nat @ A @ N )
% 7.75/5.67 = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_mod_eq
% 7.75/5.67 thf(fact_2186_mod__plus__right,axiom,
% 7.75/5.67 ! [A: nat,X: nat,M: nat,B: nat] :
% 7.75/5.67 ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ X ) @ M )
% 7.75/5.67 = ( modulo_modulo_nat @ ( plus_plus_nat @ B @ X ) @ M ) )
% 7.75/5.67 = ( ( modulo_modulo_nat @ A @ M )
% 7.75/5.67 = ( modulo_modulo_nat @ B @ M ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_plus_right
% 7.75/5.67 thf(fact_2187_even__set__bit__iff,axiom,
% 7.75/5.67 ! [M: nat,A: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 7.75/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 & ( M != zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_set_bit_iff
% 7.75/5.67 thf(fact_2188_even__set__bit__iff,axiom,
% 7.75/5.67 ! [M: nat,A: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 7.75/5.67 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 & ( M != zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_set_bit_iff
% 7.75/5.67 thf(fact_2189_even__set__bit__iff,axiom,
% 7.75/5.67 ! [M: nat,A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 7.75/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 & ( M != zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_set_bit_iff
% 7.75/5.67 thf(fact_2190_pinf_I9_J,axiom,
% 7.75/5.67 ! [D2: real,S: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.67 => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S ) )
% 7.75/5.67 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(9)
% 7.75/5.67 thf(fact_2191_pinf_I9_J,axiom,
% 7.75/5.67 ! [D2: rat,S: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.67 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S ) )
% 7.75/5.67 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(9)
% 7.75/5.67 thf(fact_2192_pinf_I9_J,axiom,
% 7.75/5.67 ! [D2: nat,S: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.67 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S ) )
% 7.75/5.67 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(9)
% 7.75/5.67 thf(fact_2193_pinf_I9_J,axiom,
% 7.75/5.67 ! [D2: int,S: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.67 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S ) )
% 7.75/5.67 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(9)
% 7.75/5.67 thf(fact_2194_pinf_I10_J,axiom,
% 7.75/5.67 ! [D2: real,S: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.67 => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S ) ) )
% 7.75/5.67 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(10)
% 7.75/5.67 thf(fact_2195_pinf_I10_J,axiom,
% 7.75/5.67 ! [D2: rat,S: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.67 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S ) ) )
% 7.75/5.67 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(10)
% 7.75/5.67 thf(fact_2196_pinf_I10_J,axiom,
% 7.75/5.67 ! [D2: nat,S: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.67 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S ) ) )
% 7.75/5.67 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(10)
% 7.75/5.67 thf(fact_2197_pinf_I10_J,axiom,
% 7.75/5.67 ! [D2: int,S: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.67 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S ) ) )
% 7.75/5.67 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pinf(10)
% 7.75/5.67 thf(fact_2198_minf_I9_J,axiom,
% 7.75/5.67 ! [D2: real,S: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.67 => ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S ) )
% 7.75/5.67 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(9)
% 7.75/5.67 thf(fact_2199_minf_I9_J,axiom,
% 7.75/5.67 ! [D2: rat,S: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.67 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S ) )
% 7.75/5.67 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(9)
% 7.75/5.67 thf(fact_2200_minf_I9_J,axiom,
% 7.75/5.67 ! [D2: nat,S: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.67 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S ) )
% 7.75/5.67 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(9)
% 7.75/5.67 thf(fact_2201_minf_I9_J,axiom,
% 7.75/5.67 ! [D2: int,S: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.67 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S ) )
% 7.75/5.67 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(9)
% 7.75/5.67 thf(fact_2202_minf_I10_J,axiom,
% 7.75/5.67 ! [D2: real,S: real] :
% 7.75/5.67 ? [Z3: real] :
% 7.75/5.67 ! [X5: real] :
% 7.75/5.67 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.67 => ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S ) ) )
% 7.75/5.67 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ S ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(10)
% 7.75/5.67 thf(fact_2203_minf_I10_J,axiom,
% 7.75/5.67 ! [D2: rat,S: rat] :
% 7.75/5.67 ? [Z3: rat] :
% 7.75/5.67 ! [X5: rat] :
% 7.75/5.67 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.67 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S ) ) )
% 7.75/5.67 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ S ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(10)
% 7.75/5.67 thf(fact_2204_minf_I10_J,axiom,
% 7.75/5.67 ! [D2: nat,S: nat] :
% 7.75/5.67 ? [Z3: nat] :
% 7.75/5.67 ! [X5: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.67 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S ) ) )
% 7.75/5.67 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X5 @ S ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(10)
% 7.75/5.67 thf(fact_2205_minf_I10_J,axiom,
% 7.75/5.67 ! [D2: int,S: int] :
% 7.75/5.67 ? [Z3: int] :
% 7.75/5.67 ! [X5: int] :
% 7.75/5.67 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.67 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S ) ) )
% 7.75/5.67 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ S ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % minf(10)
% 7.75/5.67 thf(fact_2206_nat__mod__lem,axiom,
% 7.75/5.67 ! [N: nat,B: nat] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.67 => ( ( ord_less_nat @ B @ N )
% 7.75/5.67 = ( ( modulo_modulo_nat @ B @ N )
% 7.75/5.67 = B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % nat_mod_lem
% 7.75/5.67 thf(fact_2207_msrevs_I2_J,axiom,
% 7.75/5.67 ! [K: nat,N: nat,M: nat] :
% 7.75/5.67 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) @ N )
% 7.75/5.67 = ( modulo_modulo_nat @ M @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % msrevs(2)
% 7.75/5.67 thf(fact_2208_set__bit__Suc,axiom,
% 7.75/5.67 ! [N: nat,A: int] :
% 7.75/5.67 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 7.75/5.67 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % set_bit_Suc
% 7.75/5.67 thf(fact_2209_set__bit__Suc,axiom,
% 7.75/5.67 ! [N: nat,A: code_integer] :
% 7.75/5.67 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % set_bit_Suc
% 7.75/5.67 thf(fact_2210_set__bit__Suc,axiom,
% 7.75/5.67 ! [N: nat,A: nat] :
% 7.75/5.67 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 7.75/5.67 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % set_bit_Suc
% 7.75/5.67 thf(fact_2211_unity__coeff__ex,axiom,
% 7.75/5.67 ! [P: rat > $o,L: rat] :
% 7.75/5.67 ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L @ X2 ) ) )
% 7.75/5.67 = ( ? [X2: rat] :
% 7.75/5.67 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 7.75/5.67 & ( P @ X2 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unity_coeff_ex
% 7.75/5.67 thf(fact_2212_unity__coeff__ex,axiom,
% 7.75/5.67 ! [P: real > $o,L: real] :
% 7.75/5.67 ( ( ? [X2: real] : ( P @ ( times_times_real @ L @ X2 ) ) )
% 7.75/5.67 = ( ? [X2: real] :
% 7.75/5.67 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X2 @ zero_zero_real ) )
% 7.75/5.67 & ( P @ X2 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unity_coeff_ex
% 7.75/5.67 thf(fact_2213_unity__coeff__ex,axiom,
% 7.75/5.67 ! [P: nat > $o,L: nat] :
% 7.75/5.67 ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L @ X2 ) ) )
% 7.75/5.67 = ( ? [X2: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 7.75/5.67 & ( P @ X2 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unity_coeff_ex
% 7.75/5.67 thf(fact_2214_unity__coeff__ex,axiom,
% 7.75/5.67 ! [P: int > $o,L: int] :
% 7.75/5.67 ( ( ? [X2: int] : ( P @ ( times_times_int @ L @ X2 ) ) )
% 7.75/5.67 = ( ? [X2: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 7.75/5.67 & ( P @ X2 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unity_coeff_ex
% 7.75/5.67 thf(fact_2215_unity__coeff__ex,axiom,
% 7.75/5.67 ! [P: code_integer > $o,L: code_integer] :
% 7.75/5.67 ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X2 ) ) )
% 7.75/5.67 = ( ? [X2: code_integer] :
% 7.75/5.67 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 7.75/5.67 & ( P @ X2 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unity_coeff_ex
% 7.75/5.67 thf(fact_2216_unity__coeff__ex,axiom,
% 7.75/5.67 ! [P: complex > $o,L: complex] :
% 7.75/5.67 ( ( ? [X2: complex] : ( P @ ( times_times_complex @ L @ X2 ) ) )
% 7.75/5.67 = ( ? [X2: complex] :
% 7.75/5.67 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X2 @ zero_zero_complex ) )
% 7.75/5.67 & ( P @ X2 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unity_coeff_ex
% 7.75/5.67 thf(fact_2217_z1pdiv2,axiom,
% 7.75/5.67 ! [B: int] :
% 7.75/5.67 ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = B ) ).
% 7.75/5.67
% 7.75/5.67 % z1pdiv2
% 7.75/5.67 thf(fact_2218_td__gal__lt,axiom,
% 7.75/5.67 ! [C: nat,A: nat,B: nat] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ C )
% 7.75/5.67 => ( ( ord_less_nat @ A @ ( times_times_nat @ B @ C ) )
% 7.75/5.67 = ( ord_less_nat @ ( divide_divide_nat @ A @ C ) @ B ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % td_gal_lt
% 7.75/5.67 thf(fact_2219_enat__ord__number_I2_J,axiom,
% 7.75/5.67 ! [M: num,N: num] :
% 7.75/5.67 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 7.75/5.67 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % enat_ord_number(2)
% 7.75/5.67 thf(fact_2220_double__eq__0__iff,axiom,
% 7.75/5.67 ! [A: real] :
% 7.75/5.67 ( ( ( plus_plus_real @ A @ A )
% 7.75/5.67 = zero_zero_real )
% 7.75/5.67 = ( A = zero_zero_real ) ) ).
% 7.75/5.67
% 7.75/5.67 % double_eq_0_iff
% 7.75/5.67 thf(fact_2221_double__eq__0__iff,axiom,
% 7.75/5.67 ! [A: rat] :
% 7.75/5.67 ( ( ( plus_plus_rat @ A @ A )
% 7.75/5.67 = zero_zero_rat )
% 7.75/5.67 = ( A = zero_zero_rat ) ) ).
% 7.75/5.67
% 7.75/5.67 % double_eq_0_iff
% 7.75/5.67 thf(fact_2222_double__eq__0__iff,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( ( plus_plus_int @ A @ A )
% 7.75/5.67 = zero_zero_int )
% 7.75/5.67 = ( A = zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % double_eq_0_iff
% 7.75/5.67 thf(fact_2223_low__inv,axiom,
% 7.75/5.67 ! [X: nat,N: nat,Y: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 7.75/5.67 = X ) ) ).
% 7.75/5.67
% 7.75/5.67 % low_inv
% 7.75/5.67 thf(fact_2224_flip__bit__Suc,axiom,
% 7.75/5.67 ! [N: nat,A: code_integer] :
% 7.75/5.67 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % flip_bit_Suc
% 7.75/5.67 thf(fact_2225_flip__bit__Suc,axiom,
% 7.75/5.67 ! [N: nat,A: int] :
% 7.75/5.67 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 7.75/5.67 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % flip_bit_Suc
% 7.75/5.67 thf(fact_2226_flip__bit__Suc,axiom,
% 7.75/5.67 ! [N: nat,A: nat] :
% 7.75/5.67 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 7.75/5.67 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % flip_bit_Suc
% 7.75/5.67 thf(fact_2227_unset__bit__0,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 7.75/5.67 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unset_bit_0
% 7.75/5.67 thf(fact_2228_unset__bit__0,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 7.75/5.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unset_bit_0
% 7.75/5.67 thf(fact_2229_unset__bit__0,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 7.75/5.67 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unset_bit_0
% 7.75/5.67 thf(fact_2230_unset__bit__Suc,axiom,
% 7.75/5.67 ! [N: nat,A: code_integer] :
% 7.75/5.67 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unset_bit_Suc
% 7.75/5.67 thf(fact_2231_unset__bit__Suc,axiom,
% 7.75/5.67 ! [N: nat,A: int] :
% 7.75/5.67 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 7.75/5.67 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unset_bit_Suc
% 7.75/5.67 thf(fact_2232_unset__bit__Suc,axiom,
% 7.75/5.67 ! [N: nat,A: nat] :
% 7.75/5.67 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 7.75/5.67 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % unset_bit_Suc
% 7.75/5.67 thf(fact_2233_low__def,axiom,
% 7.75/5.67 ( vEBT_VEBT_low
% 7.75/5.67 = ( ^ [X2: nat,N3: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % low_def
% 7.75/5.67 thf(fact_2234_word__rot__lem,axiom,
% 7.75/5.67 ! [L: nat,K: nat,D2: nat,N: nat] :
% 7.75/5.67 ( ( ( plus_plus_nat @ L @ K )
% 7.75/5.67 = ( plus_plus_nat @ D2 @ ( modulo_modulo_nat @ K @ L ) ) )
% 7.75/5.67 => ( ( ord_less_nat @ N @ L )
% 7.75/5.67 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ D2 @ N ) @ L )
% 7.75/5.67 = N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % word_rot_lem
% 7.75/5.67 thf(fact_2235_dbl__simps_I3_J,axiom,
% 7.75/5.67 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 7.75/5.67 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(3)
% 7.75/5.67 thf(fact_2236_dbl__simps_I3_J,axiom,
% 7.75/5.67 ( ( neg_numeral_dbl_real @ one_one_real )
% 7.75/5.67 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(3)
% 7.75/5.67 thf(fact_2237_dbl__simps_I3_J,axiom,
% 7.75/5.67 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 7.75/5.67 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(3)
% 7.75/5.67 thf(fact_2238_dbl__simps_I3_J,axiom,
% 7.75/5.67 ( ( neg_numeral_dbl_int @ one_one_int )
% 7.75/5.67 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(3)
% 7.75/5.67 thf(fact_2239_mlex__snd__decrI,axiom,
% 7.75/5.67 ! [A: nat,A4: nat,B: nat,B6: nat,N4: nat] :
% 7.75/5.67 ( ( A = A4 )
% 7.75/5.67 => ( ( ord_less_nat @ B @ B6 )
% 7.75/5.67 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N4 ) @ B6 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mlex_snd_decrI
% 7.75/5.67 thf(fact_2240_bit__split__inv,axiom,
% 7.75/5.67 ! [X: nat,D2: nat] :
% 7.75/5.67 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D2 ) @ ( vEBT_VEBT_low @ X @ D2 ) @ D2 )
% 7.75/5.67 = X ) ).
% 7.75/5.67
% 7.75/5.67 % bit_split_inv
% 7.75/5.67 thf(fact_2241_i0__less,axiom,
% 7.75/5.67 ! [N: extended_enat] :
% 7.75/5.67 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 7.75/5.67 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 7.75/5.67
% 7.75/5.67 % i0_less
% 7.75/5.67 thf(fact_2242_set__bit__negative__int__iff,axiom,
% 7.75/5.67 ! [N: nat,K: int] :
% 7.75/5.67 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 7.75/5.67 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % set_bit_negative_int_iff
% 7.75/5.67 thf(fact_2243_flip__bit__negative__int__iff,axiom,
% 7.75/5.67 ! [N: nat,K: int] :
% 7.75/5.67 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 7.75/5.67 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % flip_bit_negative_int_iff
% 7.75/5.67 thf(fact_2244_unset__bit__negative__int__iff,axiom,
% 7.75/5.67 ! [N: nat,K: int] :
% 7.75/5.67 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 7.75/5.67 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % unset_bit_negative_int_iff
% 7.75/5.67 thf(fact_2245_dbl__simps_I2_J,axiom,
% 7.75/5.67 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 7.75/5.67 = zero_zero_complex ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(2)
% 7.75/5.67 thf(fact_2246_dbl__simps_I2_J,axiom,
% 7.75/5.67 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 7.75/5.67 = zero_zero_real ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(2)
% 7.75/5.67 thf(fact_2247_dbl__simps_I2_J,axiom,
% 7.75/5.67 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 7.75/5.67 = zero_zero_rat ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(2)
% 7.75/5.67 thf(fact_2248_dbl__simps_I2_J,axiom,
% 7.75/5.67 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 7.75/5.67 = zero_zero_int ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(2)
% 7.75/5.67 thf(fact_2249_dbl__simps_I5_J,axiom,
% 7.75/5.67 ! [K: num] :
% 7.75/5.67 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 7.75/5.67 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(5)
% 7.75/5.67 thf(fact_2250_dbl__simps_I5_J,axiom,
% 7.75/5.67 ! [K: num] :
% 7.75/5.67 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 7.75/5.67 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(5)
% 7.75/5.67 thf(fact_2251_dbl__simps_I5_J,axiom,
% 7.75/5.67 ! [K: num] :
% 7.75/5.67 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 7.75/5.67 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(5)
% 7.75/5.67 thf(fact_2252_dbl__simps_I5_J,axiom,
% 7.75/5.67 ! [K: num] :
% 7.75/5.67 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 7.75/5.67 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_simps(5)
% 7.75/5.67 thf(fact_2253_times__int__code_I2_J,axiom,
% 7.75/5.67 ! [L: int] :
% 7.75/5.67 ( ( times_times_int @ zero_zero_int @ L )
% 7.75/5.67 = zero_zero_int ) ).
% 7.75/5.67
% 7.75/5.67 % times_int_code(2)
% 7.75/5.67 thf(fact_2254_times__int__code_I1_J,axiom,
% 7.75/5.67 ! [K: int] :
% 7.75/5.67 ( ( times_times_int @ K @ zero_zero_int )
% 7.75/5.67 = zero_zero_int ) ).
% 7.75/5.67
% 7.75/5.67 % times_int_code(1)
% 7.75/5.67 thf(fact_2255_zmod__eq__0D,axiom,
% 7.75/5.67 ! [M: int,D2: int] :
% 7.75/5.67 ( ( ( modulo_modulo_int @ M @ D2 )
% 7.75/5.67 = zero_zero_int )
% 7.75/5.67 => ? [Q5: int] :
% 7.75/5.67 ( M
% 7.75/5.67 = ( times_times_int @ D2 @ Q5 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zmod_eq_0D
% 7.75/5.67 thf(fact_2256_zdvd__mult__cancel,axiom,
% 7.75/5.67 ! [K: int,M: int,N: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 7.75/5.67 => ( ( K != zero_zero_int )
% 7.75/5.67 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zdvd_mult_cancel
% 7.75/5.67 thf(fact_2257_zdvd__mono,axiom,
% 7.75/5.67 ! [K: int,M: int,T: int] :
% 7.75/5.67 ( ( K != zero_zero_int )
% 7.75/5.67 => ( ( dvd_dvd_int @ M @ T )
% 7.75/5.67 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zdvd_mono
% 7.75/5.67 thf(fact_2258_zmod__eq__0__iff,axiom,
% 7.75/5.67 ! [M: int,D2: int] :
% 7.75/5.67 ( ( ( modulo_modulo_int @ M @ D2 )
% 7.75/5.67 = zero_zero_int )
% 7.75/5.67 = ( ? [Q6: int] :
% 7.75/5.67 ( M
% 7.75/5.67 = ( times_times_int @ D2 @ Q6 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zmod_eq_0_iff
% 7.75/5.67 thf(fact_2259_zmult__zless__mono2,axiom,
% 7.75/5.67 ! [I: int,J: int,K: int] :
% 7.75/5.67 ( ( ord_less_int @ I @ J )
% 7.75/5.67 => ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.67 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zmult_zless_mono2
% 7.75/5.67 thf(fact_2260_pos__zmult__eq__1__iff,axiom,
% 7.75/5.67 ! [M: int,N: int] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ M )
% 7.75/5.67 => ( ( ( times_times_int @ M @ N )
% 7.75/5.67 = one_one_int )
% 7.75/5.67 = ( ( M = one_one_int )
% 7.75/5.67 & ( N = one_one_int ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % pos_zmult_eq_1_iff
% 7.75/5.67 thf(fact_2261_enat__0__less__mult__iff,axiom,
% 7.75/5.67 ! [M: extended_enat,N: extended_enat] :
% 7.75/5.67 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 7.75/5.67 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 7.75/5.67 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % enat_0_less_mult_iff
% 7.75/5.67 thf(fact_2262_zmod__helper,axiom,
% 7.75/5.67 ! [N: int,M: int,K: int,A: int] :
% 7.75/5.67 ( ( ( modulo_modulo_int @ N @ M )
% 7.75/5.67 = K )
% 7.75/5.67 => ( ( modulo_modulo_int @ ( plus_plus_int @ N @ A ) @ M )
% 7.75/5.67 = ( modulo_modulo_int @ ( plus_plus_int @ K @ A ) @ M ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zmod_helper
% 7.75/5.67 thf(fact_2263_mod__plus__cong,axiom,
% 7.75/5.67 ! [B: int,B6: int,X: int,X6: int,Y: int,Y5: int,Z5: int] :
% 7.75/5.67 ( ( B = B6 )
% 7.75/5.67 => ( ( ( modulo_modulo_int @ X @ B6 )
% 7.75/5.67 = ( modulo_modulo_int @ X6 @ B6 ) )
% 7.75/5.67 => ( ( ( modulo_modulo_int @ Y @ B6 )
% 7.75/5.67 = ( modulo_modulo_int @ Y5 @ B6 ) )
% 7.75/5.67 => ( ( ( plus_plus_int @ X6 @ Y5 )
% 7.75/5.67 = Z5 )
% 7.75/5.67 => ( ( modulo_modulo_int @ ( plus_plus_int @ X @ Y ) @ B )
% 7.75/5.67 = ( modulo_modulo_int @ Z5 @ B6 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mod_plus_cong
% 7.75/5.67 thf(fact_2264_odd__less__0__iff,axiom,
% 7.75/5.67 ! [Z: int] :
% 7.75/5.67 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 7.75/5.67 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % odd_less_0_iff
% 7.75/5.67 thf(fact_2265_zless__add1__eq,axiom,
% 7.75/5.67 ! [W: int,Z: int] :
% 7.75/5.67 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 7.75/5.67 = ( ( ord_less_int @ W @ Z )
% 7.75/5.67 | ( W = Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zless_add1_eq
% 7.75/5.67 thf(fact_2266_int__gr__induct,axiom,
% 7.75/5.67 ! [K: int,I: int,P: int > $o] :
% 7.75/5.67 ( ( ord_less_int @ K @ I )
% 7.75/5.67 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 7.75/5.67 => ( ! [I3: int] :
% 7.75/5.67 ( ( ord_less_int @ K @ I3 )
% 7.75/5.67 => ( ( P @ I3 )
% 7.75/5.67 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 7.75/5.67 => ( P @ I ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % int_gr_induct
% 7.75/5.67 thf(fact_2267_odd__nonzero,axiom,
% 7.75/5.67 ! [Z: int] :
% 7.75/5.67 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 7.75/5.67 != zero_zero_int ) ).
% 7.75/5.67
% 7.75/5.67 % odd_nonzero
% 7.75/5.67 thf(fact_2268_plus__int__code_I1_J,axiom,
% 7.75/5.67 ! [K: int] :
% 7.75/5.67 ( ( plus_plus_int @ K @ zero_zero_int )
% 7.75/5.67 = K ) ).
% 7.75/5.67
% 7.75/5.67 % plus_int_code(1)
% 7.75/5.67 thf(fact_2269_plus__int__code_I2_J,axiom,
% 7.75/5.67 ! [L: int] :
% 7.75/5.67 ( ( plus_plus_int @ zero_zero_int @ L )
% 7.75/5.67 = L ) ).
% 7.75/5.67
% 7.75/5.67 % plus_int_code(2)
% 7.75/5.67 thf(fact_2270_neg__mod__bound,axiom,
% 7.75/5.67 ! [L: int,K: int] :
% 7.75/5.67 ( ( ord_less_int @ L @ zero_zero_int )
% 7.75/5.67 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % neg_mod_bound
% 7.75/5.67 thf(fact_2271_Euclidean__Division_Opos__mod__bound,axiom,
% 7.75/5.67 ! [L: int,K: int] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ L )
% 7.75/5.67 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 7.75/5.67
% 7.75/5.67 % Euclidean_Division.pos_mod_bound
% 7.75/5.67 thf(fact_2272_enat__less__induct,axiom,
% 7.75/5.67 ! [P: extended_enat > $o,N: extended_enat] :
% 7.75/5.67 ( ! [N2: extended_enat] :
% 7.75/5.67 ( ! [M3: extended_enat] :
% 7.75/5.67 ( ( ord_le72135733267957522d_enat @ M3 @ N2 )
% 7.75/5.67 => ( P @ M3 ) )
% 7.75/5.67 => ( P @ N2 ) )
% 7.75/5.67 => ( P @ N ) ) ).
% 7.75/5.67
% 7.75/5.67 % enat_less_induct
% 7.75/5.67 thf(fact_2273_not__iless0,axiom,
% 7.75/5.67 ! [N: extended_enat] :
% 7.75/5.67 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 7.75/5.67
% 7.75/5.67 % not_iless0
% 7.75/5.67 thf(fact_2274_less__int__code_I1_J,axiom,
% 7.75/5.67 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 7.75/5.67
% 7.75/5.67 % less_int_code(1)
% 7.75/5.67 thf(fact_2275_zdvd__not__zless,axiom,
% 7.75/5.67 ! [M: int,N: int] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ M )
% 7.75/5.67 => ( ( ord_less_int @ M @ N )
% 7.75/5.67 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % zdvd_not_zless
% 7.75/5.67 thf(fact_2276_dbl__def,axiom,
% 7.75/5.67 ( neg_numeral_dbl_real
% 7.75/5.67 = ( ^ [X2: real] : ( plus_plus_real @ X2 @ X2 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_def
% 7.75/5.67 thf(fact_2277_dbl__def,axiom,
% 7.75/5.67 ( neg_numeral_dbl_rat
% 7.75/5.67 = ( ^ [X2: rat] : ( plus_plus_rat @ X2 @ X2 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_def
% 7.75/5.67 thf(fact_2278_dbl__def,axiom,
% 7.75/5.67 ( neg_numeral_dbl_int
% 7.75/5.67 = ( ^ [X2: int] : ( plus_plus_int @ X2 @ X2 ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % dbl_def
% 7.75/5.67 thf(fact_2279_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 7.75/5.67 ! [X: nat,N: nat,M: nat] :
% 7.75/5.67 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 7.75/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.67 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.67 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % VEBT_internal.exp_split_high_low(2)
% 7.75/5.67 thf(fact_2280_even__unset__bit__iff,axiom,
% 7.75/5.67 ! [M: nat,A: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 7.75/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 | ( M = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_unset_bit_iff
% 7.75/5.67 thf(fact_2281_even__unset__bit__iff,axiom,
% 7.75/5.67 ! [M: nat,A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 7.75/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 | ( M = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_unset_bit_iff
% 7.75/5.67 thf(fact_2282_even__flip__bit__iff,axiom,
% 7.75/5.67 ! [M: nat,A: int] :
% 7.75/5.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 7.75/5.67 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 != ( M = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_flip_bit_iff
% 7.75/5.67 thf(fact_2283_even__flip__bit__iff,axiom,
% 7.75/5.67 ! [M: nat,A: nat] :
% 7.75/5.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 7.75/5.67 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.67 != ( M = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % even_flip_bit_iff
% 7.75/5.67 thf(fact_2284_mlex__bound,axiom,
% 7.75/5.67 ! [A: nat,A2: nat,B: nat,N4: nat] :
% 7.75/5.67 ( ( ord_less_nat @ A @ A2 )
% 7.75/5.67 => ( ( ord_less_nat @ B @ N4 )
% 7.75/5.67 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( times_times_nat @ A2 @ N4 ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mlex_bound
% 7.75/5.67 thf(fact_2285_mlex__fst__decrI,axiom,
% 7.75/5.67 ! [A: nat,A4: nat,B: nat,N4: nat,B6: nat] :
% 7.75/5.67 ( ( ord_less_nat @ A @ A4 )
% 7.75/5.67 => ( ( ord_less_nat @ B @ N4 )
% 7.75/5.67 => ( ( ord_less_nat @ B6 @ N4 )
% 7.75/5.67 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N4 ) @ B6 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mlex_fst_decrI
% 7.75/5.67 thf(fact_2286_Comparator__Generator_OAll__less__Suc,axiom,
% 7.75/5.67 ! [X: nat,P: nat > $o] :
% 7.75/5.67 ( ( ! [I2: nat] :
% 7.75/5.67 ( ( ord_less_nat @ I2 @ ( suc @ X ) )
% 7.75/5.67 => ( P @ I2 ) ) )
% 7.75/5.67 = ( ( P @ zero_zero_nat )
% 7.75/5.67 & ! [I2: nat] :
% 7.75/5.67 ( ( ord_less_nat @ I2 @ X )
% 7.75/5.67 => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % Comparator_Generator.All_less_Suc
% 7.75/5.67 thf(fact_2287_forall__finite_I2_J,axiom,
% 7.75/5.67 ! [P: nat > $o] :
% 7.75/5.67 ( ( ! [I2: nat] :
% 7.75/5.67 ( ( ord_less_nat @ I2 @ ( suc @ zero_zero_nat ) )
% 7.75/5.67 => ( P @ I2 ) ) )
% 7.75/5.67 = ( P @ zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % forall_finite(2)
% 7.75/5.67 thf(fact_2288_forall__finite_I3_J,axiom,
% 7.75/5.67 ! [X: nat,P: nat > $o] :
% 7.75/5.67 ( ( ! [I2: nat] :
% 7.75/5.67 ( ( ord_less_nat @ I2 @ ( suc @ ( suc @ X ) ) )
% 7.75/5.67 => ( P @ I2 ) ) )
% 7.75/5.67 = ( ( P @ zero_zero_nat )
% 7.75/5.67 & ! [I2: nat] :
% 7.75/5.67 ( ( ord_less_nat @ I2 @ ( suc @ X ) )
% 7.75/5.67 => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % forall_finite(3)
% 7.75/5.67 thf(fact_2289_flip__bit__0,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % flip_bit_0
% 7.75/5.67 thf(fact_2290_flip__bit__0,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 7.75/5.67 = ( 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 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % flip_bit_0
% 7.75/5.67 thf(fact_2291_flip__bit__0,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 7.75/5.67 = ( 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 ) ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % flip_bit_0
% 7.75/5.67 thf(fact_2292_add__scale__eq__noteq,axiom,
% 7.75/5.67 ! [R2: rat,A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.67 ( ( R2 != zero_zero_rat )
% 7.75/5.67 => ( ( ( A = B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 7.75/5.67 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D2 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_scale_eq_noteq
% 7.75/5.67 thf(fact_2293_add__scale__eq__noteq,axiom,
% 7.75/5.67 ! [R2: real,A: real,B: real,C: real,D2: real] :
% 7.75/5.67 ( ( R2 != zero_zero_real )
% 7.75/5.67 => ( ( ( A = B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 7.75/5.67 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D2 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_scale_eq_noteq
% 7.75/5.67 thf(fact_2294_add__scale__eq__noteq,axiom,
% 7.75/5.67 ! [R2: nat,A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.67 ( ( R2 != zero_zero_nat )
% 7.75/5.67 => ( ( ( A = B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 7.75/5.67 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D2 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_scale_eq_noteq
% 7.75/5.67 thf(fact_2295_add__scale__eq__noteq,axiom,
% 7.75/5.67 ! [R2: int,A: int,B: int,C: int,D2: int] :
% 7.75/5.67 ( ( R2 != zero_zero_int )
% 7.75/5.67 => ( ( ( A = B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 7.75/5.67 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D2 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_scale_eq_noteq
% 7.75/5.67 thf(fact_2296_add__scale__eq__noteq,axiom,
% 7.75/5.67 ! [R2: code_integer,A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.67 ( ( R2 != zero_z3403309356797280102nteger )
% 7.75/5.67 => ( ( ( A = B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R2 @ C ) )
% 7.75/5.67 != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R2 @ D2 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_scale_eq_noteq
% 7.75/5.67 thf(fact_2297_add__scale__eq__noteq,axiom,
% 7.75/5.67 ! [R2: complex,A: complex,B: complex,C: complex,D2: complex] :
% 7.75/5.67 ( ( R2 != zero_zero_complex )
% 7.75/5.67 => ( ( ( A = B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 7.75/5.67 != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D2 ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_scale_eq_noteq
% 7.75/5.67 thf(fact_2298_of__bool__eq__0__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n1201886186963655149omplex @ P )
% 7.75/5.67 = zero_zero_complex )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_0_iff
% 7.75/5.67 thf(fact_2299_of__bool__eq__0__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n3304061248610475627l_real @ P )
% 7.75/5.67 = zero_zero_real )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_0_iff
% 7.75/5.67 thf(fact_2300_of__bool__eq__0__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 7.75/5.67 = zero_zero_rat )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_0_iff
% 7.75/5.67 thf(fact_2301_of__bool__eq__0__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 7.75/5.67 = zero_zero_nat )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_0_iff
% 7.75/5.67 thf(fact_2302_of__bool__eq__0__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n2684676970156552555ol_int @ P )
% 7.75/5.67 = zero_zero_int )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_0_iff
% 7.75/5.67 thf(fact_2303_of__bool__eq__0__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n356916108424825756nteger @ P )
% 7.75/5.67 = zero_z3403309356797280102nteger )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_0_iff
% 7.75/5.67 thf(fact_2304_of__bool__eq_I1_J,axiom,
% 7.75/5.67 ( ( zero_n1201886186963655149omplex @ $false )
% 7.75/5.67 = zero_zero_complex ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(1)
% 7.75/5.67 thf(fact_2305_of__bool__eq_I1_J,axiom,
% 7.75/5.67 ( ( zero_n3304061248610475627l_real @ $false )
% 7.75/5.67 = zero_zero_real ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(1)
% 7.75/5.67 thf(fact_2306_of__bool__eq_I1_J,axiom,
% 7.75/5.67 ( ( zero_n2052037380579107095ol_rat @ $false )
% 7.75/5.67 = zero_zero_rat ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(1)
% 7.75/5.67 thf(fact_2307_of__bool__eq_I1_J,axiom,
% 7.75/5.67 ( ( zero_n2687167440665602831ol_nat @ $false )
% 7.75/5.67 = zero_zero_nat ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(1)
% 7.75/5.67 thf(fact_2308_of__bool__eq_I1_J,axiom,
% 7.75/5.67 ( ( zero_n2684676970156552555ol_int @ $false )
% 7.75/5.67 = zero_zero_int ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(1)
% 7.75/5.67 thf(fact_2309_of__bool__eq_I1_J,axiom,
% 7.75/5.67 ( ( zero_n356916108424825756nteger @ $false )
% 7.75/5.67 = zero_z3403309356797280102nteger ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(1)
% 7.75/5.67 thf(fact_2310_of__bool__less__iff,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 7.75/5.67 = ( ~ P
% 7.75/5.67 & Q ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_iff
% 7.75/5.67 thf(fact_2311_of__bool__less__iff,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 7.75/5.67 = ( ~ P
% 7.75/5.67 & Q ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_iff
% 7.75/5.67 thf(fact_2312_of__bool__less__iff,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 7.75/5.67 = ( ~ P
% 7.75/5.67 & Q ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_iff
% 7.75/5.67 thf(fact_2313_of__bool__less__iff,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 7.75/5.67 = ( ~ P
% 7.75/5.67 & Q ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_iff
% 7.75/5.67 thf(fact_2314_of__bool__less__iff,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 7.75/5.67 = ( ~ P
% 7.75/5.67 & Q ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_iff
% 7.75/5.67 thf(fact_2315_of__bool__eq__1__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n3304061248610475627l_real @ P )
% 7.75/5.67 = one_one_real )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_1_iff
% 7.75/5.67 thf(fact_2316_of__bool__eq__1__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 7.75/5.67 = one_one_rat )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_1_iff
% 7.75/5.67 thf(fact_2317_of__bool__eq__1__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 7.75/5.67 = one_one_nat )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_1_iff
% 7.75/5.67 thf(fact_2318_of__bool__eq__1__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n2684676970156552555ol_int @ P )
% 7.75/5.67 = one_one_int )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_1_iff
% 7.75/5.67 thf(fact_2319_of__bool__eq__1__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ( zero_n356916108424825756nteger @ P )
% 7.75/5.67 = one_one_Code_integer )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_1_iff
% 7.75/5.67 thf(fact_2320_of__bool__eq_I2_J,axiom,
% 7.75/5.67 ( ( zero_n3304061248610475627l_real @ $true )
% 7.75/5.67 = one_one_real ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(2)
% 7.75/5.67 thf(fact_2321_of__bool__eq_I2_J,axiom,
% 7.75/5.67 ( ( zero_n2052037380579107095ol_rat @ $true )
% 7.75/5.67 = one_one_rat ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(2)
% 7.75/5.67 thf(fact_2322_of__bool__eq_I2_J,axiom,
% 7.75/5.67 ( ( zero_n2687167440665602831ol_nat @ $true )
% 7.75/5.67 = one_one_nat ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(2)
% 7.75/5.67 thf(fact_2323_of__bool__eq_I2_J,axiom,
% 7.75/5.67 ( ( zero_n2684676970156552555ol_int @ $true )
% 7.75/5.67 = one_one_int ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(2)
% 7.75/5.67 thf(fact_2324_of__bool__eq_I2_J,axiom,
% 7.75/5.67 ( ( zero_n356916108424825756nteger @ $true )
% 7.75/5.67 = one_one_Code_integer ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq(2)
% 7.75/5.67 thf(fact_2325_zero__less__of__bool__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % zero_less_of_bool_iff
% 7.75/5.67 thf(fact_2326_zero__less__of__bool__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % zero_less_of_bool_iff
% 7.75/5.67 thf(fact_2327_zero__less__of__bool__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % zero_less_of_bool_iff
% 7.75/5.67 thf(fact_2328_zero__less__of__bool__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % zero_less_of_bool_iff
% 7.75/5.67 thf(fact_2329_zero__less__of__bool__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 7.75/5.67 = P ) ).
% 7.75/5.67
% 7.75/5.67 % zero_less_of_bool_iff
% 7.75/5.67 thf(fact_2330_of__bool__less__one__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_one_iff
% 7.75/5.67 thf(fact_2331_of__bool__less__one__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_one_iff
% 7.75/5.67 thf(fact_2332_of__bool__less__one__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_one_iff
% 7.75/5.67 thf(fact_2333_of__bool__less__one__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_one_iff
% 7.75/5.67 thf(fact_2334_of__bool__less__one__iff,axiom,
% 7.75/5.67 ! [P: $o] :
% 7.75/5.67 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 7.75/5.67 = ~ P ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_less_one_iff
% 7.75/5.67 thf(fact_2335_Suc__0__mod__eq,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.75/5.67 = ( zero_n2687167440665602831ol_nat
% 7.75/5.67 @ ( N
% 7.75/5.67 != ( suc @ zero_zero_nat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % Suc_0_mod_eq
% 7.75/5.67 thf(fact_2336_odd__of__bool__self,axiom,
% 7.75/5.67 ! [P4: $o] :
% 7.75/5.67 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P4 ) ) )
% 7.75/5.67 = P4 ) ).
% 7.75/5.67
% 7.75/5.67 % odd_of_bool_self
% 7.75/5.67 thf(fact_2337_odd__of__bool__self,axiom,
% 7.75/5.67 ! [P4: $o] :
% 7.75/5.67 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P4 ) ) )
% 7.75/5.67 = P4 ) ).
% 7.75/5.67
% 7.75/5.67 % odd_of_bool_self
% 7.75/5.67 thf(fact_2338_odd__of__bool__self,axiom,
% 7.75/5.67 ! [P4: $o] :
% 7.75/5.67 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P4 ) ) )
% 7.75/5.67 = P4 ) ).
% 7.75/5.67
% 7.75/5.67 % odd_of_bool_self
% 7.75/5.67 thf(fact_2339_of__bool__half__eq__0,axiom,
% 7.75/5.67 ! [B: $o] :
% 7.75/5.67 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_nat ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_half_eq_0
% 7.75/5.67 thf(fact_2340_of__bool__half__eq__0,axiom,
% 7.75/5.67 ! [B: $o] :
% 7.75/5.67 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_zero_int ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_half_eq_0
% 7.75/5.67 thf(fact_2341_of__bool__half__eq__0,axiom,
% 7.75/5.67 ! [B: $o] :
% 7.75/5.67 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 = zero_z3403309356797280102nteger ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_half_eq_0
% 7.75/5.67 thf(fact_2342_one__div__2__pow__eq,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_div_2_pow_eq
% 7.75/5.67 thf(fact_2343_one__div__2__pow__eq,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_div_2_pow_eq
% 7.75/5.67 thf(fact_2344_one__div__2__pow__eq,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_div_2_pow_eq
% 7.75/5.67 thf(fact_2345_bits__1__div__exp,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % bits_1_div_exp
% 7.75/5.67 thf(fact_2346_bits__1__div__exp,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % bits_1_div_exp
% 7.75/5.67 thf(fact_2347_bits__1__div__exp,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % bits_1_div_exp
% 7.75/5.67 thf(fact_2348_one__mod__2__pow__eq,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_mod_2_pow_eq
% 7.75/5.67 thf(fact_2349_one__mod__2__pow__eq,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_mod_2_pow_eq
% 7.75/5.67 thf(fact_2350_one__mod__2__pow__eq,axiom,
% 7.75/5.67 ! [N: nat] :
% 7.75/5.67 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % one_mod_2_pow_eq
% 7.75/5.67 thf(fact_2351_imult__is__0,axiom,
% 7.75/5.67 ! [M: extended_enat,N: extended_enat] :
% 7.75/5.67 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 7.75/5.67 = zero_z5237406670263579293d_enat )
% 7.75/5.67 = ( ( M = zero_z5237406670263579293d_enat )
% 7.75/5.67 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % imult_is_0
% 7.75/5.67 thf(fact_2352_iadd__is__0,axiom,
% 7.75/5.67 ! [M: extended_enat,N: extended_enat] :
% 7.75/5.67 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 7.75/5.67 = zero_z5237406670263579293d_enat )
% 7.75/5.67 = ( ( M = zero_z5237406670263579293d_enat )
% 7.75/5.67 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % iadd_is_0
% 7.75/5.67 thf(fact_2353_zero__one__enat__neq_I1_J,axiom,
% 7.75/5.67 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 7.75/5.67
% 7.75/5.67 % zero_one_enat_neq(1)
% 7.75/5.67 thf(fact_2354_of__bool__eq__iff,axiom,
% 7.75/5.67 ! [P4: $o,Q3: $o] :
% 7.75/5.67 ( ( ( zero_n2687167440665602831ol_nat @ P4 )
% 7.75/5.67 = ( zero_n2687167440665602831ol_nat @ Q3 ) )
% 7.75/5.67 = ( P4 = Q3 ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_iff
% 7.75/5.67 thf(fact_2355_of__bool__eq__iff,axiom,
% 7.75/5.67 ! [P4: $o,Q3: $o] :
% 7.75/5.67 ( ( ( zero_n2684676970156552555ol_int @ P4 )
% 7.75/5.67 = ( zero_n2684676970156552555ol_int @ Q3 ) )
% 7.75/5.67 = ( P4 = Q3 ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_iff
% 7.75/5.67 thf(fact_2356_of__bool__eq__iff,axiom,
% 7.75/5.67 ! [P4: $o,Q3: $o] :
% 7.75/5.67 ( ( ( zero_n356916108424825756nteger @ P4 )
% 7.75/5.67 = ( zero_n356916108424825756nteger @ Q3 ) )
% 7.75/5.67 = ( P4 = Q3 ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_eq_iff
% 7.75/5.67 thf(fact_2357_of__bool__conj,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( zero_n3304061248610475627l_real
% 7.75/5.67 @ ( P
% 7.75/5.67 & Q ) )
% 7.75/5.67 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_conj
% 7.75/5.67 thf(fact_2358_of__bool__conj,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( zero_n1201886186963655149omplex
% 7.75/5.67 @ ( P
% 7.75/5.67 & Q ) )
% 7.75/5.67 = ( times_times_complex @ ( zero_n1201886186963655149omplex @ P ) @ ( zero_n1201886186963655149omplex @ Q ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_conj
% 7.75/5.67 thf(fact_2359_of__bool__conj,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( zero_n2687167440665602831ol_nat
% 7.75/5.67 @ ( P
% 7.75/5.67 & Q ) )
% 7.75/5.67 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_conj
% 7.75/5.67 thf(fact_2360_of__bool__conj,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( zero_n2684676970156552555ol_int
% 7.75/5.67 @ ( P
% 7.75/5.67 & Q ) )
% 7.75/5.67 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_conj
% 7.75/5.67 thf(fact_2361_of__bool__conj,axiom,
% 7.75/5.67 ! [P: $o,Q: $o] :
% 7.75/5.67 ( ( zero_n356916108424825756nteger
% 7.75/5.67 @ ( P
% 7.75/5.67 & Q ) )
% 7.75/5.67 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_conj
% 7.75/5.67 thf(fact_2362_split__of__bool__asm,axiom,
% 7.75/5.67 ! [P: complex > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n1201886186963655149omplex @ P4 ) )
% 7.75/5.67 = ( ~ ( ( P4
% 7.75/5.67 & ~ ( P @ one_one_complex ) )
% 7.75/5.67 | ( ~ P4
% 7.75/5.67 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool_asm
% 7.75/5.67 thf(fact_2363_split__of__bool__asm,axiom,
% 7.75/5.67 ! [P: real > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n3304061248610475627l_real @ P4 ) )
% 7.75/5.67 = ( ~ ( ( P4
% 7.75/5.67 & ~ ( P @ one_one_real ) )
% 7.75/5.67 | ( ~ P4
% 7.75/5.67 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool_asm
% 7.75/5.67 thf(fact_2364_split__of__bool__asm,axiom,
% 7.75/5.67 ! [P: rat > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 7.75/5.67 = ( ~ ( ( P4
% 7.75/5.67 & ~ ( P @ one_one_rat ) )
% 7.75/5.67 | ( ~ P4
% 7.75/5.67 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool_asm
% 7.75/5.67 thf(fact_2365_split__of__bool__asm,axiom,
% 7.75/5.67 ! [P: nat > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 7.75/5.67 = ( ~ ( ( P4
% 7.75/5.67 & ~ ( P @ one_one_nat ) )
% 7.75/5.67 | ( ~ P4
% 7.75/5.67 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool_asm
% 7.75/5.67 thf(fact_2366_split__of__bool__asm,axiom,
% 7.75/5.67 ! [P: int > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 7.75/5.67 = ( ~ ( ( P4
% 7.75/5.67 & ~ ( P @ one_one_int ) )
% 7.75/5.67 | ( ~ P4
% 7.75/5.67 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool_asm
% 7.75/5.67 thf(fact_2367_split__of__bool__asm,axiom,
% 7.75/5.67 ! [P: code_integer > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 7.75/5.67 = ( ~ ( ( P4
% 7.75/5.67 & ~ ( P @ one_one_Code_integer ) )
% 7.75/5.67 | ( ~ P4
% 7.75/5.67 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool_asm
% 7.75/5.67 thf(fact_2368_split__of__bool,axiom,
% 7.75/5.67 ! [P: complex > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n1201886186963655149omplex @ P4 ) )
% 7.75/5.67 = ( ( P4
% 7.75/5.67 => ( P @ one_one_complex ) )
% 7.75/5.67 & ( ~ P4
% 7.75/5.67 => ( P @ zero_zero_complex ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool
% 7.75/5.67 thf(fact_2369_split__of__bool,axiom,
% 7.75/5.67 ! [P: real > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n3304061248610475627l_real @ P4 ) )
% 7.75/5.67 = ( ( P4
% 7.75/5.67 => ( P @ one_one_real ) )
% 7.75/5.67 & ( ~ P4
% 7.75/5.67 => ( P @ zero_zero_real ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool
% 7.75/5.67 thf(fact_2370_split__of__bool,axiom,
% 7.75/5.67 ! [P: rat > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 7.75/5.67 = ( ( P4
% 7.75/5.67 => ( P @ one_one_rat ) )
% 7.75/5.67 & ( ~ P4
% 7.75/5.67 => ( P @ zero_zero_rat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool
% 7.75/5.67 thf(fact_2371_split__of__bool,axiom,
% 7.75/5.67 ! [P: nat > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 7.75/5.67 = ( ( P4
% 7.75/5.67 => ( P @ one_one_nat ) )
% 7.75/5.67 & ( ~ P4
% 7.75/5.67 => ( P @ zero_zero_nat ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool
% 7.75/5.67 thf(fact_2372_split__of__bool,axiom,
% 7.75/5.67 ! [P: int > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 7.75/5.67 = ( ( P4
% 7.75/5.67 => ( P @ one_one_int ) )
% 7.75/5.67 & ( ~ P4
% 7.75/5.67 => ( P @ zero_zero_int ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool
% 7.75/5.67 thf(fact_2373_split__of__bool,axiom,
% 7.75/5.67 ! [P: code_integer > $o,P4: $o] :
% 7.75/5.67 ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 7.75/5.67 = ( ( P4
% 7.75/5.67 => ( P @ one_one_Code_integer ) )
% 7.75/5.67 & ( ~ P4
% 7.75/5.67 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % split_of_bool
% 7.75/5.67 thf(fact_2374_of__bool__def,axiom,
% 7.75/5.67 ( zero_n1201886186963655149omplex
% 7.75/5.67 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_def
% 7.75/5.67 thf(fact_2375_of__bool__def,axiom,
% 7.75/5.67 ( zero_n3304061248610475627l_real
% 7.75/5.67 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_def
% 7.75/5.67 thf(fact_2376_of__bool__def,axiom,
% 7.75/5.67 ( zero_n2052037380579107095ol_rat
% 7.75/5.67 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_def
% 7.75/5.67 thf(fact_2377_of__bool__def,axiom,
% 7.75/5.67 ( zero_n2687167440665602831ol_nat
% 7.75/5.67 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_def
% 7.75/5.67 thf(fact_2378_of__bool__def,axiom,
% 7.75/5.67 ( zero_n2684676970156552555ol_int
% 7.75/5.67 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_def
% 7.75/5.67 thf(fact_2379_of__bool__def,axiom,
% 7.75/5.67 ( zero_n356916108424825756nteger
% 7.75/5.67 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_def
% 7.75/5.67 thf(fact_2380_of__bool__odd__eq__mod__2,axiom,
% 7.75/5.67 ! [A: nat] :
% 7.75/5.67 ( ( zero_n2687167440665602831ol_nat
% 7.75/5.67 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 7.75/5.67 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_odd_eq_mod_2
% 7.75/5.67 thf(fact_2381_of__bool__odd__eq__mod__2,axiom,
% 7.75/5.67 ! [A: int] :
% 7.75/5.67 ( ( zero_n2684676970156552555ol_int
% 7.75/5.67 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 7.75/5.67 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_odd_eq_mod_2
% 7.75/5.67 thf(fact_2382_of__bool__odd__eq__mod__2,axiom,
% 7.75/5.67 ! [A: code_integer] :
% 7.75/5.67 ( ( zero_n356916108424825756nteger
% 7.75/5.67 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 7.75/5.67 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % of_bool_odd_eq_mod_2
% 7.75/5.67 thf(fact_2383_bits__induct,axiom,
% 7.75/5.67 ! [P: nat > $o,A: nat] :
% 7.75/5.67 ( ! [A5: nat] :
% 7.75/5.67 ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = A5 )
% 7.75/5.67 => ( P @ A5 ) )
% 7.75/5.67 => ( ! [A5: nat,B2: $o] :
% 7.75/5.67 ( ( P @ A5 )
% 7.75/5.67 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.67 = A5 )
% 7.75/5.67 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 7.75/5.67 => ( P @ A ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % bits_induct
% 7.75/5.67 thf(fact_2384_bits__induct,axiom,
% 7.75/5.67 ! [P: int > $o,A: int] :
% 7.75/5.67 ( ! [A5: int] :
% 7.75/5.67 ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = A5 )
% 7.75/5.67 => ( P @ A5 ) )
% 7.75/5.67 => ( ! [A5: int,B2: $o] :
% 7.75/5.67 ( ( P @ A5 )
% 7.75/5.67 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.67 = A5 )
% 7.75/5.67 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B2 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 7.75/5.67 => ( P @ A ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % bits_induct
% 7.75/5.67 thf(fact_2385_bits__induct,axiom,
% 7.75/5.67 ! [P: code_integer > $o,A: code_integer] :
% 7.75/5.67 ( ! [A5: code_integer] :
% 7.75/5.67 ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 = A5 )
% 7.75/5.67 => ( P @ A5 ) )
% 7.75/5.67 => ( ! [A5: code_integer,B2: $o] :
% 7.75/5.67 ( ( P @ A5 )
% 7.75/5.67 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.67 = A5 )
% 7.75/5.67 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B2 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 7.75/5.67 => ( P @ A ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % bits_induct
% 7.75/5.67 thf(fact_2386_exp__mod__exp,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % exp_mod_exp
% 7.75/5.67 thf(fact_2387_exp__mod__exp,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % exp_mod_exp
% 7.75/5.67 thf(fact_2388_exp__mod__exp,axiom,
% 7.75/5.67 ! [M: nat,N: nat] :
% 7.75/5.67 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.67 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % exp_mod_exp
% 7.75/5.67 thf(fact_2389_add__0__iff,axiom,
% 7.75/5.67 ! [B: complex,A: complex] :
% 7.75/5.67 ( ( B
% 7.75/5.67 = ( plus_plus_complex @ B @ A ) )
% 7.75/5.67 = ( A = zero_zero_complex ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_0_iff
% 7.75/5.67 thf(fact_2390_add__0__iff,axiom,
% 7.75/5.67 ! [B: real,A: real] :
% 7.75/5.67 ( ( B
% 7.75/5.67 = ( plus_plus_real @ B @ A ) )
% 7.75/5.67 = ( A = zero_zero_real ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_0_iff
% 7.75/5.67 thf(fact_2391_add__0__iff,axiom,
% 7.75/5.67 ! [B: rat,A: rat] :
% 7.75/5.67 ( ( B
% 7.75/5.67 = ( plus_plus_rat @ B @ A ) )
% 7.75/5.67 = ( A = zero_zero_rat ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_0_iff
% 7.75/5.67 thf(fact_2392_add__0__iff,axiom,
% 7.75/5.67 ! [B: nat,A: nat] :
% 7.75/5.67 ( ( B
% 7.75/5.67 = ( plus_plus_nat @ B @ A ) )
% 7.75/5.67 = ( A = zero_zero_nat ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_0_iff
% 7.75/5.67 thf(fact_2393_add__0__iff,axiom,
% 7.75/5.67 ! [B: int,A: int] :
% 7.75/5.67 ( ( B
% 7.75/5.67 = ( plus_plus_int @ B @ A ) )
% 7.75/5.67 = ( A = zero_zero_int ) ) ).
% 7.75/5.67
% 7.75/5.67 % add_0_iff
% 7.75/5.67 thf(fact_2394_crossproduct__noteq,axiom,
% 7.75/5.67 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.67 ( ( ( A != B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 7.75/5.67 != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_noteq
% 7.75/5.67 thf(fact_2395_crossproduct__noteq,axiom,
% 7.75/5.67 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.67 ( ( ( A != B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) )
% 7.75/5.67 != ( plus_plus_real @ ( times_times_real @ A @ D2 ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_noteq
% 7.75/5.67 thf(fact_2396_crossproduct__noteq,axiom,
% 7.75/5.67 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.67 ( ( ( A != B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 7.75/5.67 != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_noteq
% 7.75/5.67 thf(fact_2397_crossproduct__noteq,axiom,
% 7.75/5.67 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.67 ( ( ( A != B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 7.75/5.67 != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_noteq
% 7.75/5.67 thf(fact_2398_crossproduct__noteq,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.67 ( ( ( A != B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) )
% 7.75/5.67 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ D2 ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_noteq
% 7.75/5.67 thf(fact_2399_crossproduct__noteq,axiom,
% 7.75/5.67 ! [A: complex,B: complex,C: complex,D2: complex] :
% 7.75/5.67 ( ( ( A != B )
% 7.75/5.67 & ( C != D2 ) )
% 7.75/5.67 = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D2 ) )
% 7.75/5.67 != ( plus_plus_complex @ ( times_times_complex @ A @ D2 ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_noteq
% 7.75/5.67 thf(fact_2400_crossproduct__eq,axiom,
% 7.75/5.67 ! [W: rat,Y: rat,X: rat,Z: rat] :
% 7.75/5.67 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 7.75/5.67 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 7.75/5.67 = ( ( W = X )
% 7.75/5.67 | ( Y = Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_eq
% 7.75/5.67 thf(fact_2401_crossproduct__eq,axiom,
% 7.75/5.67 ! [W: real,Y: real,X: real,Z: real] :
% 7.75/5.67 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X @ Z ) )
% 7.75/5.67 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y ) ) )
% 7.75/5.67 = ( ( W = X )
% 7.75/5.67 | ( Y = Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_eq
% 7.75/5.67 thf(fact_2402_crossproduct__eq,axiom,
% 7.75/5.67 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 7.75/5.67 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 7.75/5.67 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 7.75/5.67 = ( ( W = X )
% 7.75/5.67 | ( Y = Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_eq
% 7.75/5.67 thf(fact_2403_crossproduct__eq,axiom,
% 7.75/5.67 ! [W: int,Y: int,X: int,Z: int] :
% 7.75/5.67 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 7.75/5.67 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 7.75/5.67 = ( ( W = X )
% 7.75/5.67 | ( Y = Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_eq
% 7.75/5.67 thf(fact_2404_crossproduct__eq,axiom,
% 7.75/5.67 ! [W: code_integer,Y: code_integer,X: code_integer,Z: code_integer] :
% 7.75/5.67 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Y ) @ ( times_3573771949741848930nteger @ X @ Z ) )
% 7.75/5.67 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Z ) @ ( times_3573771949741848930nteger @ X @ Y ) ) )
% 7.75/5.67 = ( ( W = X )
% 7.75/5.67 | ( Y = Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_eq
% 7.75/5.67 thf(fact_2405_crossproduct__eq,axiom,
% 7.75/5.67 ! [W: complex,Y: complex,X: complex,Z: complex] :
% 7.75/5.67 ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y ) @ ( times_times_complex @ X @ Z ) )
% 7.75/5.67 = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X @ Y ) ) )
% 7.75/5.67 = ( ( W = X )
% 7.75/5.67 | ( Y = Z ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % crossproduct_eq
% 7.75/5.67 thf(fact_2406_forall__finite_I1_J,axiom,
% 7.75/5.67 ! [P: nat > $o,I4: nat] :
% 7.75/5.67 ( ( ord_less_nat @ I4 @ zero_zero_nat )
% 7.75/5.67 => ( P @ I4 ) ) ).
% 7.75/5.67
% 7.75/5.67 % forall_finite(1)
% 7.75/5.67 thf(fact_2407_mult__less__iff1,axiom,
% 7.75/5.67 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 7.75/5.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 7.75/5.67 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 7.75/5.67 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_less_iff1
% 7.75/5.67 thf(fact_2408_mult__less__iff1,axiom,
% 7.75/5.67 ! [Z: real,X: real,Y: real] :
% 7.75/5.67 ( ( ord_less_real @ zero_zero_real @ Z )
% 7.75/5.67 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 7.75/5.67 = ( ord_less_real @ X @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_less_iff1
% 7.75/5.67 thf(fact_2409_mult__less__iff1,axiom,
% 7.75/5.67 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.67 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 7.75/5.67 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 7.75/5.67 = ( ord_less_rat @ X @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_less_iff1
% 7.75/5.67 thf(fact_2410_mult__less__iff1,axiom,
% 7.75/5.67 ! [Z: int,X: int,Y: int] :
% 7.75/5.67 ( ( ord_less_int @ zero_zero_int @ Z )
% 7.75/5.67 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 7.75/5.67 = ( ord_less_int @ X @ Y ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % mult_less_iff1
% 7.75/5.67 thf(fact_2411_divmod__digit__1_I1_J,axiom,
% 7.75/5.67 ! [A: code_integer,B: code_integer] :
% 7.75/5.67 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.67 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.67 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 7.75/5.67 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 7.75/5.67 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divmod_digit_1(1)
% 7.75/5.67 thf(fact_2412_divmod__digit__1_I1_J,axiom,
% 7.75/5.67 ! [A: nat,B: nat] :
% 7.75/5.67 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.67 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.67 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 7.75/5.67 => ( ( 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 )
% 7.75/5.67 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divmod_digit_1(1)
% 7.75/5.67 thf(fact_2413_divmod__digit__1_I1_J,axiom,
% 7.75/5.67 ! [A: int,B: int] :
% 7.75/5.67 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.67 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.67 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 7.75/5.67 => ( ( 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 )
% 7.75/5.67 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % divmod_digit_1(1)
% 7.75/5.67 thf(fact_2414_power__le__zero__eq__numeral,axiom,
% 7.75/5.67 ! [A: real,W: num] :
% 7.75/5.67 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 7.75/5.67 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 7.75/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.67 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 7.75/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.67 & ( A = zero_zero_real ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % power_le_zero_eq_numeral
% 7.75/5.67 thf(fact_2415_power__le__zero__eq__numeral,axiom,
% 7.75/5.67 ! [A: code_integer,W: num] :
% 7.75/5.67 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) @ zero_z3403309356797280102nteger )
% 7.75/5.67 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 7.75/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.67 & ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 7.75/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.67 & ( A = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % power_le_zero_eq_numeral
% 7.75/5.67 thf(fact_2416_power__le__zero__eq__numeral,axiom,
% 7.75/5.67 ! [A: rat,W: num] :
% 7.75/5.67 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 7.75/5.67 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 7.75/5.67 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.67 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 7.75/5.67 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.67 & ( A = zero_zero_rat ) ) ) ) ) ).
% 7.75/5.67
% 7.75/5.67 % power_le_zero_eq_numeral
% 7.75/5.67 thf(fact_2417_power__le__zero__eq__numeral,axiom,
% 7.75/5.68 ! [A: int,W: num] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 7.75/5.68 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 7.75/5.68 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 & ( A = zero_zero_int ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_zero_eq_numeral
% 7.75/5.68 thf(fact_2418_signed__take__bit__Suc,axiom,
% 7.75/5.68 ! [N: nat,A: code_integer] :
% 7.75/5.68 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 7.75/5.68 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_Suc
% 7.75/5.68 thf(fact_2419_signed__take__bit__Suc,axiom,
% 7.75/5.68 ! [N: nat,A: int] :
% 7.75/5.68 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 7.75/5.68 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_Suc
% 7.75/5.68 thf(fact_2420_num_Osize__gen_I2_J,axiom,
% 7.75/5.68 ! [X22: num] :
% 7.75/5.68 ( ( size_num @ ( bit0 @ X22 ) )
% 7.75/5.68 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % num.size_gen(2)
% 7.75/5.68 thf(fact_2421_sb__inc__lem,axiom,
% 7.75/5.68 ! [A: int,K: nat] :
% 7.75/5.68 ( ( ord_less_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % sb_inc_lem
% 7.75/5.68 thf(fact_2422_arith__geo__mean,axiom,
% 7.75/5.68 ! [U: real,X: real,Y: real] :
% 7.75/5.68 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.68 = ( times_times_real @ X @ Y ) )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % arith_geo_mean
% 7.75/5.68 thf(fact_2423_arith__geo__mean,axiom,
% 7.75/5.68 ! [U: rat,X: rat,Y: rat] :
% 7.75/5.68 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.68 = ( times_times_rat @ X @ Y ) )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % arith_geo_mean
% 7.75/5.68 thf(fact_2424_less__option__None,axiom,
% 7.75/5.68 ! [X: option_nat] :
% 7.75/5.68 ~ ( ord_less_option_nat @ X @ none_nat ) ).
% 7.75/5.68
% 7.75/5.68 % less_option_None
% 7.75/5.68 thf(fact_2425_less__option__None,axiom,
% 7.75/5.68 ! [X: option_num] :
% 7.75/5.68 ~ ( ord_less_option_num @ X @ none_num ) ).
% 7.75/5.68
% 7.75/5.68 % less_option_None
% 7.75/5.68 thf(fact_2426_min__in__set__def,axiom,
% 7.75/5.68 ( vEBT_VEBT_min_in_set
% 7.75/5.68 = ( ^ [Xs: set_nat,X2: nat] :
% 7.75/5.68 ( ( member_nat @ X2 @ Xs )
% 7.75/5.68 & ! [Y6: nat] :
% 7.75/5.68 ( ( member_nat @ Y6 @ Xs )
% 7.75/5.68 => ( ord_less_eq_nat @ X2 @ Y6 ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % min_in_set_def
% 7.75/5.68 thf(fact_2427_max__in__set__def,axiom,
% 7.75/5.68 ( vEBT_VEBT_max_in_set
% 7.75/5.68 = ( ^ [Xs: set_nat,X2: nat] :
% 7.75/5.68 ( ( member_nat @ X2 @ Xs )
% 7.75/5.68 & ! [Y6: nat] :
% 7.75/5.68 ( ( member_nat @ Y6 @ Xs )
% 7.75/5.68 => ( ord_less_eq_nat @ Y6 @ X2 ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % max_in_set_def
% 7.75/5.68 thf(fact_2428_semiring__norm_I71_J,axiom,
% 7.75/5.68 ! [M: num,N: num] :
% 7.75/5.68 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 7.75/5.68 = ( ord_less_eq_num @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % semiring_norm(71)
% 7.75/5.68 thf(fact_2429_semiring__norm_I68_J,axiom,
% 7.75/5.68 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 7.75/5.68
% 7.75/5.68 % semiring_norm(68)
% 7.75/5.68 thf(fact_2430_Suc__le__mono,axiom,
% 7.75/5.68 ! [N: nat,M: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 7.75/5.68 = ( ord_less_eq_nat @ N @ M ) ) ).
% 7.75/5.68
% 7.75/5.68 % Suc_le_mono
% 7.75/5.68 thf(fact_2431_bot__nat__0_Oextremum,axiom,
% 7.75/5.68 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 7.75/5.68
% 7.75/5.68 % bot_nat_0.extremum
% 7.75/5.68 thf(fact_2432_le0,axiom,
% 7.75/5.68 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 7.75/5.68
% 7.75/5.68 % le0
% 7.75/5.68 thf(fact_2433_nat__add__left__cancel__le,axiom,
% 7.75/5.68 ! [K: nat,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_add_left_cancel_le
% 7.75/5.68 thf(fact_2434_less__eq__option__None__code,axiom,
% 7.75/5.68 ! [X: option_nat] : ( ord_le5914376470875661696on_nat @ none_nat @ X ) ).
% 7.75/5.68
% 7.75/5.68 % less_eq_option_None_code
% 7.75/5.68 thf(fact_2435_less__eq__option__None__code,axiom,
% 7.75/5.68 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 7.75/5.68
% 7.75/5.68 % less_eq_option_None_code
% 7.75/5.68 thf(fact_2436_le__zero__eq,axiom,
% 7.75/5.68 ! [N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 7.75/5.68 = ( N = zero_zero_nat ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_zero_eq
% 7.75/5.68 thf(fact_2437_numeral__le__iff,axiom,
% 7.75/5.68 ! [M: num,N: num] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.68 = ( ord_less_eq_num @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % numeral_le_iff
% 7.75/5.68 thf(fact_2438_numeral__le__iff,axiom,
% 7.75/5.68 ! [M: num,N: num] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 7.75/5.68 = ( ord_less_eq_num @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % numeral_le_iff
% 7.75/5.68 thf(fact_2439_numeral__le__iff,axiom,
% 7.75/5.68 ! [M: num,N: num] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 7.75/5.68 = ( ord_less_eq_num @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % numeral_le_iff
% 7.75/5.68 thf(fact_2440_numeral__le__iff,axiom,
% 7.75/5.68 ! [M: num,N: num] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 7.75/5.68 = ( ord_less_eq_num @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % numeral_le_iff
% 7.75/5.68 thf(fact_2441_add__le__cancel__right,axiom,
% 7.75/5.68 ! [A: real,C: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 7.75/5.68 = ( ord_less_eq_real @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_cancel_right
% 7.75/5.68 thf(fact_2442_add__le__cancel__right,axiom,
% 7.75/5.68 ! [A: rat,C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_cancel_right
% 7.75/5.68 thf(fact_2443_add__le__cancel__right,axiom,
% 7.75/5.68 ! [A: nat,C: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 7.75/5.68 = ( ord_less_eq_nat @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_cancel_right
% 7.75/5.68 thf(fact_2444_add__le__cancel__right,axiom,
% 7.75/5.68 ! [A: int,C: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 7.75/5.68 = ( ord_less_eq_int @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_cancel_right
% 7.75/5.68 thf(fact_2445_add__le__cancel__left,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_real @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_cancel_left
% 7.75/5.68 thf(fact_2446_add__le__cancel__left,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_cancel_left
% 7.75/5.68 thf(fact_2447_add__le__cancel__left,axiom,
% 7.75/5.68 ! [C: nat,A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_nat @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_cancel_left
% 7.75/5.68 thf(fact_2448_add__le__cancel__left,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_int @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_cancel_left
% 7.75/5.68 thf(fact_2449_semiring__norm_I69_J,axiom,
% 7.75/5.68 ! [M: num] :
% 7.75/5.68 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 7.75/5.68
% 7.75/5.68 % semiring_norm(69)
% 7.75/5.68 thf(fact_2450_signed__take__bit__of__0,axiom,
% 7.75/5.68 ! [N: nat] :
% 7.75/5.68 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 7.75/5.68 = zero_zero_int ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_of_0
% 7.75/5.68 thf(fact_2451_of__bool__less__eq__iff,axiom,
% 7.75/5.68 ! [P: $o,Q: $o] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 7.75/5.68 = ( P
% 7.75/5.68 => Q ) ) ).
% 7.75/5.68
% 7.75/5.68 % of_bool_less_eq_iff
% 7.75/5.68 thf(fact_2452_of__bool__less__eq__iff,axiom,
% 7.75/5.68 ! [P: $o,Q: $o] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 7.75/5.68 = ( P
% 7.75/5.68 => Q ) ) ).
% 7.75/5.68
% 7.75/5.68 % of_bool_less_eq_iff
% 7.75/5.68 thf(fact_2453_of__bool__less__eq__iff,axiom,
% 7.75/5.68 ! [P: $o,Q: $o] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 7.75/5.68 = ( P
% 7.75/5.68 => Q ) ) ).
% 7.75/5.68
% 7.75/5.68 % of_bool_less_eq_iff
% 7.75/5.68 thf(fact_2454_of__bool__less__eq__iff,axiom,
% 7.75/5.68 ! [P: $o,Q: $o] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 7.75/5.68 = ( P
% 7.75/5.68 => Q ) ) ).
% 7.75/5.68
% 7.75/5.68 % of_bool_less_eq_iff
% 7.75/5.68 thf(fact_2455_enat__ord__number_I1_J,axiom,
% 7.75/5.68 ! [M: num,N: num] :
% 7.75/5.68 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % enat_ord_number(1)
% 7.75/5.68 thf(fact_2456_zero__le__double__add__iff__zero__le__single__add,axiom,
% 7.75/5.68 ! [A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 7.75/5.68 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_double_add_iff_zero_le_single_add
% 7.75/5.68 thf(fact_2457_zero__le__double__add__iff__zero__le__single__add,axiom,
% 7.75/5.68 ! [A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 7.75/5.68 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_double_add_iff_zero_le_single_add
% 7.75/5.68 thf(fact_2458_zero__le__double__add__iff__zero__le__single__add,axiom,
% 7.75/5.68 ! [A: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 7.75/5.68 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_double_add_iff_zero_le_single_add
% 7.75/5.68 thf(fact_2459_double__add__le__zero__iff__single__add__le__zero,axiom,
% 7.75/5.68 ! [A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 7.75/5.68 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 7.75/5.68
% 7.75/5.68 % double_add_le_zero_iff_single_add_le_zero
% 7.75/5.68 thf(fact_2460_double__add__le__zero__iff__single__add__le__zero,axiom,
% 7.75/5.68 ! [A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.68
% 7.75/5.68 % double_add_le_zero_iff_single_add_le_zero
% 7.75/5.68 thf(fact_2461_double__add__le__zero__iff__single__add__le__zero,axiom,
% 7.75/5.68 ! [A: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 7.75/5.68 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 7.75/5.68
% 7.75/5.68 % double_add_le_zero_iff_single_add_le_zero
% 7.75/5.68 thf(fact_2462_le__add__same__cancel2,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 7.75/5.68 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add_same_cancel2
% 7.75/5.68 thf(fact_2463_le__add__same__cancel2,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 7.75/5.68 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add_same_cancel2
% 7.75/5.68 thf(fact_2464_le__add__same__cancel2,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 7.75/5.68 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add_same_cancel2
% 7.75/5.68 thf(fact_2465_le__add__same__cancel2,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 7.75/5.68 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add_same_cancel2
% 7.75/5.68 thf(fact_2466_le__add__same__cancel1,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 7.75/5.68 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add_same_cancel1
% 7.75/5.68 thf(fact_2467_le__add__same__cancel1,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.68 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add_same_cancel1
% 7.75/5.68 thf(fact_2468_le__add__same__cancel1,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 7.75/5.68 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add_same_cancel1
% 7.75/5.68 thf(fact_2469_le__add__same__cancel1,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 7.75/5.68 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add_same_cancel1
% 7.75/5.68 thf(fact_2470_add__le__same__cancel2,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 7.75/5.68 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_same_cancel2
% 7.75/5.68 thf(fact_2471_add__le__same__cancel2,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_same_cancel2
% 7.75/5.68 thf(fact_2472_add__le__same__cancel2,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 7.75/5.68 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_same_cancel2
% 7.75/5.68 thf(fact_2473_add__le__same__cancel2,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 7.75/5.68 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_same_cancel2
% 7.75/5.68 thf(fact_2474_add__le__same__cancel1,axiom,
% 7.75/5.68 ! [B: real,A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 7.75/5.68 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_same_cancel1
% 7.75/5.68 thf(fact_2475_add__le__same__cancel1,axiom,
% 7.75/5.68 ! [B: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_same_cancel1
% 7.75/5.68 thf(fact_2476_add__le__same__cancel1,axiom,
% 7.75/5.68 ! [B: nat,A: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 7.75/5.68 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_same_cancel1
% 7.75/5.68 thf(fact_2477_add__le__same__cancel1,axiom,
% 7.75/5.68 ! [B: int,A: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 7.75/5.68 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_same_cancel1
% 7.75/5.68 thf(fact_2478_one__le__mult__iff,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 7.75/5.68 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 7.75/5.68 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_mult_iff
% 7.75/5.68 thf(fact_2479_mult__le__cancel2,axiom,
% 7.75/5.68 ! [M: nat,K: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 7.75/5.68 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel2
% 7.75/5.68 thf(fact_2480_nat__mult__le__cancel__disj,axiom,
% 7.75/5.68 ! [K: nat,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.68 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_mult_le_cancel_disj
% 7.75/5.68 thf(fact_2481_signed__take__bit__Suc__1,axiom,
% 7.75/5.68 ! [N: nat] :
% 7.75/5.68 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 7.75/5.68 = one_one_int ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_Suc_1
% 7.75/5.68 thf(fact_2482_signed__take__bit__numeral__of__1,axiom,
% 7.75/5.68 ! [K: num] :
% 7.75/5.68 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 7.75/5.68 = one_one_int ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_numeral_of_1
% 7.75/5.68 thf(fact_2483_unset__bit__nonnegative__int__iff,axiom,
% 7.75/5.68 ! [N: nat,K: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 7.75/5.68 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 7.75/5.68
% 7.75/5.68 % unset_bit_nonnegative_int_iff
% 7.75/5.68 thf(fact_2484_set__bit__nonnegative__int__iff,axiom,
% 7.75/5.68 ! [N: nat,K: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 7.75/5.68 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 7.75/5.68
% 7.75/5.68 % set_bit_nonnegative_int_iff
% 7.75/5.68 thf(fact_2485_flip__bit__nonnegative__int__iff,axiom,
% 7.75/5.68 ! [N: nat,K: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 7.75/5.68 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 7.75/5.68
% 7.75/5.68 % flip_bit_nonnegative_int_iff
% 7.75/5.68 thf(fact_2486_numeral__le__one__iff,axiom,
% 7.75/5.68 ! [N: num] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 7.75/5.68 = ( ord_less_eq_num @ N @ one ) ) ).
% 7.75/5.68
% 7.75/5.68 % numeral_le_one_iff
% 7.75/5.68 thf(fact_2487_numeral__le__one__iff,axiom,
% 7.75/5.68 ! [N: num] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 7.75/5.68 = ( ord_less_eq_num @ N @ one ) ) ).
% 7.75/5.68
% 7.75/5.68 % numeral_le_one_iff
% 7.75/5.68 thf(fact_2488_numeral__le__one__iff,axiom,
% 7.75/5.68 ! [N: num] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 7.75/5.68 = ( ord_less_eq_num @ N @ one ) ) ).
% 7.75/5.68
% 7.75/5.68 % numeral_le_one_iff
% 7.75/5.68 thf(fact_2489_numeral__le__one__iff,axiom,
% 7.75/5.68 ! [N: num] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 7.75/5.68 = ( ord_less_eq_num @ N @ one ) ) ).
% 7.75/5.68
% 7.75/5.68 % numeral_le_one_iff
% 7.75/5.68 thf(fact_2490_divide__le__0__1__iff,axiom,
% 7.75/5.68 ! [A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 7.75/5.68 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_0_1_iff
% 7.75/5.68 thf(fact_2491_divide__le__0__1__iff,axiom,
% 7.75/5.68 ! [A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_0_1_iff
% 7.75/5.68 thf(fact_2492_zero__le__divide__1__iff,axiom,
% 7.75/5.68 ! [A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 7.75/5.68 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_divide_1_iff
% 7.75/5.68 thf(fact_2493_zero__le__divide__1__iff,axiom,
% 7.75/5.68 ! [A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 7.75/5.68 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_divide_1_iff
% 7.75/5.68 thf(fact_2494_power__increasing__iff,axiom,
% 7.75/5.68 ! [B: code_integer,X: nat,Y: nat] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 7.75/5.68 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing_iff
% 7.75/5.68 thf(fact_2495_power__increasing__iff,axiom,
% 7.75/5.68 ! [B: real,X: nat,Y: nat] :
% 7.75/5.68 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 7.75/5.68 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing_iff
% 7.75/5.68 thf(fact_2496_power__increasing__iff,axiom,
% 7.75/5.68 ! [B: rat,X: nat,Y: nat] :
% 7.75/5.68 ( ( ord_less_rat @ one_one_rat @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 7.75/5.68 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing_iff
% 7.75/5.68 thf(fact_2497_power__increasing__iff,axiom,
% 7.75/5.68 ! [B: nat,X: nat,Y: nat] :
% 7.75/5.68 ( ( ord_less_nat @ one_one_nat @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 7.75/5.68 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing_iff
% 7.75/5.68 thf(fact_2498_power__increasing__iff,axiom,
% 7.75/5.68 ! [B: int,X: nat,Y: nat] :
% 7.75/5.68 ( ( ord_less_int @ one_one_int @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 7.75/5.68 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing_iff
% 7.75/5.68 thf(fact_2499_divide__le__eq__numeral1_I1_J,axiom,
% 7.75/5.68 ! [B: real,W: num,A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 7.75/5.68 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq_numeral1(1)
% 7.75/5.68 thf(fact_2500_divide__le__eq__numeral1_I1_J,axiom,
% 7.75/5.68 ! [B: rat,W: num,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 7.75/5.68 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq_numeral1(1)
% 7.75/5.68 thf(fact_2501_le__divide__eq__numeral1_I1_J,axiom,
% 7.75/5.68 ! [A: real,B: real,W: num] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.68 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq_numeral1(1)
% 7.75/5.68 thf(fact_2502_le__divide__eq__numeral1_I1_J,axiom,
% 7.75/5.68 ! [A: rat,B: rat,W: num] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 7.75/5.68 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq_numeral1(1)
% 7.75/5.68 thf(fact_2503_zle__add1__eq__le,axiom,
% 7.75/5.68 ! [W: int,Z: int] :
% 7.75/5.68 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 7.75/5.68 = ( ord_less_eq_int @ W @ Z ) ) ).
% 7.75/5.68
% 7.75/5.68 % zle_add1_eq_le
% 7.75/5.68 thf(fact_2504_mod__neg__neg__trivial,axiom,
% 7.75/5.68 ! [K: int,L: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_int @ L @ K )
% 7.75/5.68 => ( ( modulo_modulo_int @ K @ L )
% 7.75/5.68 = K ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mod_neg_neg_trivial
% 7.75/5.68 thf(fact_2505_mod__pos__pos__trivial,axiom,
% 7.75/5.68 ! [K: int,L: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.68 => ( ( ord_less_int @ K @ L )
% 7.75/5.68 => ( ( modulo_modulo_int @ K @ L )
% 7.75/5.68 = K ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mod_pos_pos_trivial
% 7.75/5.68 thf(fact_2506_div__pos__pos__trivial,axiom,
% 7.75/5.68 ! [K: int,L: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.68 => ( ( ord_less_int @ K @ L )
% 7.75/5.68 => ( ( divide_divide_int @ K @ L )
% 7.75/5.68 = zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_pos_pos_trivial
% 7.75/5.68 thf(fact_2507_div__neg__neg__trivial,axiom,
% 7.75/5.68 ! [K: int,L: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_int @ L @ K )
% 7.75/5.68 => ( ( divide_divide_int @ K @ L )
% 7.75/5.68 = zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_neg_neg_trivial
% 7.75/5.68 thf(fact_2508_divide__le__eq__1__neg,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 7.75/5.68 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq_1_neg
% 7.75/5.68 thf(fact_2509_divide__le__eq__1__neg,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq_1_neg
% 7.75/5.68 thf(fact_2510_divide__le__eq__1__pos,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 7.75/5.68 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq_1_pos
% 7.75/5.68 thf(fact_2511_divide__le__eq__1__pos,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 7.75/5.68 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq_1_pos
% 7.75/5.68 thf(fact_2512_le__divide__eq__1__neg,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 7.75/5.68 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq_1_neg
% 7.75/5.68 thf(fact_2513_le__divide__eq__1__neg,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 7.75/5.68 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq_1_neg
% 7.75/5.68 thf(fact_2514_le__divide__eq__1__pos,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 7.75/5.68 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq_1_pos
% 7.75/5.68 thf(fact_2515_le__divide__eq__1__pos,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq_1_pos
% 7.75/5.68 thf(fact_2516_power__decreasing__iff,axiom,
% 7.75/5.68 ! [B: code_integer,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing_iff
% 7.75/5.68 thf(fact_2517_power__decreasing__iff,axiom,
% 7.75/5.68 ! [B: real,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ( ord_less_real @ B @ one_one_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing_iff
% 7.75/5.68 thf(fact_2518_power__decreasing__iff,axiom,
% 7.75/5.68 ! [B: rat,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ( ord_less_rat @ B @ one_one_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing_iff
% 7.75/5.68 thf(fact_2519_power__decreasing__iff,axiom,
% 7.75/5.68 ! [B: nat,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ( ord_less_nat @ B @ one_one_nat )
% 7.75/5.68 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing_iff
% 7.75/5.68 thf(fact_2520_power__decreasing__iff,axiom,
% 7.75/5.68 ! [B: int,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_int @ B @ one_one_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing_iff
% 7.75/5.68 thf(fact_2521_power__mono__iff,axiom,
% 7.75/5.68 ! [A: real,B: real,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 7.75/5.68 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono_iff
% 7.75/5.68 thf(fact_2522_power__mono__iff,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,N: nat] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 7.75/5.68 = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono_iff
% 7.75/5.68 thf(fact_2523_power__mono__iff,axiom,
% 7.75/5.68 ! [A: rat,B: rat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono_iff
% 7.75/5.68 thf(fact_2524_power__mono__iff,axiom,
% 7.75/5.68 ! [A: nat,B: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono_iff
% 7.75/5.68 thf(fact_2525_power__mono__iff,axiom,
% 7.75/5.68 ! [A: int,B: int,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 7.75/5.68 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono_iff
% 7.75/5.68 thf(fact_2526_signed__take__bit__Suc__bit0,axiom,
% 7.75/5.68 ! [N: nat,K: num] :
% 7.75/5.68 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 7.75/5.68 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_Suc_bit0
% 7.75/5.68 thf(fact_2527_power2__less__eq__zero__iff,axiom,
% 7.75/5.68 ! [A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 7.75/5.68 = ( A = zero_zero_real ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_less_eq_zero_iff
% 7.75/5.68 thf(fact_2528_power2__less__eq__zero__iff,axiom,
% 7.75/5.68 ! [A: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_z3403309356797280102nteger )
% 7.75/5.68 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_less_eq_zero_iff
% 7.75/5.68 thf(fact_2529_power2__less__eq__zero__iff,axiom,
% 7.75/5.68 ! [A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 7.75/5.68 = ( A = zero_zero_rat ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_less_eq_zero_iff
% 7.75/5.68 thf(fact_2530_power2__less__eq__zero__iff,axiom,
% 7.75/5.68 ! [A: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 7.75/5.68 = ( A = zero_zero_int ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_less_eq_zero_iff
% 7.75/5.68 thf(fact_2531_power2__eq__iff__nonneg,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.68 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.68 = ( X = Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_eq_iff_nonneg
% 7.75/5.68 thf(fact_2532_power2__eq__iff__nonneg,axiom,
% 7.75/5.68 ! [X: code_integer,Y: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 7.75/5.68 => ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.68 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.68 = ( X = Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_eq_iff_nonneg
% 7.75/5.68 thf(fact_2533_power2__eq__iff__nonneg,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.68 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.68 = ( X = Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_eq_iff_nonneg
% 7.75/5.68 thf(fact_2534_power2__eq__iff__nonneg,axiom,
% 7.75/5.68 ! [X: nat,Y: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 7.75/5.68 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.68 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.68 = ( X = Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_eq_iff_nonneg
% 7.75/5.68 thf(fact_2535_power2__eq__iff__nonneg,axiom,
% 7.75/5.68 ! [X: int,Y: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.68 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.68 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.68 = ( X = Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_eq_iff_nonneg
% 7.75/5.68 thf(fact_2536_half__nonnegative__int__iff,axiom,
% 7.75/5.68 ! [K: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 7.75/5.68 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 7.75/5.68
% 7.75/5.68 % half_nonnegative_int_iff
% 7.75/5.68 thf(fact_2537_zero__le__power__eq__numeral,axiom,
% 7.75/5.68 ! [A: real,W: num] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 7.75/5.68 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_power_eq_numeral
% 7.75/5.68 thf(fact_2538_zero__le__power__eq__numeral,axiom,
% 7.75/5.68 ! [A: code_integer,W: num] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) )
% 7.75/5.68 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_power_eq_numeral
% 7.75/5.68 thf(fact_2539_zero__le__power__eq__numeral,axiom,
% 7.75/5.68 ! [A: rat,W: num] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 7.75/5.68 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_power_eq_numeral
% 7.75/5.68 thf(fact_2540_zero__le__power__eq__numeral,axiom,
% 7.75/5.68 ! [A: int,W: num] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 7.75/5.68 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.68 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_power_eq_numeral
% 7.75/5.68 thf(fact_2541_lift__Suc__mono__le,axiom,
% 7.75/5.68 ! [F: nat > set_nat,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_mono_le
% 7.75/5.68 thf(fact_2542_lift__Suc__mono__le,axiom,
% 7.75/5.68 ! [F: nat > rat,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_mono_le
% 7.75/5.68 thf(fact_2543_lift__Suc__mono__le,axiom,
% 7.75/5.68 ! [F: nat > num,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_mono_le
% 7.75/5.68 thf(fact_2544_lift__Suc__mono__le,axiom,
% 7.75/5.68 ! [F: nat > nat,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_mono_le
% 7.75/5.68 thf(fact_2545_lift__Suc__mono__le,axiom,
% 7.75/5.68 ! [F: nat > int,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_mono_le
% 7.75/5.68 thf(fact_2546_lift__Suc__antimono__le,axiom,
% 7.75/5.68 ! [F: nat > set_nat,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_antimono_le
% 7.75/5.68 thf(fact_2547_lift__Suc__antimono__le,axiom,
% 7.75/5.68 ! [F: nat > rat,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_antimono_le
% 7.75/5.68 thf(fact_2548_lift__Suc__antimono__le,axiom,
% 7.75/5.68 ! [F: nat > num,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_antimono_le
% 7.75/5.68 thf(fact_2549_lift__Suc__antimono__le,axiom,
% 7.75/5.68 ! [F: nat > nat,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_antimono_le
% 7.75/5.68 thf(fact_2550_lift__Suc__antimono__le,axiom,
% 7.75/5.68 ! [F: nat > int,N: nat,N5: nat] :
% 7.75/5.68 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ N5 )
% 7.75/5.68 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % lift_Suc_antimono_le
% 7.75/5.68 thf(fact_2551_verit__comp__simplify1_I2_J,axiom,
% 7.75/5.68 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(2)
% 7.75/5.68 thf(fact_2552_verit__comp__simplify1_I2_J,axiom,
% 7.75/5.68 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(2)
% 7.75/5.68 thf(fact_2553_verit__comp__simplify1_I2_J,axiom,
% 7.75/5.68 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(2)
% 7.75/5.68 thf(fact_2554_verit__comp__simplify1_I2_J,axiom,
% 7.75/5.68 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(2)
% 7.75/5.68 thf(fact_2555_verit__comp__simplify1_I2_J,axiom,
% 7.75/5.68 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(2)
% 7.75/5.68 thf(fact_2556_verit__la__generic,axiom,
% 7.75/5.68 ! [A: int,X: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ X )
% 7.75/5.68 | ( A = X )
% 7.75/5.68 | ( ord_less_eq_int @ X @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_la_generic
% 7.75/5.68 thf(fact_2557_verit__la__disequality,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( A = B )
% 7.75/5.68 | ~ ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_la_disequality
% 7.75/5.68 thf(fact_2558_verit__la__disequality,axiom,
% 7.75/5.68 ! [A: num,B: num] :
% 7.75/5.68 ( ( A = B )
% 7.75/5.68 | ~ ( ord_less_eq_num @ A @ B )
% 7.75/5.68 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_la_disequality
% 7.75/5.68 thf(fact_2559_verit__la__disequality,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( A = B )
% 7.75/5.68 | ~ ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_la_disequality
% 7.75/5.68 thf(fact_2560_verit__la__disequality,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( A = B )
% 7.75/5.68 | ~ ( ord_less_eq_int @ A @ B )
% 7.75/5.68 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_la_disequality
% 7.75/5.68 thf(fact_2561_less__eq__option__None,axiom,
% 7.75/5.68 ! [X: option_nat] : ( ord_le5914376470875661696on_nat @ none_nat @ X ) ).
% 7.75/5.68
% 7.75/5.68 % less_eq_option_None
% 7.75/5.68 thf(fact_2562_less__eq__option__None,axiom,
% 7.75/5.68 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 7.75/5.68
% 7.75/5.68 % less_eq_option_None
% 7.75/5.68 thf(fact_2563_less__eq__option__None__is__None,axiom,
% 7.75/5.68 ! [X: option_nat] :
% 7.75/5.68 ( ( ord_le5914376470875661696on_nat @ X @ none_nat )
% 7.75/5.68 => ( X = none_nat ) ) ).
% 7.75/5.68
% 7.75/5.68 % less_eq_option_None_is_None
% 7.75/5.68 thf(fact_2564_less__eq__option__None__is__None,axiom,
% 7.75/5.68 ! [X: option_num] :
% 7.75/5.68 ( ( ord_le6622620407824499402on_num @ X @ none_num )
% 7.75/5.68 => ( X = none_num ) ) ).
% 7.75/5.68
% 7.75/5.68 % less_eq_option_None_is_None
% 7.75/5.68 thf(fact_2565_subset__decode__imp__le,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % subset_decode_imp_le
% 7.75/5.68 thf(fact_2566_power__increasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: real] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_less_eq_real @ one_one_real @ A )
% 7.75/5.68 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing
% 7.75/5.68 thf(fact_2567_power__increasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: code_integer] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing
% 7.75/5.68 thf(fact_2568_power__increasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 7.75/5.68 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing
% 7.75/5.68 thf(fact_2569_power__increasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 7.75/5.68 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing
% 7.75/5.68 thf(fact_2570_power__increasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: int] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_less_eq_int @ one_one_int @ A )
% 7.75/5.68 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_increasing
% 7.75/5.68 thf(fact_2571_signed__take__bit__add,axiom,
% 7.75/5.68 ! [N: nat,K: int,L: int] :
% 7.75/5.68 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 7.75/5.68 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_add
% 7.75/5.68 thf(fact_2572_signed__take__bit__mult,axiom,
% 7.75/5.68 ! [N: nat,K: int,L: int] :
% 7.75/5.68 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 7.75/5.68 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_mult
% 7.75/5.68 thf(fact_2573_zero__le,axiom,
% 7.75/5.68 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le
% 7.75/5.68 thf(fact_2574_le__numeral__extra_I3_J,axiom,
% 7.75/5.68 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 7.75/5.68
% 7.75/5.68 % le_numeral_extra(3)
% 7.75/5.68 thf(fact_2575_le__numeral__extra_I3_J,axiom,
% 7.75/5.68 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 7.75/5.68
% 7.75/5.68 % le_numeral_extra(3)
% 7.75/5.68 thf(fact_2576_le__numeral__extra_I3_J,axiom,
% 7.75/5.68 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 7.75/5.68
% 7.75/5.68 % le_numeral_extra(3)
% 7.75/5.68 thf(fact_2577_le__numeral__extra_I3_J,axiom,
% 7.75/5.68 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 7.75/5.68
% 7.75/5.68 % le_numeral_extra(3)
% 7.75/5.68 thf(fact_2578_verit__comp__simplify1_I3_J,axiom,
% 7.75/5.68 ! [B6: real,A4: real] :
% 7.75/5.68 ( ( ~ ( ord_less_eq_real @ B6 @ A4 ) )
% 7.75/5.68 = ( ord_less_real @ A4 @ B6 ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(3)
% 7.75/5.68 thf(fact_2579_verit__comp__simplify1_I3_J,axiom,
% 7.75/5.68 ! [B6: rat,A4: rat] :
% 7.75/5.68 ( ( ~ ( ord_less_eq_rat @ B6 @ A4 ) )
% 7.75/5.68 = ( ord_less_rat @ A4 @ B6 ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(3)
% 7.75/5.68 thf(fact_2580_verit__comp__simplify1_I3_J,axiom,
% 7.75/5.68 ! [B6: num,A4: num] :
% 7.75/5.68 ( ( ~ ( ord_less_eq_num @ B6 @ A4 ) )
% 7.75/5.68 = ( ord_less_num @ A4 @ B6 ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(3)
% 7.75/5.68 thf(fact_2581_verit__comp__simplify1_I3_J,axiom,
% 7.75/5.68 ! [B6: nat,A4: nat] :
% 7.75/5.68 ( ( ~ ( ord_less_eq_nat @ B6 @ A4 ) )
% 7.75/5.68 = ( ord_less_nat @ A4 @ B6 ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(3)
% 7.75/5.68 thf(fact_2582_verit__comp__simplify1_I3_J,axiom,
% 7.75/5.68 ! [B6: int,A4: int] :
% 7.75/5.68 ( ( ~ ( ord_less_eq_int @ B6 @ A4 ) )
% 7.75/5.68 = ( ord_less_int @ A4 @ B6 ) ) ).
% 7.75/5.68
% 7.75/5.68 % verit_comp_simplify1(3)
% 7.75/5.68 thf(fact_2583_pinf_I6_J,axiom,
% 7.75/5.68 ! [T: real] :
% 7.75/5.68 ? [Z3: real] :
% 7.75/5.68 ! [X5: real] :
% 7.75/5.68 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.68 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(6)
% 7.75/5.68 thf(fact_2584_pinf_I6_J,axiom,
% 7.75/5.68 ! [T: rat] :
% 7.75/5.68 ? [Z3: rat] :
% 7.75/5.68 ! [X5: rat] :
% 7.75/5.68 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.68 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(6)
% 7.75/5.68 thf(fact_2585_pinf_I6_J,axiom,
% 7.75/5.68 ! [T: num] :
% 7.75/5.68 ? [Z3: num] :
% 7.75/5.68 ! [X5: num] :
% 7.75/5.68 ( ( ord_less_num @ Z3 @ X5 )
% 7.75/5.68 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(6)
% 7.75/5.68 thf(fact_2586_pinf_I6_J,axiom,
% 7.75/5.68 ! [T: nat] :
% 7.75/5.68 ? [Z3: nat] :
% 7.75/5.68 ! [X5: nat] :
% 7.75/5.68 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.68 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(6)
% 7.75/5.68 thf(fact_2587_pinf_I6_J,axiom,
% 7.75/5.68 ! [T: int] :
% 7.75/5.68 ? [Z3: int] :
% 7.75/5.68 ! [X5: int] :
% 7.75/5.68 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.68 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(6)
% 7.75/5.68 thf(fact_2588_pinf_I8_J,axiom,
% 7.75/5.68 ! [T: real] :
% 7.75/5.68 ? [Z3: real] :
% 7.75/5.68 ! [X5: real] :
% 7.75/5.68 ( ( ord_less_real @ Z3 @ X5 )
% 7.75/5.68 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(8)
% 7.75/5.68 thf(fact_2589_pinf_I8_J,axiom,
% 7.75/5.68 ! [T: rat] :
% 7.75/5.68 ? [Z3: rat] :
% 7.75/5.68 ! [X5: rat] :
% 7.75/5.68 ( ( ord_less_rat @ Z3 @ X5 )
% 7.75/5.68 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(8)
% 7.75/5.68 thf(fact_2590_pinf_I8_J,axiom,
% 7.75/5.68 ! [T: num] :
% 7.75/5.68 ? [Z3: num] :
% 7.75/5.68 ! [X5: num] :
% 7.75/5.68 ( ( ord_less_num @ Z3 @ X5 )
% 7.75/5.68 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(8)
% 7.75/5.68 thf(fact_2591_pinf_I8_J,axiom,
% 7.75/5.68 ! [T: nat] :
% 7.75/5.68 ? [Z3: nat] :
% 7.75/5.68 ! [X5: nat] :
% 7.75/5.68 ( ( ord_less_nat @ Z3 @ X5 )
% 7.75/5.68 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(8)
% 7.75/5.68 thf(fact_2592_pinf_I8_J,axiom,
% 7.75/5.68 ! [T: int] :
% 7.75/5.68 ? [Z3: int] :
% 7.75/5.68 ! [X5: int] :
% 7.75/5.68 ( ( ord_less_int @ Z3 @ X5 )
% 7.75/5.68 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % pinf(8)
% 7.75/5.68 thf(fact_2593_minf_I6_J,axiom,
% 7.75/5.68 ! [T: real] :
% 7.75/5.68 ? [Z3: real] :
% 7.75/5.68 ! [X5: real] :
% 7.75/5.68 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.68 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(6)
% 7.75/5.68 thf(fact_2594_minf_I6_J,axiom,
% 7.75/5.68 ! [T: rat] :
% 7.75/5.68 ? [Z3: rat] :
% 7.75/5.68 ! [X5: rat] :
% 7.75/5.68 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.68 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(6)
% 7.75/5.68 thf(fact_2595_minf_I6_J,axiom,
% 7.75/5.68 ! [T: num] :
% 7.75/5.68 ? [Z3: num] :
% 7.75/5.68 ! [X5: num] :
% 7.75/5.68 ( ( ord_less_num @ X5 @ Z3 )
% 7.75/5.68 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(6)
% 7.75/5.68 thf(fact_2596_minf_I6_J,axiom,
% 7.75/5.68 ! [T: nat] :
% 7.75/5.68 ? [Z3: nat] :
% 7.75/5.68 ! [X5: nat] :
% 7.75/5.68 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.68 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(6)
% 7.75/5.68 thf(fact_2597_minf_I6_J,axiom,
% 7.75/5.68 ! [T: int] :
% 7.75/5.68 ? [Z3: int] :
% 7.75/5.68 ! [X5: int] :
% 7.75/5.68 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.68 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(6)
% 7.75/5.68 thf(fact_2598_minf_I8_J,axiom,
% 7.75/5.68 ! [T: real] :
% 7.75/5.68 ? [Z3: real] :
% 7.75/5.68 ! [X5: real] :
% 7.75/5.68 ( ( ord_less_real @ X5 @ Z3 )
% 7.75/5.68 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(8)
% 7.75/5.68 thf(fact_2599_minf_I8_J,axiom,
% 7.75/5.68 ! [T: rat] :
% 7.75/5.68 ? [Z3: rat] :
% 7.75/5.68 ! [X5: rat] :
% 7.75/5.68 ( ( ord_less_rat @ X5 @ Z3 )
% 7.75/5.68 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(8)
% 7.75/5.68 thf(fact_2600_minf_I8_J,axiom,
% 7.75/5.68 ! [T: num] :
% 7.75/5.68 ? [Z3: num] :
% 7.75/5.68 ! [X5: num] :
% 7.75/5.68 ( ( ord_less_num @ X5 @ Z3 )
% 7.75/5.68 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(8)
% 7.75/5.68 thf(fact_2601_minf_I8_J,axiom,
% 7.75/5.68 ! [T: nat] :
% 7.75/5.68 ? [Z3: nat] :
% 7.75/5.68 ! [X5: nat] :
% 7.75/5.68 ( ( ord_less_nat @ X5 @ Z3 )
% 7.75/5.68 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(8)
% 7.75/5.68 thf(fact_2602_minf_I8_J,axiom,
% 7.75/5.68 ! [T: int] :
% 7.75/5.68 ? [Z3: int] :
% 7.75/5.68 ! [X5: int] :
% 7.75/5.68 ( ( ord_less_int @ X5 @ Z3 )
% 7.75/5.68 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 7.75/5.68
% 7.75/5.68 % minf(8)
% 7.75/5.68 thf(fact_2603_add__le__imp__le__right,axiom,
% 7.75/5.68 ! [A: real,C: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 7.75/5.68 => ( ord_less_eq_real @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_imp_le_right
% 7.75/5.68 thf(fact_2604_add__le__imp__le__right,axiom,
% 7.75/5.68 ! [A: rat,C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_imp_le_right
% 7.75/5.68 thf(fact_2605_add__le__imp__le__right,axiom,
% 7.75/5.68 ! [A: nat,C: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 7.75/5.68 => ( ord_less_eq_nat @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_imp_le_right
% 7.75/5.68 thf(fact_2606_add__le__imp__le__right,axiom,
% 7.75/5.68 ! [A: int,C: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 7.75/5.68 => ( ord_less_eq_int @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_imp_le_right
% 7.75/5.68 thf(fact_2607_add__le__imp__le__left,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 7.75/5.68 => ( ord_less_eq_real @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_imp_le_left
% 7.75/5.68 thf(fact_2608_add__le__imp__le__left,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_imp_le_left
% 7.75/5.68 thf(fact_2609_add__le__imp__le__left,axiom,
% 7.75/5.68 ! [C: nat,A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 7.75/5.68 => ( ord_less_eq_nat @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_imp_le_left
% 7.75/5.68 thf(fact_2610_add__le__imp__le__left,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 7.75/5.68 => ( ord_less_eq_int @ A @ B ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_imp_le_left
% 7.75/5.68 thf(fact_2611_le__iff__add,axiom,
% 7.75/5.68 ( ord_less_eq_nat
% 7.75/5.68 = ( ^ [A3: nat,B4: nat] :
% 7.75/5.68 ? [C4: nat] :
% 7.75/5.68 ( B4
% 7.75/5.68 = ( plus_plus_nat @ A3 @ C4 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_iff_add
% 7.75/5.68 thf(fact_2612_add__right__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_right_mono
% 7.75/5.68 thf(fact_2613_add__right__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_right_mono
% 7.75/5.68 thf(fact_2614_add__right__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_right_mono
% 7.75/5.68 thf(fact_2615_add__right__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_right_mono
% 7.75/5.68 thf(fact_2616_less__eqE,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ~ ! [C3: nat] :
% 7.75/5.68 ( B
% 7.75/5.68 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % less_eqE
% 7.75/5.68 thf(fact_2617_add__left__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_left_mono
% 7.75/5.68 thf(fact_2618_add__left__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_left_mono
% 7.75/5.68 thf(fact_2619_add__left__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_left_mono
% 7.75/5.68 thf(fact_2620_add__left__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_left_mono
% 7.75/5.68 thf(fact_2621_add__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ D2 )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono
% 7.75/5.68 thf(fact_2622_add__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ D2 )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono
% 7.75/5.68 thf(fact_2623_add__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ C @ D2 )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono
% 7.75/5.68 thf(fact_2624_add__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ C @ D2 )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono
% 7.75/5.68 thf(fact_2625_add__mono__thms__linordered__semiring_I1_J,axiom,
% 7.75/5.68 ! [I: real,J: real,K: real,L: real] :
% 7.75/5.68 ( ( ( ord_less_eq_real @ I @ J )
% 7.75/5.68 & ( ord_less_eq_real @ K @ L ) )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(1)
% 7.75/5.68 thf(fact_2626_add__mono__thms__linordered__semiring_I1_J,axiom,
% 7.75/5.68 ! [I: rat,J: rat,K: rat,L: rat] :
% 7.75/5.68 ( ( ( ord_less_eq_rat @ I @ J )
% 7.75/5.68 & ( ord_less_eq_rat @ K @ L ) )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(1)
% 7.75/5.68 thf(fact_2627_add__mono__thms__linordered__semiring_I1_J,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.68 ( ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 & ( ord_less_eq_nat @ K @ L ) )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(1)
% 7.75/5.68 thf(fact_2628_add__mono__thms__linordered__semiring_I1_J,axiom,
% 7.75/5.68 ! [I: int,J: int,K: int,L: int] :
% 7.75/5.68 ( ( ( ord_less_eq_int @ I @ J )
% 7.75/5.68 & ( ord_less_eq_int @ K @ L ) )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(1)
% 7.75/5.68 thf(fact_2629_add__mono__thms__linordered__semiring_I2_J,axiom,
% 7.75/5.68 ! [I: real,J: real,K: real,L: real] :
% 7.75/5.68 ( ( ( I = J )
% 7.75/5.68 & ( ord_less_eq_real @ K @ L ) )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(2)
% 7.75/5.68 thf(fact_2630_add__mono__thms__linordered__semiring_I2_J,axiom,
% 7.75/5.68 ! [I: rat,J: rat,K: rat,L: rat] :
% 7.75/5.68 ( ( ( I = J )
% 7.75/5.68 & ( ord_less_eq_rat @ K @ L ) )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(2)
% 7.75/5.68 thf(fact_2631_add__mono__thms__linordered__semiring_I2_J,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.68 ( ( ( I = J )
% 7.75/5.68 & ( ord_less_eq_nat @ K @ L ) )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(2)
% 7.75/5.68 thf(fact_2632_add__mono__thms__linordered__semiring_I2_J,axiom,
% 7.75/5.68 ! [I: int,J: int,K: int,L: int] :
% 7.75/5.68 ( ( ( I = J )
% 7.75/5.68 & ( ord_less_eq_int @ K @ L ) )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(2)
% 7.75/5.68 thf(fact_2633_add__mono__thms__linordered__semiring_I3_J,axiom,
% 7.75/5.68 ! [I: real,J: real,K: real,L: real] :
% 7.75/5.68 ( ( ( ord_less_eq_real @ I @ J )
% 7.75/5.68 & ( K = L ) )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(3)
% 7.75/5.68 thf(fact_2634_add__mono__thms__linordered__semiring_I3_J,axiom,
% 7.75/5.68 ! [I: rat,J: rat,K: rat,L: rat] :
% 7.75/5.68 ( ( ( ord_less_eq_rat @ I @ J )
% 7.75/5.68 & ( K = L ) )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(3)
% 7.75/5.68 thf(fact_2635_add__mono__thms__linordered__semiring_I3_J,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.68 ( ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 & ( K = L ) )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(3)
% 7.75/5.68 thf(fact_2636_add__mono__thms__linordered__semiring_I3_J,axiom,
% 7.75/5.68 ! [I: int,J: int,K: int,L: int] :
% 7.75/5.68 ( ( ( ord_less_eq_int @ I @ J )
% 7.75/5.68 & ( K = L ) )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_semiring(3)
% 7.75/5.68 thf(fact_2637_le__numeral__extra_I4_J,axiom,
% 7.75/5.68 ord_less_eq_real @ one_one_real @ one_one_real ).
% 7.75/5.68
% 7.75/5.68 % le_numeral_extra(4)
% 7.75/5.68 thf(fact_2638_le__numeral__extra_I4_J,axiom,
% 7.75/5.68 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 7.75/5.68
% 7.75/5.68 % le_numeral_extra(4)
% 7.75/5.68 thf(fact_2639_le__numeral__extra_I4_J,axiom,
% 7.75/5.68 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 7.75/5.68
% 7.75/5.68 % le_numeral_extra(4)
% 7.75/5.68 thf(fact_2640_le__numeral__extra_I4_J,axiom,
% 7.75/5.68 ord_less_eq_int @ one_one_int @ one_one_int ).
% 7.75/5.68
% 7.75/5.68 % le_numeral_extra(4)
% 7.75/5.68 thf(fact_2641_le__num__One__iff,axiom,
% 7.75/5.68 ! [X: num] :
% 7.75/5.68 ( ( ord_less_eq_num @ X @ one )
% 7.75/5.68 = ( X = one ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_num_One_iff
% 7.75/5.68 thf(fact_2642_Suc__leD,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % Suc_leD
% 7.75/5.68 thf(fact_2643_le__SucE,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.68 => ( ~ ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( M
% 7.75/5.68 = ( suc @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_SucE
% 7.75/5.68 thf(fact_2644_le__SucI,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_SucI
% 7.75/5.68 thf(fact_2645_Suc__le__D,axiom,
% 7.75/5.68 ! [N: nat,M6: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 7.75/5.68 => ? [M2: nat] :
% 7.75/5.68 ( M6
% 7.75/5.68 = ( suc @ M2 ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % Suc_le_D
% 7.75/5.68 thf(fact_2646_le__Suc__eq,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.68 = ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 | ( M
% 7.75/5.68 = ( suc @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_Suc_eq
% 7.75/5.68 thf(fact_2647_Suc__n__not__le__n,axiom,
% 7.75/5.68 ! [N: nat] :
% 7.75/5.68 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 7.75/5.68
% 7.75/5.68 % Suc_n_not_le_n
% 7.75/5.68 thf(fact_2648_not__less__eq__eq,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 7.75/5.68
% 7.75/5.68 % not_less_eq_eq
% 7.75/5.68 thf(fact_2649_full__nat__induct,axiom,
% 7.75/5.68 ! [P: nat > $o,N: nat] :
% 7.75/5.68 ( ! [N2: nat] :
% 7.75/5.68 ( ! [M3: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N2 )
% 7.75/5.68 => ( P @ M3 ) )
% 7.75/5.68 => ( P @ N2 ) )
% 7.75/5.68 => ( P @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % full_nat_induct
% 7.75/5.68 thf(fact_2650_nat__induct__at__least,axiom,
% 7.75/5.68 ! [M: nat,N: nat,P: nat > $o] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( ( P @ M )
% 7.75/5.68 => ( ! [N2: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N2 )
% 7.75/5.68 => ( ( P @ N2 )
% 7.75/5.68 => ( P @ ( suc @ N2 ) ) ) )
% 7.75/5.68 => ( P @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_induct_at_least
% 7.75/5.68 thf(fact_2651_transitive__stepwise__le,axiom,
% 7.75/5.68 ! [M: nat,N: nat,R: nat > nat > $o] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 7.75/5.68 => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 7.75/5.68 ( ( R @ X3 @ Y3 )
% 7.75/5.68 => ( ( R @ Y3 @ Z3 )
% 7.75/5.68 => ( R @ X3 @ Z3 ) ) )
% 7.75/5.68 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 7.75/5.68 => ( R @ M @ N ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % transitive_stepwise_le
% 7.75/5.68 thf(fact_2652_less__eq__nat_Osimps_I1_J,axiom,
% 7.75/5.68 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 7.75/5.68
% 7.75/5.68 % less_eq_nat.simps(1)
% 7.75/5.68 thf(fact_2653_bot__nat__0_Oextremum__unique,axiom,
% 7.75/5.68 ! [A: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 7.75/5.68 = ( A = zero_zero_nat ) ) ).
% 7.75/5.68
% 7.75/5.68 % bot_nat_0.extremum_unique
% 7.75/5.68 thf(fact_2654_bot__nat__0_Oextremum__uniqueI,axiom,
% 7.75/5.68 ! [A: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 7.75/5.68 => ( A = zero_zero_nat ) ) ).
% 7.75/5.68
% 7.75/5.68 % bot_nat_0.extremum_uniqueI
% 7.75/5.68 thf(fact_2655_le__0__eq,axiom,
% 7.75/5.68 ! [N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 7.75/5.68 = ( N = zero_zero_nat ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_0_eq
% 7.75/5.68 thf(fact_2656_exists__leI,axiom,
% 7.75/5.68 ! [N: nat,P: nat > $o] :
% 7.75/5.68 ( ( ! [N6: nat] :
% 7.75/5.68 ( ( ord_less_nat @ N6 @ N )
% 7.75/5.68 => ~ ( P @ N6 ) )
% 7.75/5.68 => ( P @ N ) )
% 7.75/5.68 => ? [N7: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N7 @ N )
% 7.75/5.68 & ( P @ N7 ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % exists_leI
% 7.75/5.68 thf(fact_2657_nat__less__le,axiom,
% 7.75/5.68 ( ord_less_nat
% 7.75/5.68 = ( ^ [M4: nat,N3: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M4 @ N3 )
% 7.75/5.68 & ( M4 != N3 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_less_le
% 7.75/5.68 thf(fact_2658_less__imp__le__nat,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_nat @ M @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % less_imp_le_nat
% 7.75/5.68 thf(fact_2659_le__eq__less__or__eq,axiom,
% 7.75/5.68 ( ord_less_eq_nat
% 7.75/5.68 = ( ^ [M4: nat,N3: nat] :
% 7.75/5.68 ( ( ord_less_nat @ M4 @ N3 )
% 7.75/5.68 | ( M4 = N3 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_eq_less_or_eq
% 7.75/5.68 thf(fact_2660_less__or__eq__imp__le,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ( ord_less_nat @ M @ N )
% 7.75/5.68 | ( M = N ) )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % less_or_eq_imp_le
% 7.75/5.68 thf(fact_2661_le__neq__implies__less,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( ( M != N )
% 7.75/5.68 => ( ord_less_nat @ M @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_neq_implies_less
% 7.75/5.68 thf(fact_2662_less__mono__imp__le__mono,axiom,
% 7.75/5.68 ! [F: nat > nat,I: nat,J: nat] :
% 7.75/5.68 ( ! [I3: nat,J3: nat] :
% 7.75/5.68 ( ( ord_less_nat @ I3 @ J3 )
% 7.75/5.68 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J3 ) ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % less_mono_imp_le_mono
% 7.75/5.68 thf(fact_2663_nat__le__iff__add,axiom,
% 7.75/5.68 ( ord_less_eq_nat
% 7.75/5.68 = ( ^ [M4: nat,N3: nat] :
% 7.75/5.68 ? [K3: nat] :
% 7.75/5.68 ( N3
% 7.75/5.68 = ( plus_plus_nat @ M4 @ K3 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_le_iff_add
% 7.75/5.68 thf(fact_2664_trans__le__add2,axiom,
% 7.75/5.68 ! [I: nat,J: nat,M: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % trans_le_add2
% 7.75/5.68 thf(fact_2665_trans__le__add1,axiom,
% 7.75/5.68 ! [I: nat,J: nat,M: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % trans_le_add1
% 7.75/5.68 thf(fact_2666_add__le__mono1,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_mono1
% 7.75/5.68 thf(fact_2667_add__le__mono,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ( ord_less_eq_nat @ K @ L )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_mono
% 7.75/5.68 thf(fact_2668_le__Suc__ex,axiom,
% 7.75/5.68 ! [K: nat,L: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ K @ L )
% 7.75/5.68 => ? [N2: nat] :
% 7.75/5.68 ( L
% 7.75/5.68 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_Suc_ex
% 7.75/5.68 thf(fact_2669_add__leD2,axiom,
% 7.75/5.68 ! [M: nat,K: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ K @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_leD2
% 7.75/5.68 thf(fact_2670_add__leD1,axiom,
% 7.75/5.68 ! [M: nat,K: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_leD1
% 7.75/5.68 thf(fact_2671_le__add2,axiom,
% 7.75/5.68 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add2
% 7.75/5.68 thf(fact_2672_le__add1,axiom,
% 7.75/5.68 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_add1
% 7.75/5.68 thf(fact_2673_add__leE,axiom,
% 7.75/5.68 ! [M: nat,K: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 7.75/5.68 => ~ ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_leE
% 7.75/5.68 thf(fact_2674_less__eq__real__def,axiom,
% 7.75/5.68 ( ord_less_eq_real
% 7.75/5.68 = ( ^ [X2: real,Y6: real] :
% 7.75/5.68 ( ( ord_less_real @ X2 @ Y6 )
% 7.75/5.68 | ( X2 = Y6 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % less_eq_real_def
% 7.75/5.68 thf(fact_2675_conj__le__cong,axiom,
% 7.75/5.68 ! [X: int,X6: int,P: $o,P3: $o] :
% 7.75/5.68 ( ( X = X6 )
% 7.75/5.68 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 7.75/5.68 => ( P = P3 ) )
% 7.75/5.68 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.68 & P )
% 7.75/5.68 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 7.75/5.68 & P3 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % conj_le_cong
% 7.75/5.68 thf(fact_2676_imp__le__cong,axiom,
% 7.75/5.68 ! [X: int,X6: int,P: $o,P3: $o] :
% 7.75/5.68 ( ( X = X6 )
% 7.75/5.68 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 7.75/5.68 => ( P = P3 ) )
% 7.75/5.68 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.68 => P )
% 7.75/5.68 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 7.75/5.68 => P3 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % imp_le_cong
% 7.75/5.68 thf(fact_2677_less__eq__int__code_I1_J,axiom,
% 7.75/5.68 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 7.75/5.68
% 7.75/5.68 % less_eq_int_code(1)
% 7.75/5.68 thf(fact_2678_div__le__mono,axiom,
% 7.75/5.68 ! [M: nat,N: nat,K: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_le_mono
% 7.75/5.68 thf(fact_2679_div__le__dividend,axiom,
% 7.75/5.68 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 7.75/5.68
% 7.75/5.68 % div_le_dividend
% 7.75/5.68 thf(fact_2680_le__cube,axiom,
% 7.75/5.68 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_cube
% 7.75/5.68 thf(fact_2681_le__square,axiom,
% 7.75/5.68 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_square
% 7.75/5.68 thf(fact_2682_mult__le__mono,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ( ord_less_eq_nat @ K @ L )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_mono
% 7.75/5.68 thf(fact_2683_mult__le__mono1,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_mono1
% 7.75/5.68 thf(fact_2684_mult__le__mono2,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_mono2
% 7.75/5.68 thf(fact_2685_mod__less__eq__dividend,axiom,
% 7.75/5.68 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 7.75/5.68
% 7.75/5.68 % mod_less_eq_dividend
% 7.75/5.68 thf(fact_2686_i0__lb,axiom,
% 7.75/5.68 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 7.75/5.68
% 7.75/5.68 % i0_lb
% 7.75/5.68 thf(fact_2687_ile0__eq,axiom,
% 7.75/5.68 ! [N: extended_enat] :
% 7.75/5.68 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 7.75/5.68 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 7.75/5.68
% 7.75/5.68 % ile0_eq
% 7.75/5.68 thf(fact_2688_power__decreasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: real] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ A @ one_one_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing
% 7.75/5.68 thf(fact_2689_power__decreasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: code_integer] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing
% 7.75/5.68 thf(fact_2690_power__decreasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing
% 7.75/5.68 thf(fact_2691_power__decreasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 7.75/5.68 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing
% 7.75/5.68 thf(fact_2692_power__decreasing,axiom,
% 7.75/5.68 ! [N: nat,N4: nat,A: int] :
% 7.75/5.68 ( ( ord_less_eq_nat @ N @ N4 )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ A @ one_one_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_decreasing
% 7.75/5.68 thf(fact_2693_power__le__imp__le__exp,axiom,
% 7.75/5.68 ! [A: code_integer,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_exp
% 7.75/5.68 thf(fact_2694_power__le__imp__le__exp,axiom,
% 7.75/5.68 ! [A: real,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_exp
% 7.75/5.68 thf(fact_2695_power__le__imp__le__exp,axiom,
% 7.75/5.68 ! [A: rat,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_rat @ one_one_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_exp
% 7.75/5.68 thf(fact_2696_power__le__imp__le__exp,axiom,
% 7.75/5.68 ! [A: nat,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_nat @ one_one_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_exp
% 7.75/5.68 thf(fact_2697_power__le__imp__le__exp,axiom,
% 7.75/5.68 ! [A: int,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_int @ one_one_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_exp
% 7.75/5.68 thf(fact_2698_unset__bit__less__eq,axiom,
% 7.75/5.68 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 7.75/5.68
% 7.75/5.68 % unset_bit_less_eq
% 7.75/5.68 thf(fact_2699_set__bit__greater__eq,axiom,
% 7.75/5.68 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 7.75/5.68
% 7.75/5.68 % set_bit_greater_eq
% 7.75/5.68 thf(fact_2700_mult__le__cancel__iff1,axiom,
% 7.75/5.68 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 7.75/5.68 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_iff1
% 7.75/5.68 thf(fact_2701_mult__le__cancel__iff1,axiom,
% 7.75/5.68 ! [Z: real,X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ Z )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 7.75/5.68 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_iff1
% 7.75/5.68 thf(fact_2702_mult__le__cancel__iff1,axiom,
% 7.75/5.68 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 7.75/5.68 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_iff1
% 7.75/5.68 thf(fact_2703_mult__le__cancel__iff1,axiom,
% 7.75/5.68 ! [Z: int,X: int,Y: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ Z )
% 7.75/5.68 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 7.75/5.68 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_iff1
% 7.75/5.68 thf(fact_2704_mult__le__cancel__iff2,axiom,
% 7.75/5.68 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z @ X ) @ ( times_3573771949741848930nteger @ Z @ Y ) )
% 7.75/5.68 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_iff2
% 7.75/5.68 thf(fact_2705_mult__le__cancel__iff2,axiom,
% 7.75/5.68 ! [Z: real,X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ Z )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 7.75/5.68 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_iff2
% 7.75/5.68 thf(fact_2706_mult__le__cancel__iff2,axiom,
% 7.75/5.68 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 7.75/5.68 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_iff2
% 7.75/5.68 thf(fact_2707_mult__le__cancel__iff2,axiom,
% 7.75/5.68 ! [Z: int,X: int,Y: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ Z )
% 7.75/5.68 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 7.75/5.68 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_iff2
% 7.75/5.68 thf(fact_2708_not__numeral__le__zero,axiom,
% 7.75/5.68 ! [N: num] :
% 7.75/5.68 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 7.75/5.68
% 7.75/5.68 % not_numeral_le_zero
% 7.75/5.68 thf(fact_2709_not__numeral__le__zero,axiom,
% 7.75/5.68 ! [N: num] :
% 7.75/5.68 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 7.75/5.68
% 7.75/5.68 % not_numeral_le_zero
% 7.75/5.68 thf(fact_2710_not__numeral__le__zero,axiom,
% 7.75/5.68 ! [N: num] :
% 7.75/5.68 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 7.75/5.68
% 7.75/5.68 % not_numeral_le_zero
% 7.75/5.68 thf(fact_2711_not__numeral__le__zero,axiom,
% 7.75/5.68 ! [N: num] :
% 7.75/5.68 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 7.75/5.68
% 7.75/5.68 % not_numeral_le_zero
% 7.75/5.68 thf(fact_2712_zero__le__numeral,axiom,
% 7.75/5.68 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_numeral
% 7.75/5.68 thf(fact_2713_zero__le__numeral,axiom,
% 7.75/5.68 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_numeral
% 7.75/5.68 thf(fact_2714_zero__le__numeral,axiom,
% 7.75/5.68 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_numeral
% 7.75/5.68 thf(fact_2715_zero__le__numeral,axiom,
% 7.75/5.68 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_numeral
% 7.75/5.68 thf(fact_2716_add__nonpos__eq__0__iff,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 7.75/5.68 => ( ( ( plus_plus_real @ X @ Y )
% 7.75/5.68 = zero_zero_real )
% 7.75/5.68 = ( ( X = zero_zero_real )
% 7.75/5.68 & ( Y = zero_zero_real ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_eq_0_iff
% 7.75/5.68 thf(fact_2717_add__nonpos__eq__0__iff,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 7.75/5.68 => ( ( ( plus_plus_rat @ X @ Y )
% 7.75/5.68 = zero_zero_rat )
% 7.75/5.68 = ( ( X = zero_zero_rat )
% 7.75/5.68 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_eq_0_iff
% 7.75/5.68 thf(fact_2718_add__nonpos__eq__0__iff,axiom,
% 7.75/5.68 ! [X: nat,Y: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 7.75/5.68 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 7.75/5.68 => ( ( ( plus_plus_nat @ X @ Y )
% 7.75/5.68 = zero_zero_nat )
% 7.75/5.68 = ( ( X = zero_zero_nat )
% 7.75/5.68 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_eq_0_iff
% 7.75/5.68 thf(fact_2719_add__nonpos__eq__0__iff,axiom,
% 7.75/5.68 ! [X: int,Y: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 7.75/5.68 => ( ( ( plus_plus_int @ X @ Y )
% 7.75/5.68 = zero_zero_int )
% 7.75/5.68 = ( ( X = zero_zero_int )
% 7.75/5.68 & ( Y = zero_zero_int ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_eq_0_iff
% 7.75/5.68 thf(fact_2720_add__nonneg__eq__0__iff,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ( ( plus_plus_real @ X @ Y )
% 7.75/5.68 = zero_zero_real )
% 7.75/5.68 = ( ( X = zero_zero_real )
% 7.75/5.68 & ( Y = zero_zero_real ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_eq_0_iff
% 7.75/5.68 thf(fact_2721_add__nonneg__eq__0__iff,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ( ( plus_plus_rat @ X @ Y )
% 7.75/5.68 = zero_zero_rat )
% 7.75/5.68 = ( ( X = zero_zero_rat )
% 7.75/5.68 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_eq_0_iff
% 7.75/5.68 thf(fact_2722_add__nonneg__eq__0__iff,axiom,
% 7.75/5.68 ! [X: nat,Y: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 7.75/5.68 => ( ( ( plus_plus_nat @ X @ Y )
% 7.75/5.68 = zero_zero_nat )
% 7.75/5.68 = ( ( X = zero_zero_nat )
% 7.75/5.68 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_eq_0_iff
% 7.75/5.68 thf(fact_2723_add__nonneg__eq__0__iff,axiom,
% 7.75/5.68 ! [X: int,Y: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.68 => ( ( ( plus_plus_int @ X @ Y )
% 7.75/5.68 = zero_zero_int )
% 7.75/5.68 = ( ( X = zero_zero_int )
% 7.75/5.68 & ( Y = zero_zero_int ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_eq_0_iff
% 7.75/5.68 thf(fact_2724_add__nonpos__nonpos,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_nonpos
% 7.75/5.68 thf(fact_2725_add__nonpos__nonpos,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_nonpos
% 7.75/5.68 thf(fact_2726_add__nonpos__nonpos,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_nonpos
% 7.75/5.68 thf(fact_2727_add__nonpos__nonpos,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_nonpos
% 7.75/5.68 thf(fact_2728_add__nonneg__nonneg,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_nonneg
% 7.75/5.68 thf(fact_2729_add__nonneg__nonneg,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_nonneg
% 7.75/5.68 thf(fact_2730_add__nonneg__nonneg,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_nonneg
% 7.75/5.68 thf(fact_2731_add__nonneg__nonneg,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_nonneg
% 7.75/5.68 thf(fact_2732_add__increasing2,axiom,
% 7.75/5.68 ! [C: real,B: real,A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ( ord_less_eq_real @ B @ A )
% 7.75/5.68 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_increasing2
% 7.75/5.68 thf(fact_2733_add__increasing2,axiom,
% 7.75/5.68 ! [C: rat,B: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ( ord_less_eq_rat @ B @ A )
% 7.75/5.68 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_increasing2
% 7.75/5.68 thf(fact_2734_add__increasing2,axiom,
% 7.75/5.68 ! [C: nat,B: nat,A: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ A )
% 7.75/5.68 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_increasing2
% 7.75/5.68 thf(fact_2735_add__increasing2,axiom,
% 7.75/5.68 ! [C: int,B: int,A: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ A )
% 7.75/5.68 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_increasing2
% 7.75/5.68 thf(fact_2736_add__decreasing2,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_decreasing2
% 7.75/5.68 thf(fact_2737_add__decreasing2,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_decreasing2
% 7.75/5.68 thf(fact_2738_add__decreasing2,axiom,
% 7.75/5.68 ! [C: nat,A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 7.75/5.68 => ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_decreasing2
% 7.75/5.68 thf(fact_2739_add__decreasing2,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_decreasing2
% 7.75/5.68 thf(fact_2740_add__increasing,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ B @ C )
% 7.75/5.68 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_increasing
% 7.75/5.68 thf(fact_2741_add__increasing,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ B @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_increasing
% 7.75/5.68 thf(fact_2742_add__increasing,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ C )
% 7.75/5.68 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_increasing
% 7.75/5.68 thf(fact_2743_add__increasing,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ C )
% 7.75/5.68 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_increasing
% 7.75/5.68 thf(fact_2744_add__decreasing,axiom,
% 7.75/5.68 ! [A: real,C: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ B )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_decreasing
% 7.75/5.68 thf(fact_2745_add__decreasing,axiom,
% 7.75/5.68 ! [A: rat,C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ B )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_decreasing
% 7.75/5.68 thf(fact_2746_add__decreasing,axiom,
% 7.75/5.68 ! [A: nat,C: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 7.75/5.68 => ( ( ord_less_eq_nat @ C @ B )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_decreasing
% 7.75/5.68 thf(fact_2747_add__decreasing,axiom,
% 7.75/5.68 ! [A: int,C: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ C @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_decreasing
% 7.75/5.68 thf(fact_2748_zero__less__one__class_Ozero__le__one,axiom,
% 7.75/5.68 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 7.75/5.68
% 7.75/5.68 % zero_less_one_class.zero_le_one
% 7.75/5.68 thf(fact_2749_zero__less__one__class_Ozero__le__one,axiom,
% 7.75/5.68 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 7.75/5.68
% 7.75/5.68 % zero_less_one_class.zero_le_one
% 7.75/5.68 thf(fact_2750_zero__less__one__class_Ozero__le__one,axiom,
% 7.75/5.68 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 7.75/5.68
% 7.75/5.68 % zero_less_one_class.zero_le_one
% 7.75/5.68 thf(fact_2751_zero__less__one__class_Ozero__le__one,axiom,
% 7.75/5.68 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 7.75/5.68
% 7.75/5.68 % zero_less_one_class.zero_le_one
% 7.75/5.68 thf(fact_2752_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 7.75/5.68 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 7.75/5.68
% 7.75/5.68 % linordered_nonzero_semiring_class.zero_le_one
% 7.75/5.68 thf(fact_2753_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 7.75/5.68 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 7.75/5.68
% 7.75/5.68 % linordered_nonzero_semiring_class.zero_le_one
% 7.75/5.68 thf(fact_2754_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 7.75/5.68 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 7.75/5.68
% 7.75/5.68 % linordered_nonzero_semiring_class.zero_le_one
% 7.75/5.68 thf(fact_2755_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 7.75/5.68 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 7.75/5.68
% 7.75/5.68 % linordered_nonzero_semiring_class.zero_le_one
% 7.75/5.68 thf(fact_2756_not__one__le__zero,axiom,
% 7.75/5.68 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 7.75/5.68
% 7.75/5.68 % not_one_le_zero
% 7.75/5.68 thf(fact_2757_not__one__le__zero,axiom,
% 7.75/5.68 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 7.75/5.68
% 7.75/5.68 % not_one_le_zero
% 7.75/5.68 thf(fact_2758_not__one__le__zero,axiom,
% 7.75/5.68 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 7.75/5.68
% 7.75/5.68 % not_one_le_zero
% 7.75/5.68 thf(fact_2759_not__one__le__zero,axiom,
% 7.75/5.68 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 7.75/5.68
% 7.75/5.68 % not_one_le_zero
% 7.75/5.68 thf(fact_2760_mult__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono
% 7.75/5.68 thf(fact_2761_mult__mono,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono
% 7.75/5.68 thf(fact_2762_mult__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono
% 7.75/5.68 thf(fact_2763_mult__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono
% 7.75/5.68 thf(fact_2764_mult__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono
% 7.75/5.68 thf(fact_2765_mult__mono_H,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono'
% 7.75/5.68 thf(fact_2766_mult__mono_H,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono'
% 7.75/5.68 thf(fact_2767_mult__mono_H,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono'
% 7.75/5.68 thf(fact_2768_mult__mono_H,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono'
% 7.75/5.68 thf(fact_2769_mult__mono_H,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_mono'
% 7.75/5.68 thf(fact_2770_zero__le__square,axiom,
% 7.75/5.68 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_square
% 7.75/5.68 thf(fact_2771_zero__le__square,axiom,
% 7.75/5.68 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_square
% 7.75/5.68 thf(fact_2772_zero__le__square,axiom,
% 7.75/5.68 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_square
% 7.75/5.68 thf(fact_2773_zero__le__square,axiom,
% 7.75/5.68 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_square
% 7.75/5.68 thf(fact_2774_split__mult__pos__le,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 7.75/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % split_mult_pos_le
% 7.75/5.68 thf(fact_2775_split__mult__pos__le,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 7.75/5.68 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.68 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % split_mult_pos_le
% 7.75/5.68 thf(fact_2776_split__mult__pos__le,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 7.75/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % split_mult_pos_le
% 7.75/5.68 thf(fact_2777_split__mult__pos__le,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 7.75/5.68 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 7.75/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % split_mult_pos_le
% 7.75/5.68 thf(fact_2778_mult__left__mono__neg,axiom,
% 7.75/5.68 ! [B: real,A: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ B @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_mono_neg
% 7.75/5.68 thf(fact_2779_mult__left__mono__neg,axiom,
% 7.75/5.68 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ B @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_mono_neg
% 7.75/5.68 thf(fact_2780_mult__left__mono__neg,axiom,
% 7.75/5.68 ! [B: rat,A: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ B @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_mono_neg
% 7.75/5.68 thf(fact_2781_mult__left__mono__neg,axiom,
% 7.75/5.68 ! [B: int,A: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ B @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_mono_neg
% 7.75/5.68 thf(fact_2782_mult__nonpos__nonpos,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonpos_nonpos
% 7.75/5.68 thf(fact_2783_mult__nonpos__nonpos,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonpos_nonpos
% 7.75/5.68 thf(fact_2784_mult__nonpos__nonpos,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonpos_nonpos
% 7.75/5.68 thf(fact_2785_mult__nonpos__nonpos,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonpos_nonpos
% 7.75/5.68 thf(fact_2786_mult__left__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_mono
% 7.75/5.68 thf(fact_2787_mult__left__mono,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_mono
% 7.75/5.68 thf(fact_2788_mult__left__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_mono
% 7.75/5.68 thf(fact_2789_mult__left__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_mono
% 7.75/5.68 thf(fact_2790_mult__left__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_mono
% 7.75/5.68 thf(fact_2791_mult__right__mono__neg,axiom,
% 7.75/5.68 ! [B: real,A: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ B @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_mono_neg
% 7.75/5.68 thf(fact_2792_mult__right__mono__neg,axiom,
% 7.75/5.68 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ B @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_mono_neg
% 7.75/5.68 thf(fact_2793_mult__right__mono__neg,axiom,
% 7.75/5.68 ! [B: rat,A: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ B @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_mono_neg
% 7.75/5.68 thf(fact_2794_mult__right__mono__neg,axiom,
% 7.75/5.68 ! [B: int,A: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ B @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_mono_neg
% 7.75/5.68 thf(fact_2795_mult__right__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_mono
% 7.75/5.68 thf(fact_2796_mult__right__mono,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_mono
% 7.75/5.68 thf(fact_2797_mult__right__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_mono
% 7.75/5.68 thf(fact_2798_mult__right__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_mono
% 7.75/5.68 thf(fact_2799_mult__right__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_mono
% 7.75/5.68 thf(fact_2800_mult__le__0__iff,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 7.75/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_0_iff
% 7.75/5.68 thf(fact_2801_mult__le__0__iff,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 7.75/5.68 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 7.75/5.68 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.68 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_0_iff
% 7.75/5.68 thf(fact_2802_mult__le__0__iff,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 7.75/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_0_iff
% 7.75/5.68 thf(fact_2803_mult__le__0__iff,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 7.75/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 7.75/5.68 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_0_iff
% 7.75/5.68 thf(fact_2804_split__mult__neg__le,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 7.75/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 7.75/5.68
% 7.75/5.68 % split_mult_neg_le
% 7.75/5.68 thf(fact_2805_split__mult__neg__le,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 7.75/5.68 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.68 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ).
% 7.75/5.68
% 7.75/5.68 % split_mult_neg_le
% 7.75/5.68 thf(fact_2806_split__mult__neg__le,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 7.75/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 7.75/5.68
% 7.75/5.68 % split_mult_neg_le
% 7.75/5.68 thf(fact_2807_split__mult__neg__le,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 7.75/5.68 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 7.75/5.68 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 7.75/5.68
% 7.75/5.68 % split_mult_neg_le
% 7.75/5.68 thf(fact_2808_split__mult__neg__le,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 7.75/5.68 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 7.75/5.68
% 7.75/5.68 % split_mult_neg_le
% 7.75/5.68 thf(fact_2809_mult__nonneg__nonneg,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonneg
% 7.75/5.68 thf(fact_2810_mult__nonneg__nonneg,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonneg
% 7.75/5.68 thf(fact_2811_mult__nonneg__nonneg,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonneg
% 7.75/5.68 thf(fact_2812_mult__nonneg__nonneg,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonneg
% 7.75/5.68 thf(fact_2813_mult__nonneg__nonneg,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonneg
% 7.75/5.68 thf(fact_2814_mult__nonneg__nonpos,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos
% 7.75/5.68 thf(fact_2815_mult__nonneg__nonpos,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos
% 7.75/5.68 thf(fact_2816_mult__nonneg__nonpos,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos
% 7.75/5.68 thf(fact_2817_mult__nonneg__nonpos,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos
% 7.75/5.68 thf(fact_2818_mult__nonneg__nonpos,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos
% 7.75/5.68 thf(fact_2819_mult__nonpos__nonneg,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonpos_nonneg
% 7.75/5.68 thf(fact_2820_mult__nonpos__nonneg,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonpos_nonneg
% 7.75/5.68 thf(fact_2821_mult__nonpos__nonneg,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonpos_nonneg
% 7.75/5.68 thf(fact_2822_mult__nonpos__nonneg,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonpos_nonneg
% 7.75/5.68 thf(fact_2823_mult__nonpos__nonneg,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonpos_nonneg
% 7.75/5.68 thf(fact_2824_mult__nonneg__nonpos2,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos2
% 7.75/5.68 thf(fact_2825_mult__nonneg__nonpos2,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos2
% 7.75/5.68 thf(fact_2826_mult__nonneg__nonpos2,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos2
% 7.75/5.68 thf(fact_2827_mult__nonneg__nonpos2,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos2
% 7.75/5.68 thf(fact_2828_mult__nonneg__nonpos2,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_nonneg_nonpos2
% 7.75/5.68 thf(fact_2829_zero__le__mult__iff,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 7.75/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_mult_iff
% 7.75/5.68 thf(fact_2830_zero__le__mult__iff,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 7.75/5.68 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 7.75/5.68 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.68 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_mult_iff
% 7.75/5.68 thf(fact_2831_zero__le__mult__iff,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 7.75/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_mult_iff
% 7.75/5.68 thf(fact_2832_zero__le__mult__iff,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 7.75/5.68 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_mult_iff
% 7.75/5.68 thf(fact_2833_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % ordered_comm_semiring_class.comm_mult_left_mono
% 7.75/5.68 thf(fact_2834_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % ordered_comm_semiring_class.comm_mult_left_mono
% 7.75/5.68 thf(fact_2835_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % ordered_comm_semiring_class.comm_mult_left_mono
% 7.75/5.68 thf(fact_2836_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % ordered_comm_semiring_class.comm_mult_left_mono
% 7.75/5.68 thf(fact_2837_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % ordered_comm_semiring_class.comm_mult_left_mono
% 7.75/5.68 thf(fact_2838_add__less__le__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.68 ( ( ord_less_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ D2 )
% 7.75/5.68 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_less_le_mono
% 7.75/5.68 thf(fact_2839_add__less__le__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.68 ( ( ord_less_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ D2 )
% 7.75/5.68 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_less_le_mono
% 7.75/5.68 thf(fact_2840_add__less__le__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.68 ( ( ord_less_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ C @ D2 )
% 7.75/5.68 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_less_le_mono
% 7.75/5.68 thf(fact_2841_add__less__le__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.68 ( ( ord_less_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ C @ D2 )
% 7.75/5.68 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_less_le_mono
% 7.75/5.68 thf(fact_2842_add__le__less__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_real @ C @ D2 )
% 7.75/5.68 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_less_mono
% 7.75/5.68 thf(fact_2843_add__le__less__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_rat @ C @ D2 )
% 7.75/5.68 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_less_mono
% 7.75/5.68 thf(fact_2844_add__le__less__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_nat @ C @ D2 )
% 7.75/5.68 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_less_mono
% 7.75/5.68 thf(fact_2845_add__le__less__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_int @ C @ D2 )
% 7.75/5.68 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_le_less_mono
% 7.75/5.68 thf(fact_2846_add__mono__thms__linordered__field_I3_J,axiom,
% 7.75/5.68 ! [I: real,J: real,K: real,L: real] :
% 7.75/5.68 ( ( ( ord_less_real @ I @ J )
% 7.75/5.68 & ( ord_less_eq_real @ K @ L ) )
% 7.75/5.68 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_field(3)
% 7.75/5.68 thf(fact_2847_add__mono__thms__linordered__field_I3_J,axiom,
% 7.75/5.68 ! [I: rat,J: rat,K: rat,L: rat] :
% 7.75/5.68 ( ( ( ord_less_rat @ I @ J )
% 7.75/5.68 & ( ord_less_eq_rat @ K @ L ) )
% 7.75/5.68 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_field(3)
% 7.75/5.68 thf(fact_2848_add__mono__thms__linordered__field_I3_J,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.68 ( ( ( ord_less_nat @ I @ J )
% 7.75/5.68 & ( ord_less_eq_nat @ K @ L ) )
% 7.75/5.68 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_field(3)
% 7.75/5.68 thf(fact_2849_add__mono__thms__linordered__field_I3_J,axiom,
% 7.75/5.68 ! [I: int,J: int,K: int,L: int] :
% 7.75/5.68 ( ( ( ord_less_int @ I @ J )
% 7.75/5.68 & ( ord_less_eq_int @ K @ L ) )
% 7.75/5.68 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_field(3)
% 7.75/5.68 thf(fact_2850_add__mono__thms__linordered__field_I4_J,axiom,
% 7.75/5.68 ! [I: real,J: real,K: real,L: real] :
% 7.75/5.68 ( ( ( ord_less_eq_real @ I @ J )
% 7.75/5.68 & ( ord_less_real @ K @ L ) )
% 7.75/5.68 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_field(4)
% 7.75/5.68 thf(fact_2851_add__mono__thms__linordered__field_I4_J,axiom,
% 7.75/5.68 ! [I: rat,J: rat,K: rat,L: rat] :
% 7.75/5.68 ( ( ( ord_less_eq_rat @ I @ J )
% 7.75/5.68 & ( ord_less_rat @ K @ L ) )
% 7.75/5.68 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_field(4)
% 7.75/5.68 thf(fact_2852_add__mono__thms__linordered__field_I4_J,axiom,
% 7.75/5.68 ! [I: nat,J: nat,K: nat,L: nat] :
% 7.75/5.68 ( ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 & ( ord_less_nat @ K @ L ) )
% 7.75/5.68 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_field(4)
% 7.75/5.68 thf(fact_2853_add__mono__thms__linordered__field_I4_J,axiom,
% 7.75/5.68 ! [I: int,J: int,K: int,L: int] :
% 7.75/5.68 ( ( ( ord_less_eq_int @ I @ J )
% 7.75/5.68 & ( ord_less_int @ K @ L ) )
% 7.75/5.68 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_mono_thms_linordered_field(4)
% 7.75/5.68 thf(fact_2854_one__le__numeral,axiom,
% 7.75/5.68 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_numeral
% 7.75/5.68 thf(fact_2855_one__le__numeral,axiom,
% 7.75/5.68 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_numeral
% 7.75/5.68 thf(fact_2856_one__le__numeral,axiom,
% 7.75/5.68 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_numeral
% 7.75/5.68 thf(fact_2857_one__le__numeral,axiom,
% 7.75/5.68 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_numeral
% 7.75/5.68 thf(fact_2858_divide__right__mono__neg,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_right_mono_neg
% 7.75/5.68 thf(fact_2859_divide__right__mono__neg,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_right_mono_neg
% 7.75/5.68 thf(fact_2860_divide__nonpos__nonpos,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonpos_nonpos
% 7.75/5.68 thf(fact_2861_divide__nonpos__nonpos,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonpos_nonpos
% 7.75/5.68 thf(fact_2862_divide__nonpos__nonneg,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonpos_nonneg
% 7.75/5.68 thf(fact_2863_divide__nonpos__nonneg,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonpos_nonneg
% 7.75/5.68 thf(fact_2864_divide__nonneg__nonpos,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonneg_nonpos
% 7.75/5.68 thf(fact_2865_divide__nonneg__nonpos,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonneg_nonpos
% 7.75/5.68 thf(fact_2866_divide__nonneg__nonneg,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonneg_nonneg
% 7.75/5.68 thf(fact_2867_divide__nonneg__nonneg,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonneg_nonneg
% 7.75/5.68 thf(fact_2868_zero__le__divide__iff,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 7.75/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_divide_iff
% 7.75/5.68 thf(fact_2869_zero__le__divide__iff,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 7.75/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_divide_iff
% 7.75/5.68 thf(fact_2870_divide__right__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_right_mono
% 7.75/5.68 thf(fact_2871_divide__right__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_right_mono
% 7.75/5.68 thf(fact_2872_divide__le__0__iff,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 7.75/5.68 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_0_iff
% 7.75/5.68 thf(fact_2873_divide__le__0__iff,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 7.75/5.68 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_0_iff
% 7.75/5.68 thf(fact_2874_zero__le__power,axiom,
% 7.75/5.68 ! [A: real,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_power
% 7.75/5.68 thf(fact_2875_zero__le__power,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_power
% 7.75/5.68 thf(fact_2876_zero__le__power,axiom,
% 7.75/5.68 ! [A: rat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_power
% 7.75/5.68 thf(fact_2877_zero__le__power,axiom,
% 7.75/5.68 ! [A: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_power
% 7.75/5.68 thf(fact_2878_zero__le__power,axiom,
% 7.75/5.68 ! [A: int,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_le_power
% 7.75/5.68 thf(fact_2879_power__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono
% 7.75/5.68 thf(fact_2880_power__mono,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,N: nat] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono
% 7.75/5.68 thf(fact_2881_power__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono
% 7.75/5.68 thf(fact_2882_power__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono
% 7.75/5.68 thf(fact_2883_power__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_mono
% 7.75/5.68 thf(fact_2884_one__le__power,axiom,
% 7.75/5.68 ! [A: real,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_real @ one_one_real @ A )
% 7.75/5.68 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_power
% 7.75/5.68 thf(fact_2885_one__le__power,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_power
% 7.75/5.68 thf(fact_2886_one__le__power,axiom,
% 7.75/5.68 ! [A: rat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 7.75/5.68 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_power
% 7.75/5.68 thf(fact_2887_one__le__power,axiom,
% 7.75/5.68 ! [A: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 7.75/5.68 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_power
% 7.75/5.68 thf(fact_2888_one__le__power,axiom,
% 7.75/5.68 ! [A: int,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_int @ one_one_int @ A )
% 7.75/5.68 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % one_le_power
% 7.75/5.68 thf(fact_2889_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 7.75/5.68 thf(fact_2890_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 7.75/5.68 thf(fact_2891_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 7.75/5.68 thf(fact_2892_nat__compl__induct_H,axiom,
% 7.75/5.68 ! [P: nat > $o,N: nat] :
% 7.75/5.68 ( ( P @ zero_zero_nat )
% 7.75/5.68 => ( ! [N2: nat] :
% 7.75/5.68 ( ! [Nn: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ Nn @ N2 )
% 7.75/5.68 => ( P @ Nn ) )
% 7.75/5.68 => ( P @ ( suc @ N2 ) ) )
% 7.75/5.68 => ( P @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_compl_induct'
% 7.75/5.68 thf(fact_2893_nat__compl__induct,axiom,
% 7.75/5.68 ! [P: nat > $o,N: nat] :
% 7.75/5.68 ( ( P @ zero_zero_nat )
% 7.75/5.68 => ( ! [N2: nat] :
% 7.75/5.68 ( ! [Nn: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ Nn @ N2 )
% 7.75/5.68 => ( P @ Nn ) )
% 7.75/5.68 => ( P @ ( suc @ N2 ) ) )
% 7.75/5.68 => ( P @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_compl_induct
% 7.75/5.68 thf(fact_2894_nat__in__between__eq_I1_J,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ( ord_less_nat @ A @ B )
% 7.75/5.68 & ( ord_less_eq_nat @ B @ ( suc @ A ) ) )
% 7.75/5.68 = ( B
% 7.75/5.68 = ( suc @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_in_between_eq(1)
% 7.75/5.68 thf(fact_2895_nat__in__between__eq_I2_J,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 & ( ord_less_nat @ B @ ( suc @ A ) ) )
% 7.75/5.68 = ( B = A ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_in_between_eq(2)
% 7.75/5.68 thf(fact_2896_le__imp__less__Suc,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_imp_less_Suc
% 7.75/5.68 thf(fact_2897_less__eq__Suc__le,axiom,
% 7.75/5.68 ( ord_less_nat
% 7.75/5.68 = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % less_eq_Suc_le
% 7.75/5.68 thf(fact_2898_less__Suc__eq__le,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % less_Suc_eq_le
% 7.75/5.68 thf(fact_2899_le__less__Suc__eq,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 7.75/5.68 = ( N = M ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_less_Suc_eq
% 7.75/5.68 thf(fact_2900_Suc__le__lessD,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 7.75/5.68 => ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % Suc_le_lessD
% 7.75/5.68 thf(fact_2901_inc__induct,axiom,
% 7.75/5.68 ! [I: nat,J: nat,P: nat > $o] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ( P @ J )
% 7.75/5.68 => ( ! [N2: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ N2 )
% 7.75/5.68 => ( ( ord_less_nat @ N2 @ J )
% 7.75/5.68 => ( ( P @ ( suc @ N2 ) )
% 7.75/5.68 => ( P @ N2 ) ) ) )
% 7.75/5.68 => ( P @ I ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % inc_induct
% 7.75/5.68 thf(fact_2902_dec__induct,axiom,
% 7.75/5.68 ! [I: nat,J: nat,P: nat > $o] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.68 => ( ( P @ I )
% 7.75/5.68 => ( ! [N2: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I @ N2 )
% 7.75/5.68 => ( ( ord_less_nat @ N2 @ J )
% 7.75/5.68 => ( ( P @ N2 )
% 7.75/5.68 => ( P @ ( suc @ N2 ) ) ) ) )
% 7.75/5.68 => ( P @ J ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dec_induct
% 7.75/5.68 thf(fact_2903_Suc__le__eq,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 7.75/5.68 = ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % Suc_le_eq
% 7.75/5.68 thf(fact_2904_Suc__leI,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_nat @ M @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % Suc_leI
% 7.75/5.68 thf(fact_2905_ex__least__nat__le,axiom,
% 7.75/5.68 ! [P: nat > $o,N: nat] :
% 7.75/5.68 ( ( P @ N )
% 7.75/5.68 => ( ~ ( P @ zero_zero_nat )
% 7.75/5.68 => ? [K2: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ K2 @ N )
% 7.75/5.68 & ! [I4: nat] :
% 7.75/5.68 ( ( ord_less_nat @ I4 @ K2 )
% 7.75/5.68 => ~ ( P @ I4 ) )
% 7.75/5.68 & ( P @ K2 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % ex_least_nat_le
% 7.75/5.68 thf(fact_2906_mono__nat__linear__lb,axiom,
% 7.75/5.68 ! [F: nat > nat,M: nat,K: nat] :
% 7.75/5.68 ( ! [M2: nat,N2: nat] :
% 7.75/5.68 ( ( ord_less_nat @ M2 @ N2 )
% 7.75/5.68 => ( ord_less_nat @ ( F @ M2 ) @ ( F @ N2 ) ) )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mono_nat_linear_lb
% 7.75/5.68 thf(fact_2907_nat__geq__1__eq__neqz,axiom,
% 7.75/5.68 ! [X: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 7.75/5.68 = ( X != zero_zero_nat ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_geq_1_eq_neqz
% 7.75/5.68 thf(fact_2908_le__imp__power__dvd,axiom,
% 7.75/5.68 ! [M: nat,N: nat,A: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_imp_power_dvd
% 7.75/5.68 thf(fact_2909_le__imp__power__dvd,axiom,
% 7.75/5.68 ! [M: nat,N: nat,A: real] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_imp_power_dvd
% 7.75/5.68 thf(fact_2910_le__imp__power__dvd,axiom,
% 7.75/5.68 ! [M: nat,N: nat,A: int] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_imp_power_dvd
% 7.75/5.68 thf(fact_2911_le__imp__power__dvd,axiom,
% 7.75/5.68 ! [M: nat,N: nat,A: complex] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_imp_power_dvd
% 7.75/5.68 thf(fact_2912_le__imp__power__dvd,axiom,
% 7.75/5.68 ! [M: nat,N: nat,A: code_integer] :
% 7.75/5.68 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_imp_power_dvd
% 7.75/5.68 thf(fact_2913_power__le__dvd,axiom,
% 7.75/5.68 ! [A: nat,N: nat,B: nat,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_dvd
% 7.75/5.68 thf(fact_2914_power__le__dvd,axiom,
% 7.75/5.68 ! [A: real,N: nat,B: real,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_dvd
% 7.75/5.68 thf(fact_2915_power__le__dvd,axiom,
% 7.75/5.68 ! [A: int,N: nat,B: int,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_dvd
% 7.75/5.68 thf(fact_2916_power__le__dvd,axiom,
% 7.75/5.68 ! [A: complex,N: nat,B: complex,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_dvd
% 7.75/5.68 thf(fact_2917_power__le__dvd,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_dvd
% 7.75/5.68 thf(fact_2918_dvd__power__le,axiom,
% 7.75/5.68 ! [X: nat,Y: nat,N: nat,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_nat @ X @ Y )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.68 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dvd_power_le
% 7.75/5.68 thf(fact_2919_dvd__power__le,axiom,
% 7.75/5.68 ! [X: real,Y: real,N: nat,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_real @ X @ Y )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.68 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dvd_power_le
% 7.75/5.68 thf(fact_2920_dvd__power__le,axiom,
% 7.75/5.68 ! [X: int,Y: int,N: nat,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_int @ X @ Y )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.68 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dvd_power_le
% 7.75/5.68 thf(fact_2921_dvd__power__le,axiom,
% 7.75/5.68 ! [X: complex,Y: complex,N: nat,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_complex @ X @ Y )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.68 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dvd_power_le
% 7.75/5.68 thf(fact_2922_dvd__power__le,axiom,
% 7.75/5.68 ! [X: code_integer,Y: code_integer,N: nat,M: nat] :
% 7.75/5.68 ( ( dvd_dvd_Code_integer @ X @ Y )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.68 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dvd_power_le
% 7.75/5.68 thf(fact_2923_Suc__div__le__mono,axiom,
% 7.75/5.68 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % Suc_div_le_mono
% 7.75/5.68 thf(fact_2924_Suc__mult__le__cancel1,axiom,
% 7.75/5.68 ! [K: nat,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % Suc_mult_le_cancel1
% 7.75/5.68 thf(fact_2925_zero__less__eq__of__bool,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_less_eq_of_bool
% 7.75/5.68 thf(fact_2926_zero__less__eq__of__bool,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_less_eq_of_bool
% 7.75/5.68 thf(fact_2927_zero__less__eq__of__bool,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_less_eq_of_bool
% 7.75/5.68 thf(fact_2928_zero__less__eq__of__bool,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_less_eq_of_bool
% 7.75/5.68 thf(fact_2929_zero__less__eq__of__bool,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 7.75/5.68
% 7.75/5.68 % zero_less_eq_of_bool
% 7.75/5.68 thf(fact_2930_mlex__leI,axiom,
% 7.75/5.68 ! [A: nat,A4: nat,B: nat,B6: nat,N4: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ A4 )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ B6 )
% 7.75/5.68 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N4 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A4 @ N4 ) @ B6 ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mlex_leI
% 7.75/5.68 thf(fact_2931_of__bool__less__eq__one,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 7.75/5.68
% 7.75/5.68 % of_bool_less_eq_one
% 7.75/5.68 thf(fact_2932_of__bool__less__eq__one,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 7.75/5.68
% 7.75/5.68 % of_bool_less_eq_one
% 7.75/5.68 thf(fact_2933_of__bool__less__eq__one,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 7.75/5.68
% 7.75/5.68 % of_bool_less_eq_one
% 7.75/5.68 thf(fact_2934_of__bool__less__eq__one,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 7.75/5.68
% 7.75/5.68 % of_bool_less_eq_one
% 7.75/5.68 thf(fact_2935_of__bool__less__eq__one,axiom,
% 7.75/5.68 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 7.75/5.68
% 7.75/5.68 % of_bool_less_eq_one
% 7.75/5.68 thf(fact_2936_mod__Suc__le__divisor,axiom,
% 7.75/5.68 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 7.75/5.68
% 7.75/5.68 % mod_Suc_le_divisor
% 7.75/5.68 thf(fact_2937_div__times__less__eq__dividend,axiom,
% 7.75/5.68 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 7.75/5.68
% 7.75/5.68 % div_times_less_eq_dividend
% 7.75/5.68 thf(fact_2938_times__div__less__eq__dividend,axiom,
% 7.75/5.68 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 7.75/5.68
% 7.75/5.68 % times_div_less_eq_dividend
% 7.75/5.68 thf(fact_2939_div__mult__le,axiom,
% 7.75/5.68 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ A ) ).
% 7.75/5.68
% 7.75/5.68 % div_mult_le
% 7.75/5.68 thf(fact_2940_int__ge__induct,axiom,
% 7.75/5.68 ! [K: int,I: int,P: int > $o] :
% 7.75/5.68 ( ( ord_less_eq_int @ K @ I )
% 7.75/5.68 => ( ( P @ K )
% 7.75/5.68 => ( ! [I3: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ K @ I3 )
% 7.75/5.68 => ( ( P @ I3 )
% 7.75/5.68 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 7.75/5.68 => ( P @ I ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % int_ge_induct
% 7.75/5.68 thf(fact_2941_zmod__le__nonneg__dividend,axiom,
% 7.75/5.68 ! [M: int,K: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 7.75/5.68 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 7.75/5.68
% 7.75/5.68 % zmod_le_nonneg_dividend
% 7.75/5.68 thf(fact_2942_zdvd__antisym__nonneg,axiom,
% 7.75/5.68 ! [M: int,N: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 7.75/5.68 => ( ( dvd_dvd_int @ M @ N )
% 7.75/5.68 => ( ( dvd_dvd_int @ N @ M )
% 7.75/5.68 => ( M = N ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zdvd_antisym_nonneg
% 7.75/5.68 thf(fact_2943_signed__take__bit__int__less__self__iff,axiom,
% 7.75/5.68 ! [N: nat,K: int] :
% 7.75/5.68 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 7.75/5.68 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_int_less_self_iff
% 7.75/5.68 thf(fact_2944_signed__take__bit__int__greater__eq__self__iff,axiom,
% 7.75/5.68 ! [K: int,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 7.75/5.68 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % signed_take_bit_int_greater_eq_self_iff
% 7.75/5.68 thf(fact_2945_field__le__epsilon,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ! [E2: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ E2 )
% 7.75/5.68 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 7.75/5.68 => ( ord_less_eq_real @ X @ Y ) ) ).
% 7.75/5.68
% 7.75/5.68 % field_le_epsilon
% 7.75/5.68 thf(fact_2946_field__le__epsilon,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ! [E2: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 7.75/5.68 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 7.75/5.68 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 7.75/5.68
% 7.75/5.68 % field_le_epsilon
% 7.75/5.68 thf(fact_2947_add__strict__increasing2,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_real @ B @ C )
% 7.75/5.68 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_strict_increasing2
% 7.75/5.68 thf(fact_2948_add__strict__increasing2,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_rat @ B @ C )
% 7.75/5.68 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_strict_increasing2
% 7.75/5.68 thf(fact_2949_add__strict__increasing2,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_nat @ B @ C )
% 7.75/5.68 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_strict_increasing2
% 7.75/5.68 thf(fact_2950_add__strict__increasing2,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_int @ B @ C )
% 7.75/5.68 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_strict_increasing2
% 7.75/5.68 thf(fact_2951_add__strict__increasing,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ B @ C )
% 7.75/5.68 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_strict_increasing
% 7.75/5.68 thf(fact_2952_add__strict__increasing,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ B @ C )
% 7.75/5.68 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_strict_increasing
% 7.75/5.68 thf(fact_2953_add__strict__increasing,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ C )
% 7.75/5.68 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_strict_increasing
% 7.75/5.68 thf(fact_2954_add__strict__increasing,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ C )
% 7.75/5.68 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_strict_increasing
% 7.75/5.68 thf(fact_2955_add__pos__nonneg,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_pos_nonneg
% 7.75/5.68 thf(fact_2956_add__pos__nonneg,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_pos_nonneg
% 7.75/5.68 thf(fact_2957_add__pos__nonneg,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_pos_nonneg
% 7.75/5.68 thf(fact_2958_add__pos__nonneg,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_pos_nonneg
% 7.75/5.68 thf(fact_2959_add__nonpos__neg,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_real @ B @ zero_zero_real )
% 7.75/5.68 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_neg
% 7.75/5.68 thf(fact_2960_add__nonpos__neg,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_neg
% 7.75/5.68 thf(fact_2961_add__nonpos__neg,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 7.75/5.68 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 7.75/5.68 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_neg
% 7.75/5.68 thf(fact_2962_add__nonpos__neg,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonpos_neg
% 7.75/5.68 thf(fact_2963_add__nonneg__pos,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_pos
% 7.75/5.68 thf(fact_2964_add__nonneg__pos,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_pos
% 7.75/5.68 thf(fact_2965_add__nonneg__pos,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_pos
% 7.75/5.68 thf(fact_2966_add__nonneg__pos,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_nonneg_pos
% 7.75/5.68 thf(fact_2967_add__neg__nonpos,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 7.75/5.68 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_neg_nonpos
% 7.75/5.68 thf(fact_2968_add__neg__nonpos,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_neg_nonpos
% 7.75/5.68 thf(fact_2969_add__neg__nonpos,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_nat @ A @ zero_zero_nat )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 7.75/5.68 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_neg_nonpos
% 7.75/5.68 thf(fact_2970_add__neg__nonpos,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % add_neg_nonpos
% 7.75/5.68 thf(fact_2971_mult__le__cancel__left,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ A @ B ) )
% 7.75/5.68 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left
% 7.75/5.68 thf(fact_2972_mult__le__cancel__left,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left
% 7.75/5.68 thf(fact_2973_mult__le__cancel__left,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left
% 7.75/5.68 thf(fact_2974_mult__le__cancel__left,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left
% 7.75/5.68 thf(fact_2975_mult__le__cancel__right,axiom,
% 7.75/5.68 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ A @ B ) )
% 7.75/5.68 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right
% 7.75/5.68 thf(fact_2976_mult__le__cancel__right,axiom,
% 7.75/5.68 ! [A: real,C: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right
% 7.75/5.68 thf(fact_2977_mult__le__cancel__right,axiom,
% 7.75/5.68 ! [A: rat,C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right
% 7.75/5.68 thf(fact_2978_mult__le__cancel__right,axiom,
% 7.75/5.68 ! [A: int,C: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right
% 7.75/5.68 thf(fact_2979_mult__left__less__imp__less,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_less_imp_less
% 7.75/5.68 thf(fact_2980_mult__left__less__imp__less,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_less_imp_less
% 7.75/5.68 thf(fact_2981_mult__left__less__imp__less,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_less_imp_less
% 7.75/5.68 thf(fact_2982_mult__left__less__imp__less,axiom,
% 7.75/5.68 ! [C: nat,A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_nat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_less_imp_less
% 7.75/5.68 thf(fact_2983_mult__left__less__imp__less,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_less_imp_less
% 7.75/5.68 thf(fact_2984_mult__strict__mono,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono
% 7.75/5.68 thf(fact_2985_mult__strict__mono,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.68 ( ( ord_less_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_real @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono
% 7.75/5.68 thf(fact_2986_mult__strict__mono,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.68 ( ( ord_less_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_rat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono
% 7.75/5.68 thf(fact_2987_mult__strict__mono,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.68 ( ( ord_less_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_nat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono
% 7.75/5.68 thf(fact_2988_mult__strict__mono,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.68 ( ( ord_less_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_int @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono
% 7.75/5.68 thf(fact_2989_mult__less__cancel__left,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ A @ B ) )
% 7.75/5.68 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left
% 7.75/5.68 thf(fact_2990_mult__less__cancel__left,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_real @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left
% 7.75/5.68 thf(fact_2991_mult__less__cancel__left,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left
% 7.75/5.68 thf(fact_2992_mult__less__cancel__left,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_int @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left
% 7.75/5.68 thf(fact_2993_mult__right__less__imp__less,axiom,
% 7.75/5.68 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_less_imp_less
% 7.75/5.68 thf(fact_2994_mult__right__less__imp__less,axiom,
% 7.75/5.68 ! [A: real,C: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_less_imp_less
% 7.75/5.68 thf(fact_2995_mult__right__less__imp__less,axiom,
% 7.75/5.68 ! [A: rat,C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_less_imp_less
% 7.75/5.68 thf(fact_2996_mult__right__less__imp__less,axiom,
% 7.75/5.68 ! [A: nat,C: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_nat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_less_imp_less
% 7.75/5.68 thf(fact_2997_mult__right__less__imp__less,axiom,
% 7.75/5.68 ! [A: int,C: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_less_imp_less
% 7.75/5.68 thf(fact_2998_mult__strict__mono_H,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono'
% 7.75/5.68 thf(fact_2999_mult__strict__mono_H,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.68 ( ( ord_less_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_real @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono'
% 7.75/5.68 thf(fact_3000_mult__strict__mono_H,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.68 ( ( ord_less_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_rat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono'
% 7.75/5.68 thf(fact_3001_mult__strict__mono_H,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.68 ( ( ord_less_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_nat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono'
% 7.75/5.68 thf(fact_3002_mult__strict__mono_H,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.68 ( ( ord_less_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_int @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_strict_mono'
% 7.75/5.68 thf(fact_3003_mult__less__cancel__right,axiom,
% 7.75/5.68 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ A @ B ) )
% 7.75/5.68 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right
% 7.75/5.68 thf(fact_3004_mult__less__cancel__right,axiom,
% 7.75/5.68 ! [A: real,C: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_real @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right
% 7.75/5.68 thf(fact_3005_mult__less__cancel__right,axiom,
% 7.75/5.68 ! [A: rat,C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right
% 7.75/5.68 thf(fact_3006_mult__less__cancel__right,axiom,
% 7.75/5.68 ! [A: int,C: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_int @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right
% 7.75/5.68 thf(fact_3007_mult__le__cancel__left__neg,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.68 = ( ord_le3102999989581377725nteger @ B @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left_neg
% 7.75/5.68 thf(fact_3008_mult__le__cancel__left__neg,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left_neg
% 7.75/5.68 thf(fact_3009_mult__le__cancel__left__neg,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left_neg
% 7.75/5.68 thf(fact_3010_mult__le__cancel__left__neg,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left_neg
% 7.75/5.68 thf(fact_3011_mult__le__cancel__left__pos,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.68 = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left_pos
% 7.75/5.68 thf(fact_3012_mult__le__cancel__left__pos,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left_pos
% 7.75/5.68 thf(fact_3013_mult__le__cancel__left__pos,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left_pos
% 7.75/5.68 thf(fact_3014_mult__le__cancel__left__pos,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.68 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left_pos
% 7.75/5.68 thf(fact_3015_mult__left__le__imp__le,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le_imp_le
% 7.75/5.68 thf(fact_3016_mult__left__le__imp__le,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le_imp_le
% 7.75/5.68 thf(fact_3017_mult__left__le__imp__le,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le_imp_le
% 7.75/5.68 thf(fact_3018_mult__left__le__imp__le,axiom,
% 7.75/5.68 ! [C: nat,A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le_imp_le
% 7.75/5.68 thf(fact_3019_mult__left__le__imp__le,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le_imp_le
% 7.75/5.68 thf(fact_3020_mult__right__le__imp__le,axiom,
% 7.75/5.68 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_le_imp_le
% 7.75/5.68 thf(fact_3021_mult__right__le__imp__le,axiom,
% 7.75/5.68 ! [A: real,C: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_le_imp_le
% 7.75/5.68 thf(fact_3022_mult__right__le__imp__le,axiom,
% 7.75/5.68 ! [A: rat,C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_le_imp_le
% 7.75/5.68 thf(fact_3023_mult__right__le__imp__le,axiom,
% 7.75/5.68 ! [A: nat,C: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_le_imp_le
% 7.75/5.68 thf(fact_3024_mult__right__le__imp__le,axiom,
% 7.75/5.68 ! [A: int,C: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_le_imp_le
% 7.75/5.68 thf(fact_3025_mult__le__less__imp__less,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_less_imp_less
% 7.75/5.68 thf(fact_3026_mult__le__less__imp__less,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_real @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_less_imp_less
% 7.75/5.68 thf(fact_3027_mult__le__less__imp__less,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_rat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_less_imp_less
% 7.75/5.68 thf(fact_3028_mult__le__less__imp__less,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_nat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_less_imp_less
% 7.75/5.68 thf(fact_3029_mult__le__less__imp__less,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_int @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_less_imp_less
% 7.75/5.68 thf(fact_3030_mult__less__le__imp__less,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_le_imp_less
% 7.75/5.68 thf(fact_3031_mult__less__le__imp__less,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.68 ( ( ord_less_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_le_imp_less
% 7.75/5.68 thf(fact_3032_mult__less__le__imp__less,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.68 ( ( ord_less_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_le_imp_less
% 7.75/5.68 thf(fact_3033_mult__less__le__imp__less,axiom,
% 7.75/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.68 ( ( ord_less_nat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_le_imp_less
% 7.75/5.68 thf(fact_3034_mult__less__le__imp__less,axiom,
% 7.75/5.68 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.68 ( ( ord_less_int @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ C @ D2 )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_le_imp_less
% 7.75/5.68 thf(fact_3035_sum__squares__ge__zero,axiom,
% 7.75/5.68 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % sum_squares_ge_zero
% 7.75/5.68 thf(fact_3036_sum__squares__ge__zero,axiom,
% 7.75/5.68 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % sum_squares_ge_zero
% 7.75/5.68 thf(fact_3037_sum__squares__ge__zero,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % sum_squares_ge_zero
% 7.75/5.68 thf(fact_3038_sum__squares__ge__zero,axiom,
% 7.75/5.68 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % sum_squares_ge_zero
% 7.75/5.68 thf(fact_3039_sum__squares__le__zero__iff,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 7.75/5.68 = ( ( X = zero_zero_real )
% 7.75/5.68 & ( Y = zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % sum_squares_le_zero_iff
% 7.75/5.68 thf(fact_3040_sum__squares__le__zero__iff,axiom,
% 7.75/5.68 ! [X: code_integer,Y: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 7.75/5.68 = ( ( X = zero_z3403309356797280102nteger )
% 7.75/5.68 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % sum_squares_le_zero_iff
% 7.75/5.68 thf(fact_3041_sum__squares__le__zero__iff,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 7.75/5.68 = ( ( X = zero_zero_rat )
% 7.75/5.68 & ( Y = zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % sum_squares_le_zero_iff
% 7.75/5.68 thf(fact_3042_sum__squares__le__zero__iff,axiom,
% 7.75/5.68 ! [X: int,Y: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 7.75/5.68 = ( ( X = zero_zero_int )
% 7.75/5.68 & ( Y = zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % sum_squares_le_zero_iff
% 7.75/5.68 thf(fact_3043_mult__left__le__one__le,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le_one_le
% 7.75/5.68 thf(fact_3044_mult__left__le__one__le,axiom,
% 7.75/5.68 ! [X: code_integer,Y: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le_one_le
% 7.75/5.68 thf(fact_3045_mult__left__le__one__le,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le_one_le
% 7.75/5.68 thf(fact_3046_mult__left__le__one__le,axiom,
% 7.75/5.68 ! [X: int,Y: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.68 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le_one_le
% 7.75/5.68 thf(fact_3047_mult__right__le__one__le,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_le_one_le
% 7.75/5.68 thf(fact_3048_mult__right__le__one__le,axiom,
% 7.75/5.68 ! [X: code_integer,Y: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_le_one_le
% 7.75/5.68 thf(fact_3049_mult__right__le__one__le,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_le_one_le
% 7.75/5.68 thf(fact_3050_mult__right__le__one__le,axiom,
% 7.75/5.68 ! [X: int,Y: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.68 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_right_le_one_le
% 7.75/5.68 thf(fact_3051_mult__le__one,axiom,
% 7.75/5.68 ! [A: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ one_one_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ B @ one_one_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_one
% 7.75/5.68 thf(fact_3052_mult__le__one,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_one
% 7.75/5.68 thf(fact_3053_mult__le__one,axiom,
% 7.75/5.68 ! [A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_one
% 7.75/5.68 thf(fact_3054_mult__le__one,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_one
% 7.75/5.68 thf(fact_3055_mult__le__one,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ one_one_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ one_one_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_one
% 7.75/5.68 thf(fact_3056_mult__left__le,axiom,
% 7.75/5.68 ! [C: real,A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ C @ one_one_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le
% 7.75/5.68 thf(fact_3057_mult__left__le,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le
% 7.75/5.68 thf(fact_3058_mult__left__le,axiom,
% 7.75/5.68 ! [C: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le
% 7.75/5.68 thf(fact_3059_mult__left__le,axiom,
% 7.75/5.68 ! [C: nat,A: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le
% 7.75/5.68 thf(fact_3060_mult__left__le,axiom,
% 7.75/5.68 ! [C: int,A: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ C @ one_one_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_left_le
% 7.75/5.68 thf(fact_3061_discrete,axiom,
% 7.75/5.68 ( ord_less_nat
% 7.75/5.68 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % discrete
% 7.75/5.68 thf(fact_3062_discrete,axiom,
% 7.75/5.68 ( ord_less_int
% 7.75/5.68 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % discrete
% 7.75/5.68 thf(fact_3063_frac__le,axiom,
% 7.75/5.68 ! [Y: real,X: real,W: real,Z: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ( ord_less_eq_real @ X @ Y )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ W )
% 7.75/5.68 => ( ( ord_less_eq_real @ W @ Z )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % frac_le
% 7.75/5.68 thf(fact_3064_frac__le,axiom,
% 7.75/5.68 ! [Y: rat,X: rat,W: rat,Z: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ( ord_less_eq_rat @ X @ Y )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 7.75/5.68 => ( ( ord_less_eq_rat @ W @ Z )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % frac_le
% 7.75/5.68 thf(fact_3065_frac__less,axiom,
% 7.75/5.68 ! [X: real,Y: real,W: real,Z: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_real @ X @ Y )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ W )
% 7.75/5.68 => ( ( ord_less_eq_real @ W @ Z )
% 7.75/5.68 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % frac_less
% 7.75/5.68 thf(fact_3066_frac__less,axiom,
% 7.75/5.68 ! [X: rat,Y: rat,W: rat,Z: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_rat @ X @ Y )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 7.75/5.68 => ( ( ord_less_eq_rat @ W @ Z )
% 7.75/5.68 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % frac_less
% 7.75/5.68 thf(fact_3067_frac__less2,axiom,
% 7.75/5.68 ! [X: real,Y: real,W: real,Z: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_eq_real @ X @ Y )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ W )
% 7.75/5.68 => ( ( ord_less_real @ W @ Z )
% 7.75/5.68 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % frac_less2
% 7.75/5.68 thf(fact_3068_frac__less2,axiom,
% 7.75/5.68 ! [X: rat,Y: rat,W: rat,Z: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_eq_rat @ X @ Y )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 7.75/5.68 => ( ( ord_less_rat @ W @ Z )
% 7.75/5.68 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % frac_less2
% 7.75/5.68 thf(fact_3069_divide__le__cancel,axiom,
% 7.75/5.68 ! [A: real,C: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_cancel
% 7.75/5.68 thf(fact_3070_divide__le__cancel,axiom,
% 7.75/5.68 ! [A: rat,C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ B ) )
% 7.75/5.68 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_cancel
% 7.75/5.68 thf(fact_3071_divide__nonneg__neg,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_real @ Y @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonneg_neg
% 7.75/5.68 thf(fact_3072_divide__nonneg__neg,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonneg_neg
% 7.75/5.68 thf(fact_3073_divide__nonneg__pos,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonneg_pos
% 7.75/5.68 thf(fact_3074_divide__nonneg__pos,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonneg_pos
% 7.75/5.68 thf(fact_3075_divide__nonpos__neg,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_real @ Y @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonpos_neg
% 7.75/5.68 thf(fact_3076_divide__nonpos__neg,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonpos_neg
% 7.75/5.68 thf(fact_3077_divide__nonpos__pos,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonpos_pos
% 7.75/5.68 thf(fact_3078_divide__nonpos__pos,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_nonpos_pos
% 7.75/5.68 thf(fact_3079_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_nat @ A @ B )
% 7.75/5.68 => ( ( divide_divide_nat @ A @ B )
% 7.75/5.68 = zero_zero_nat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.div_less
% 7.75/5.68 thf(fact_3080_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_int @ A @ B )
% 7.75/5.68 => ( ( divide_divide_int @ A @ B )
% 7.75/5.68 = zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.div_less
% 7.75/5.68 thf(fact_3081_div__positive,axiom,
% 7.75/5.68 ! [B: nat,A: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ( ord_less_eq_nat @ B @ A )
% 7.75/5.68 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_positive
% 7.75/5.68 thf(fact_3082_div__positive,axiom,
% 7.75/5.68 ! [B: int,A: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ B @ A )
% 7.75/5.68 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_positive
% 7.75/5.68 thf(fact_3083_power__less__imp__less__base,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat,B: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_less_imp_less_base
% 7.75/5.68 thf(fact_3084_power__less__imp__less__base,axiom,
% 7.75/5.68 ! [A: real,N: nat,B: real] :
% 7.75/5.68 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ord_less_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_less_imp_less_base
% 7.75/5.68 thf(fact_3085_power__less__imp__less__base,axiom,
% 7.75/5.68 ! [A: rat,N: nat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ord_less_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_less_imp_less_base
% 7.75/5.68 thf(fact_3086_power__less__imp__less__base,axiom,
% 7.75/5.68 ! [A: nat,N: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ord_less_nat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_less_imp_less_base
% 7.75/5.68 thf(fact_3087_power__less__imp__less__base,axiom,
% 7.75/5.68 ! [A: int,N: nat,B: int] :
% 7.75/5.68 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_int @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_less_imp_less_base
% 7.75/5.68 thf(fact_3088_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.68 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 7.75/5.68 thf(fact_3089_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 7.75/5.68 ! [C: nat,A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.68 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 7.75/5.68 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 7.75/5.68 thf(fact_3090_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 7.75/5.68 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 7.75/5.68 thf(fact_3091_power__le__one,axiom,
% 7.75/5.68 ! [A: real,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ A @ one_one_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_one
% 7.75/5.68 thf(fact_3092_power__le__one,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_one
% 7.75/5.68 thf(fact_3093_power__le__one,axiom,
% 7.75/5.68 ! [A: rat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_one
% 7.75/5.68 thf(fact_3094_power__le__one,axiom,
% 7.75/5.68 ! [A: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 7.75/5.68 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_one
% 7.75/5.68 thf(fact_3095_power__le__one,axiom,
% 7.75/5.68 ! [A: int,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ A @ one_one_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_one
% 7.75/5.68 thf(fact_3096_power__inject__base,axiom,
% 7.75/5.68 ! [A: real,N: nat,B: real] :
% 7.75/5.68 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 7.75/5.68 = ( power_power_real @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( A = B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_inject_base
% 7.75/5.68 thf(fact_3097_power__inject__base,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat,B: code_integer] :
% 7.75/5.68 ( ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 7.75/5.68 = ( power_8256067586552552935nteger @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( A = B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_inject_base
% 7.75/5.68 thf(fact_3098_power__inject__base,axiom,
% 7.75/5.68 ! [A: rat,N: nat,B: rat] :
% 7.75/5.68 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 7.75/5.68 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( A = B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_inject_base
% 7.75/5.68 thf(fact_3099_power__inject__base,axiom,
% 7.75/5.68 ! [A: nat,N: nat,B: nat] :
% 7.75/5.68 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 7.75/5.68 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( A = B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_inject_base
% 7.75/5.68 thf(fact_3100_power__inject__base,axiom,
% 7.75/5.68 ! [A: int,N: nat,B: int] :
% 7.75/5.68 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 7.75/5.68 = ( power_power_int @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( A = B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_inject_base
% 7.75/5.68 thf(fact_3101_power__le__imp__le__base,axiom,
% 7.75/5.68 ! [A: real,N: nat,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_base
% 7.75/5.68 thf(fact_3102_power__le__imp__le__base,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ ( power_8256067586552552935nteger @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_base
% 7.75/5.68 thf(fact_3103_power__le__imp__le__base,axiom,
% 7.75/5.68 ! [A: rat,N: nat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_base
% 7.75/5.68 thf(fact_3104_power__le__imp__le__base,axiom,
% 7.75/5.68 ! [A: nat,N: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_base
% 7.75/5.68 thf(fact_3105_power__le__imp__le__base,axiom,
% 7.75/5.68 ! [A: int,N: nat,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_le_imp_le_base
% 7.75/5.68 thf(fact_3106_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 7.75/5.68 ! [B: code_integer,A: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 7.75/5.68 thf(fact_3107_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 7.75/5.68 ! [B: nat,A: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 7.75/5.68 thf(fact_3108_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 7.75/5.68 ! [B: int,A: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 7.75/5.68 thf(fact_3109_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 7.75/5.68 ! [A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.68 => ( ( modulo364778990260209775nteger @ A @ B )
% 7.75/5.68 = A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.mod_less
% 7.75/5.68 thf(fact_3110_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 7.75/5.68 ! [A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_nat @ A @ B )
% 7.75/5.68 => ( ( modulo_modulo_nat @ A @ B )
% 7.75/5.68 = A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.mod_less
% 7.75/5.68 thf(fact_3111_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_int @ A @ B )
% 7.75/5.68 => ( ( modulo_modulo_int @ A @ B )
% 7.75/5.68 = A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % unique_euclidean_semiring_numeral_class.mod_less
% 7.75/5.68 thf(fact_3112_ex__least__nat__less,axiom,
% 7.75/5.68 ! [P: nat > $o,N: nat] :
% 7.75/5.68 ( ( P @ N )
% 7.75/5.68 => ( ~ ( P @ zero_zero_nat )
% 7.75/5.68 => ? [K2: nat] :
% 7.75/5.68 ( ( ord_less_nat @ K2 @ N )
% 7.75/5.68 & ! [I4: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ I4 @ K2 )
% 7.75/5.68 => ~ ( P @ I4 ) )
% 7.75/5.68 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % ex_least_nat_less
% 7.75/5.68 thf(fact_3113_nat__one__le__power,axiom,
% 7.75/5.68 ! [I: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 7.75/5.68 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_one_le_power
% 7.75/5.68 thf(fact_3114_div__le__mono2,axiom,
% 7.75/5.68 ! [M: nat,N: nat,K: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_le_mono2
% 7.75/5.68 thf(fact_3115_div__greater__zero__iff,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 7.75/5.68 = ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.68 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_greater_zero_iff
% 7.75/5.68 thf(fact_3116_nat__mult__le__cancel1,axiom,
% 7.75/5.68 ! [K: nat,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.68 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 7.75/5.68 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_mult_le_cancel1
% 7.75/5.68 thf(fact_3117_dvd__imp__le,axiom,
% 7.75/5.68 ! [K: nat,N: nat] :
% 7.75/5.68 ( ( dvd_dvd_nat @ K @ N )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dvd_imp_le
% 7.75/5.68 thf(fact_3118_mod__le__divisor,axiom,
% 7.75/5.68 ! [N: nat,M: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % mod_le_divisor
% 7.75/5.68 thf(fact_3119_int__one__le__iff__zero__less,axiom,
% 7.75/5.68 ! [Z: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ one_one_int @ Z )
% 7.75/5.68 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 7.75/5.68
% 7.75/5.68 % int_one_le_iff_zero_less
% 7.75/5.68 thf(fact_3120_zless__imp__add1__zle,axiom,
% 7.75/5.68 ! [W: int,Z: int] :
% 7.75/5.68 ( ( ord_less_int @ W @ Z )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 7.75/5.68
% 7.75/5.68 % zless_imp_add1_zle
% 7.75/5.68 thf(fact_3121_add1__zle__eq,axiom,
% 7.75/5.68 ! [W: int,Z: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 7.75/5.68 = ( ord_less_int @ W @ Z ) ) ).
% 7.75/5.68
% 7.75/5.68 % add1_zle_eq
% 7.75/5.68 thf(fact_3122_neg__mod__sign,axiom,
% 7.75/5.68 ! [L: int,K: int] :
% 7.75/5.68 ( ( ord_less_int @ L @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 7.75/5.68
% 7.75/5.68 % neg_mod_sign
% 7.75/5.68 thf(fact_3123_Euclidean__Division_Opos__mod__sign,axiom,
% 7.75/5.68 ! [L: int,K: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ L )
% 7.75/5.68 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % Euclidean_Division.pos_mod_sign
% 7.75/5.68 thf(fact_3124_int__mod__lem,axiom,
% 7.75/5.68 ! [N: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ N )
% 7.75/5.68 => ( ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 & ( ord_less_int @ B @ N ) )
% 7.75/5.68 = ( ( modulo_modulo_int @ B @ N )
% 7.75/5.68 = B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % int_mod_lem
% 7.75/5.68 thf(fact_3125_zmod__trivial__iff,axiom,
% 7.75/5.68 ! [I: int,K: int] :
% 7.75/5.68 ( ( ( modulo_modulo_int @ I @ K )
% 7.75/5.68 = I )
% 7.75/5.68 = ( ( K = zero_zero_int )
% 7.75/5.68 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 7.75/5.68 & ( ord_less_int @ I @ K ) )
% 7.75/5.68 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 7.75/5.68 & ( ord_less_int @ K @ I ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zmod_trivial_iff
% 7.75/5.68 thf(fact_3126_int__mod__eq,axiom,
% 7.75/5.68 ! [B: int,N: int,A: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_int @ B @ N )
% 7.75/5.68 => ( ( ( modulo_modulo_int @ A @ N )
% 7.75/5.68 = ( modulo_modulo_int @ B @ N ) )
% 7.75/5.68 => ( ( modulo_modulo_int @ A @ N )
% 7.75/5.68 = B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % int_mod_eq
% 7.75/5.68 thf(fact_3127_pos__mod__conj,axiom,
% 7.75/5.68 ! [B: int,A: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 7.75/5.68 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % pos_mod_conj
% 7.75/5.68 thf(fact_3128_neg__mod__conj,axiom,
% 7.75/5.68 ! [B: int,A: int] :
% 7.75/5.68 ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 7.75/5.68 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % neg_mod_conj
% 7.75/5.68 thf(fact_3129_int__mod__ge,axiom,
% 7.75/5.68 ! [A: int,N: int] :
% 7.75/5.68 ( ( ord_less_int @ A @ N )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ N )
% 7.75/5.68 => ( ord_less_eq_int @ A @ ( modulo_modulo_int @ A @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % int_mod_ge
% 7.75/5.68 thf(fact_3130_mod__eq__nat1E,axiom,
% 7.75/5.68 ! [M: nat,Q3: nat,N: nat] :
% 7.75/5.68 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 7.75/5.68 = ( modulo_modulo_nat @ N @ Q3 ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.68 => ~ ! [S2: nat] :
% 7.75/5.68 ( M
% 7.75/5.68 != ( plus_plus_nat @ N @ ( times_times_nat @ Q3 @ S2 ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mod_eq_nat1E
% 7.75/5.68 thf(fact_3131_mod__eq__nat2E,axiom,
% 7.75/5.68 ! [M: nat,Q3: nat,N: nat] :
% 7.75/5.68 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 7.75/5.68 = ( modulo_modulo_nat @ N @ Q3 ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.68 => ~ ! [S2: nat] :
% 7.75/5.68 ( N
% 7.75/5.68 != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S2 ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mod_eq_nat2E
% 7.75/5.68 thf(fact_3132_nat__mod__eq__lemma,axiom,
% 7.75/5.68 ! [X: nat,N: nat,Y: nat] :
% 7.75/5.68 ( ( ( modulo_modulo_nat @ X @ N )
% 7.75/5.68 = ( modulo_modulo_nat @ Y @ N ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ Y @ X )
% 7.75/5.68 => ? [Q5: nat] :
% 7.75/5.68 ( X
% 7.75/5.68 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q5 ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nat_mod_eq_lemma
% 7.75/5.68 thf(fact_3133_nonneg1__imp__zdiv__pos__iff,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 7.75/5.68 = ( ( ord_less_eq_int @ B @ A )
% 7.75/5.68 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nonneg1_imp_zdiv_pos_iff
% 7.75/5.68 thf(fact_3134_pos__imp__zdiv__nonneg__iff,axiom,
% 7.75/5.68 ! [B: int,A: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 7.75/5.68 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % pos_imp_zdiv_nonneg_iff
% 7.75/5.68 thf(fact_3135_neg__imp__zdiv__nonneg__iff,axiom,
% 7.75/5.68 ! [B: int,A: int] :
% 7.75/5.68 ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 7.75/5.68 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % neg_imp_zdiv_nonneg_iff
% 7.75/5.68 thf(fact_3136_zdiv__le__dividend,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zdiv_le_dividend
% 7.75/5.68 thf(fact_3137_pos__imp__zdiv__pos__iff,axiom,
% 7.75/5.68 ! [K: int,I: int] :
% 7.75/5.68 ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 7.75/5.68 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % pos_imp_zdiv_pos_iff
% 7.75/5.68 thf(fact_3138_div__nonpos__pos__le0,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_nonpos_pos_le0
% 7.75/5.68 thf(fact_3139_div__nonneg__neg__le0,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_nonneg_neg_le0
% 7.75/5.68 thf(fact_3140_div__positive__int,axiom,
% 7.75/5.68 ! [L: int,K: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ L @ K )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ L )
% 7.75/5.68 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_positive_int
% 7.75/5.68 thf(fact_3141_div__int__pos__iff,axiom,
% 7.75/5.68 ! [K: int,L: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 7.75/5.68 = ( ( K = zero_zero_int )
% 7.75/5.68 | ( L = zero_zero_int )
% 7.75/5.68 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.68 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 7.75/5.68 | ( ( ord_less_int @ K @ zero_zero_int )
% 7.75/5.68 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_int_pos_iff
% 7.75/5.68 thf(fact_3142_zdiv__mono2__neg,axiom,
% 7.75/5.68 ! [A: int,B6: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 7.75/5.68 => ( ( ord_less_eq_int @ B6 @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B6 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zdiv_mono2_neg
% 7.75/5.68 thf(fact_3143_zdiv__mono1__neg,axiom,
% 7.75/5.68 ! [A: int,A4: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ A4 )
% 7.75/5.68 => ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zdiv_mono1_neg
% 7.75/5.68 thf(fact_3144_zdiv__eq__0__iff,axiom,
% 7.75/5.68 ! [I: int,K: int] :
% 7.75/5.68 ( ( ( divide_divide_int @ I @ K )
% 7.75/5.68 = zero_zero_int )
% 7.75/5.68 = ( ( K = zero_zero_int )
% 7.75/5.68 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 7.75/5.68 & ( ord_less_int @ I @ K ) )
% 7.75/5.68 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 7.75/5.68 & ( ord_less_int @ K @ I ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zdiv_eq_0_iff
% 7.75/5.68 thf(fact_3145_zdiv__mono2,axiom,
% 7.75/5.68 ! [A: int,B6: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 7.75/5.68 => ( ( ord_less_eq_int @ B6 @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B6 ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zdiv_mono2
% 7.75/5.68 thf(fact_3146_zdiv__mono1,axiom,
% 7.75/5.68 ! [A: int,A4: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ A @ A4 )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zdiv_mono1
% 7.75/5.68 thf(fact_3147_zdvd__imp__le,axiom,
% 7.75/5.68 ! [Z: int,N: int] :
% 7.75/5.68 ( ( dvd_dvd_int @ Z @ N )
% 7.75/5.68 => ( ( ord_less_int @ zero_zero_int @ N )
% 7.75/5.68 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zdvd_imp_le
% 7.75/5.68 thf(fact_3148_zdiv__zmult2__eq,axiom,
% 7.75/5.68 ! [C: int,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 7.75/5.68 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % zdiv_zmult2_eq
% 7.75/5.68 thf(fact_3149_nonneg__mod__div,axiom,
% 7.75/5.68 ! [A: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 7.75/5.68 & ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % nonneg_mod_div
% 7.75/5.68 thf(fact_3150_mult__le__cancel__left1,axiom,
% 7.75/5.68 ! [C: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 7.75/5.68 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left1
% 7.75/5.68 thf(fact_3151_mult__le__cancel__left1,axiom,
% 7.75/5.68 ! [C: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ one_one_real @ B ) )
% 7.75/5.68 & ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left1
% 7.75/5.68 thf(fact_3152_mult__le__cancel__left1,axiom,
% 7.75/5.68 ! [C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 7.75/5.68 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left1
% 7.75/5.68 thf(fact_3153_mult__le__cancel__left1,axiom,
% 7.75/5.68 ! [C: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ one_one_int @ B ) )
% 7.75/5.68 & ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left1
% 7.75/5.68 thf(fact_3154_mult__le__cancel__left2,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 7.75/5.68 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 7.75/5.68 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left2
% 7.75/5.68 thf(fact_3155_mult__le__cancel__left2,axiom,
% 7.75/5.68 ! [C: real,A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ A @ one_one_real ) )
% 7.75/5.68 & ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left2
% 7.75/5.68 thf(fact_3156_mult__le__cancel__left2,axiom,
% 7.75/5.68 ! [C: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 7.75/5.68 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left2
% 7.75/5.68 thf(fact_3157_mult__le__cancel__left2,axiom,
% 7.75/5.68 ! [C: int,A: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 7.75/5.68 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ A @ one_one_int ) )
% 7.75/5.68 & ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_left2
% 7.75/5.68 thf(fact_3158_mult__le__cancel__right1,axiom,
% 7.75/5.68 ! [C: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 7.75/5.68 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right1
% 7.75/5.68 thf(fact_3159_mult__le__cancel__right1,axiom,
% 7.75/5.68 ! [C: real,B: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ one_one_real @ B ) )
% 7.75/5.68 & ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right1
% 7.75/5.68 thf(fact_3160_mult__le__cancel__right1,axiom,
% 7.75/5.68 ! [C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 7.75/5.68 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right1
% 7.75/5.68 thf(fact_3161_mult__le__cancel__right1,axiom,
% 7.75/5.68 ! [C: int,B: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ one_one_int @ B ) )
% 7.75/5.68 & ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right1
% 7.75/5.68 thf(fact_3162_mult__le__cancel__right2,axiom,
% 7.75/5.68 ! [A: code_integer,C: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 7.75/5.68 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 7.75/5.68 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right2
% 7.75/5.68 thf(fact_3163_mult__le__cancel__right2,axiom,
% 7.75/5.68 ! [A: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ A @ one_one_real ) )
% 7.75/5.68 & ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right2
% 7.75/5.68 thf(fact_3164_mult__le__cancel__right2,axiom,
% 7.75/5.68 ! [A: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 7.75/5.68 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right2
% 7.75/5.68 thf(fact_3165_mult__le__cancel__right2,axiom,
% 7.75/5.68 ! [A: int,C: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 7.75/5.68 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_eq_int @ A @ one_one_int ) )
% 7.75/5.68 & ( ( ord_less_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_le_cancel_right2
% 7.75/5.68 thf(fact_3166_mult__less__cancel__left1,axiom,
% 7.75/5.68 ! [C: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 7.75/5.68 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left1
% 7.75/5.68 thf(fact_3167_mult__less__cancel__left1,axiom,
% 7.75/5.68 ! [C: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ one_one_real @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left1
% 7.75/5.68 thf(fact_3168_mult__less__cancel__left1,axiom,
% 7.75/5.68 ! [C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ one_one_rat @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left1
% 7.75/5.68 thf(fact_3169_mult__less__cancel__left1,axiom,
% 7.75/5.68 ! [C: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 7.75/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ one_one_int @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left1
% 7.75/5.68 thf(fact_3170_mult__less__cancel__left2,axiom,
% 7.75/5.68 ! [C: code_integer,A: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 7.75/5.68 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 7.75/5.68 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left2
% 7.75/5.68 thf(fact_3171_mult__less__cancel__left2,axiom,
% 7.75/5.68 ! [C: real,A: real] :
% 7.75/5.68 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ A @ one_one_real ) )
% 7.75/5.68 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left2
% 7.75/5.68 thf(fact_3172_mult__less__cancel__left2,axiom,
% 7.75/5.68 ! [C: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ A @ one_one_rat ) )
% 7.75/5.68 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left2
% 7.75/5.68 thf(fact_3173_mult__less__cancel__left2,axiom,
% 7.75/5.68 ! [C: int,A: int] :
% 7.75/5.68 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 7.75/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ A @ one_one_int ) )
% 7.75/5.68 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_left2
% 7.75/5.68 thf(fact_3174_mult__less__cancel__right1,axiom,
% 7.75/5.68 ! [C: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 7.75/5.68 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right1
% 7.75/5.68 thf(fact_3175_mult__less__cancel__right1,axiom,
% 7.75/5.68 ! [C: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ one_one_real @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right1
% 7.75/5.68 thf(fact_3176_mult__less__cancel__right1,axiom,
% 7.75/5.68 ! [C: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ one_one_rat @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right1
% 7.75/5.68 thf(fact_3177_mult__less__cancel__right1,axiom,
% 7.75/5.68 ! [C: int,B: int] :
% 7.75/5.68 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ one_one_int @ B ) )
% 7.75/5.68 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right1
% 7.75/5.68 thf(fact_3178_mult__less__cancel__right2,axiom,
% 7.75/5.68 ! [A: code_integer,C: code_integer] :
% 7.75/5.68 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 7.75/5.68 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 7.75/5.68 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right2
% 7.75/5.68 thf(fact_3179_mult__less__cancel__right2,axiom,
% 7.75/5.68 ! [A: real,C: real] :
% 7.75/5.68 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 7.75/5.68 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_real @ A @ one_one_real ) )
% 7.75/5.68 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right2
% 7.75/5.68 thf(fact_3180_mult__less__cancel__right2,axiom,
% 7.75/5.68 ! [A: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 7.75/5.68 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_rat @ A @ one_one_rat ) )
% 7.75/5.68 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right2
% 7.75/5.68 thf(fact_3181_mult__less__cancel__right2,axiom,
% 7.75/5.68 ! [A: int,C: int] :
% 7.75/5.68 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 7.75/5.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.68 => ( ord_less_int @ A @ one_one_int ) )
% 7.75/5.68 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 7.75/5.68 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_less_cancel_right2
% 7.75/5.68 thf(fact_3182_field__le__mult__one__interval,axiom,
% 7.75/5.68 ! [X: real,Y: real] :
% 7.75/5.68 ( ! [Z3: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 7.75/5.68 => ( ( ord_less_real @ Z3 @ one_one_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ Y ) ) )
% 7.75/5.68 => ( ord_less_eq_real @ X @ Y ) ) ).
% 7.75/5.68
% 7.75/5.68 % field_le_mult_one_interval
% 7.75/5.68 thf(fact_3183_field__le__mult__one__interval,axiom,
% 7.75/5.68 ! [X: rat,Y: rat] :
% 7.75/5.68 ( ! [Z3: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 7.75/5.68 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y ) ) )
% 7.75/5.68 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 7.75/5.68
% 7.75/5.68 % field_le_mult_one_interval
% 7.75/5.68 thf(fact_3184_convex__bound__le,axiom,
% 7.75/5.68 ! [X: real,A: real,Y: real,U: real,V: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ X @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ Y @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 7.75/5.68 => ( ( ( plus_plus_real @ U @ V )
% 7.75/5.68 = one_one_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % convex_bound_le
% 7.75/5.68 thf(fact_3185_convex__bound__le,axiom,
% 7.75/5.68 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ X @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 7.75/5.68 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 7.75/5.68 = one_one_Code_integer )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % convex_bound_le
% 7.75/5.68 thf(fact_3186_convex__bound__le,axiom,
% 7.75/5.68 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ X @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ Y @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 7.75/5.68 => ( ( ( plus_plus_rat @ U @ V )
% 7.75/5.68 = one_one_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % convex_bound_le
% 7.75/5.68 thf(fact_3187_convex__bound__le,axiom,
% 7.75/5.68 ! [X: int,A: int,Y: int,U: int,V: int] :
% 7.75/5.68 ( ( ord_less_eq_int @ X @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ Y @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 7.75/5.68 => ( ( ( plus_plus_int @ U @ V )
% 7.75/5.68 = one_one_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % convex_bound_le
% 7.75/5.68 thf(fact_3188_divide__le__eq__1,axiom,
% 7.75/5.68 ! [B: real,A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.68 & ( ord_less_eq_real @ B @ A ) )
% 7.75/5.68 | ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.68 & ( ord_less_eq_real @ A @ B ) )
% 7.75/5.68 | ( A = zero_zero_real ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq_1
% 7.75/5.68 thf(fact_3189_divide__le__eq__1,axiom,
% 7.75/5.68 ! [B: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.68 & ( ord_less_eq_rat @ B @ A ) )
% 7.75/5.68 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.68 & ( ord_less_eq_rat @ A @ B ) )
% 7.75/5.68 | ( A = zero_zero_rat ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq_1
% 7.75/5.68 thf(fact_3190_le__divide__eq__1,axiom,
% 7.75/5.68 ! [B: real,A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.68 & ( ord_less_eq_real @ A @ B ) )
% 7.75/5.68 | ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.68 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq_1
% 7.75/5.68 thf(fact_3191_le__divide__eq__1,axiom,
% 7.75/5.68 ! [B: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.68 & ( ord_less_eq_rat @ A @ B ) )
% 7.75/5.68 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.68 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq_1
% 7.75/5.68 thf(fact_3192_divide__le__eq,axiom,
% 7.75/5.68 ! [B: real,C: real,A: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 7.75/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 7.75/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq
% 7.75/5.68 thf(fact_3193_divide__le__eq,axiom,
% 7.75/5.68 ! [B: rat,C: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 7.75/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 7.75/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_le_eq
% 7.75/5.68 thf(fact_3194_le__divide__eq,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 7.75/5.68 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 7.75/5.68 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq
% 7.75/5.68 thf(fact_3195_le__divide__eq,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.68 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 7.75/5.68 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 7.75/5.68 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % le_divide_eq
% 7.75/5.68 thf(fact_3196_divide__left__mono,axiom,
% 7.75/5.68 ! [B: real,A: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ B @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_left_mono
% 7.75/5.68 thf(fact_3197_divide__left__mono,axiom,
% 7.75/5.68 ! [B: rat,A: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ B @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_left_mono
% 7.75/5.68 thf(fact_3198_neg__divide__le__eq,axiom,
% 7.75/5.68 ! [C: real,B: real,A: real] :
% 7.75/5.68 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 7.75/5.68 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % neg_divide_le_eq
% 7.75/5.68 thf(fact_3199_neg__divide__le__eq,axiom,
% 7.75/5.68 ! [C: rat,B: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 7.75/5.68 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % neg_divide_le_eq
% 7.75/5.68 thf(fact_3200_neg__le__divide__eq,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 7.75/5.68 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % neg_le_divide_eq
% 7.75/5.68 thf(fact_3201_neg__le__divide__eq,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.68 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % neg_le_divide_eq
% 7.75/5.68 thf(fact_3202_pos__divide__le__eq,axiom,
% 7.75/5.68 ! [C: real,B: real,A: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 7.75/5.68 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % pos_divide_le_eq
% 7.75/5.68 thf(fact_3203_pos__divide__le__eq,axiom,
% 7.75/5.68 ! [C: rat,B: rat,A: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 7.75/5.68 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % pos_divide_le_eq
% 7.75/5.68 thf(fact_3204_pos__le__divide__eq,axiom,
% 7.75/5.68 ! [C: real,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.68 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 7.75/5.68 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % pos_le_divide_eq
% 7.75/5.68 thf(fact_3205_pos__le__divide__eq,axiom,
% 7.75/5.68 ! [C: rat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.68 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.68 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % pos_le_divide_eq
% 7.75/5.68 thf(fact_3206_mult__imp__div__pos__le,axiom,
% 7.75/5.68 ! [Y: real,X: real,Z: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y ) )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_imp_div_pos_le
% 7.75/5.68 thf(fact_3207_mult__imp__div__pos__le,axiom,
% 7.75/5.68 ! [Y: rat,X: rat,Z: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_imp_div_pos_le
% 7.75/5.68 thf(fact_3208_mult__imp__le__div__pos,axiom,
% 7.75/5.68 ! [Y: real,Z: real,X: real] :
% 7.75/5.68 ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.68 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X )
% 7.75/5.68 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_imp_le_div_pos
% 7.75/5.68 thf(fact_3209_mult__imp__le__div__pos,axiom,
% 7.75/5.68 ! [Y: rat,Z: rat,X: rat] :
% 7.75/5.68 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 7.75/5.68 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 7.75/5.68 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % mult_imp_le_div_pos
% 7.75/5.68 thf(fact_3210_divide__left__mono__neg,axiom,
% 7.75/5.68 ! [A: real,B: real,C: real] :
% 7.75/5.68 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 7.75/5.68 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 7.75/5.68 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_left_mono_neg
% 7.75/5.68 thf(fact_3211_divide__left__mono__neg,axiom,
% 7.75/5.68 ! [A: rat,B: rat,C: rat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.68 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 7.75/5.68 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.68 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % divide_left_mono_neg
% 7.75/5.68 thf(fact_3212_power__Suc__le__self,axiom,
% 7.75/5.68 ! [A: real,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ A @ one_one_real )
% 7.75/5.68 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_Suc_le_self
% 7.75/5.68 thf(fact_3213_power__Suc__le__self,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_Suc_le_self
% 7.75/5.68 thf(fact_3214_power__Suc__le__self,axiom,
% 7.75/5.68 ! [A: rat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 7.75/5.68 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_Suc_le_self
% 7.75/5.68 thf(fact_3215_power__Suc__le__self,axiom,
% 7.75/5.68 ! [A: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 7.75/5.68 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_Suc_le_self
% 7.75/5.68 thf(fact_3216_power__Suc__le__self,axiom,
% 7.75/5.68 ! [A: int,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ A @ one_one_int )
% 7.75/5.68 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_Suc_le_self
% 7.75/5.68 thf(fact_3217_power__eq__imp__eq__base,axiom,
% 7.75/5.68 ! [A: real,N: nat,B: real] :
% 7.75/5.68 ( ( ( power_power_real @ A @ N )
% 7.75/5.68 = ( power_power_real @ B @ N ) )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_imp_eq_base
% 7.75/5.68 thf(fact_3218_power__eq__imp__eq__base,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat,B: code_integer] :
% 7.75/5.68 ( ( ( power_8256067586552552935nteger @ A @ N )
% 7.75/5.68 = ( power_8256067586552552935nteger @ B @ N ) )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_imp_eq_base
% 7.75/5.68 thf(fact_3219_power__eq__imp__eq__base,axiom,
% 7.75/5.68 ! [A: rat,N: nat,B: rat] :
% 7.75/5.68 ( ( ( power_power_rat @ A @ N )
% 7.75/5.68 = ( power_power_rat @ B @ N ) )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_imp_eq_base
% 7.75/5.68 thf(fact_3220_power__eq__imp__eq__base,axiom,
% 7.75/5.68 ! [A: nat,N: nat,B: nat] :
% 7.75/5.68 ( ( ( power_power_nat @ A @ N )
% 7.75/5.68 = ( power_power_nat @ B @ N ) )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_imp_eq_base
% 7.75/5.68 thf(fact_3221_power__eq__imp__eq__base,axiom,
% 7.75/5.68 ! [A: int,N: nat,B: int] :
% 7.75/5.68 ( ( ( power_power_int @ A @ N )
% 7.75/5.68 = ( power_power_int @ B @ N ) )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_imp_eq_base
% 7.75/5.68 thf(fact_3222_power__eq__iff__eq__base,axiom,
% 7.75/5.68 ! [N: nat,A: real,B: real] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.68 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.68 => ( ( ( power_power_real @ A @ N )
% 7.75/5.68 = ( power_power_real @ B @ N ) )
% 7.75/5.68 = ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_iff_eq_base
% 7.75/5.68 thf(fact_3223_power__eq__iff__eq__base,axiom,
% 7.75/5.68 ! [N: nat,A: code_integer,B: code_integer] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.68 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.68 => ( ( ( power_8256067586552552935nteger @ A @ N )
% 7.75/5.68 = ( power_8256067586552552935nteger @ B @ N ) )
% 7.75/5.68 = ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_iff_eq_base
% 7.75/5.68 thf(fact_3224_power__eq__iff__eq__base,axiom,
% 7.75/5.68 ! [N: nat,A: rat,B: rat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.68 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.68 => ( ( ( power_power_rat @ A @ N )
% 7.75/5.68 = ( power_power_rat @ B @ N ) )
% 7.75/5.68 = ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_iff_eq_base
% 7.75/5.68 thf(fact_3225_power__eq__iff__eq__base,axiom,
% 7.75/5.68 ! [N: nat,A: nat,B: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.68 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 7.75/5.68 => ( ( ( power_power_nat @ A @ N )
% 7.75/5.68 = ( power_power_nat @ B @ N ) )
% 7.75/5.68 = ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_iff_eq_base
% 7.75/5.68 thf(fact_3226_power__eq__iff__eq__base,axiom,
% 7.75/5.68 ! [N: nat,A: int,B: int] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.68 => ( ( ( power_power_int @ A @ N )
% 7.75/5.68 = ( power_power_int @ B @ N ) )
% 7.75/5.68 = ( A = B ) ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % power_eq_iff_eq_base
% 7.75/5.68 thf(fact_3227_self__le__power,axiom,
% 7.75/5.68 ! [A: real,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_real @ one_one_real @ A )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % self_le_power
% 7.75/5.68 thf(fact_3228_self__le__power,axiom,
% 7.75/5.68 ! [A: code_integer,N: nat] :
% 7.75/5.68 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % self_le_power
% 7.75/5.68 thf(fact_3229_self__le__power,axiom,
% 7.75/5.68 ! [A: rat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % self_le_power
% 7.75/5.68 thf(fact_3230_self__le__power,axiom,
% 7.75/5.68 ! [A: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % self_le_power
% 7.75/5.68 thf(fact_3231_self__le__power,axiom,
% 7.75/5.68 ! [A: int,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_int @ one_one_int @ A )
% 7.75/5.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.68 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % self_le_power
% 7.75/5.68 thf(fact_3232_dvd__power__iff,axiom,
% 7.75/5.68 ! [X: nat,M: nat,N: nat] :
% 7.75/5.68 ( ( X != zero_zero_nat )
% 7.75/5.68 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 7.75/5.68 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 7.75/5.68 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dvd_power_iff
% 7.75/5.68 thf(fact_3233_dvd__power__iff,axiom,
% 7.75/5.68 ! [X: int,M: nat,N: nat] :
% 7.75/5.68 ( ( X != zero_zero_int )
% 7.75/5.68 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 7.75/5.68 = ( ( dvd_dvd_int @ X @ one_one_int )
% 7.75/5.68 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dvd_power_iff
% 7.75/5.68 thf(fact_3234_dvd__power__iff,axiom,
% 7.75/5.68 ! [X: code_integer,M: nat,N: nat] :
% 7.75/5.68 ( ( X != zero_z3403309356797280102nteger )
% 7.75/5.68 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 7.75/5.68 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 7.75/5.68 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % dvd_power_iff
% 7.75/5.68 thf(fact_3235_self__le__ge2__pow,axiom,
% 7.75/5.68 ! [K: nat,M: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % self_le_ge2_pow
% 7.75/5.68 thf(fact_3236_power2__nat__le__eq__le,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.68 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_nat_le_eq_le
% 7.75/5.68 thf(fact_3237_power2__nat__le__imp__le,axiom,
% 7.75/5.68 ! [M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 7.75/5.68 => ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.68
% 7.75/5.68 % power2_nat_le_imp_le
% 7.75/5.68 thf(fact_3238_div__nat__eqI,axiom,
% 7.75/5.68 ! [N: nat,Q3: nat,M: nat] :
% 7.75/5.68 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M )
% 7.75/5.68 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 7.75/5.68 => ( ( divide_divide_nat @ M @ N )
% 7.75/5.68 = Q3 ) ) ) ).
% 7.75/5.68
% 7.75/5.68 % div_nat_eqI
% 7.75/5.68 thf(fact_3239_less__eq__div__iff__mult__less__eq,axiom,
% 7.75/5.68 ! [Q3: nat,M: nat,N: nat] :
% 7.75/5.68 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 7.75/5.69 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q3 ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_eq_div_iff_mult_less_eq
% 7.75/5.69 thf(fact_3240_td__gal,axiom,
% 7.75/5.69 ! [C: nat,B: nat,A: nat] :
% 7.75/5.69 ( ( ord_less_nat @ zero_zero_nat @ C )
% 7.75/5.69 => ( ( ord_less_eq_nat @ ( times_times_nat @ B @ C ) @ A )
% 7.75/5.69 = ( ord_less_eq_nat @ B @ ( divide_divide_nat @ A @ C ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % td_gal
% 7.75/5.69 thf(fact_3241_power__dvd__imp__le,axiom,
% 7.75/5.69 ! [I: nat,M: nat,N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 7.75/5.69 => ( ( ord_less_nat @ one_one_nat @ I )
% 7.75/5.69 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_dvd_imp_le
% 7.75/5.69 thf(fact_3242_le__imp__0__less,axiom,
% 7.75/5.69 ! [Z: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.69 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_imp_0_less
% 7.75/5.69 thf(fact_3243_pos__mult__pos__ge,axiom,
% 7.75/5.69 ! [X: int,N: int] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ X )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 7.75/5.69 => ( ord_less_eq_int @ ( times_times_int @ N @ one_one_int ) @ ( times_times_int @ N @ X ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % pos_mult_pos_ge
% 7.75/5.69 thf(fact_3244_q__pos__lemma,axiom,
% 7.75/5.69 ! [B6: int,Q7: int,R4: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q7 ) @ R4 ) )
% 7.75/5.69 => ( ( ord_less_int @ R4 @ B6 )
% 7.75/5.69 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 7.75/5.69 => ( ord_less_eq_int @ zero_zero_int @ Q7 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % q_pos_lemma
% 7.75/5.69 thf(fact_3245_zdiv__mono2__lemma,axiom,
% 7.75/5.69 ! [B: int,Q3: int,R2: int,B6: int,Q7: int,R4: int] :
% 7.75/5.69 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ B6 @ Q7 ) @ R4 ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q7 ) @ R4 ) )
% 7.75/5.69 => ( ( ord_less_int @ R4 @ B6 )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 7.75/5.69 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 7.75/5.69 => ( ( ord_less_eq_int @ B6 @ B )
% 7.75/5.69 => ( ord_less_eq_int @ Q3 @ Q7 ) ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zdiv_mono2_lemma
% 7.75/5.69 thf(fact_3246_incr__mult__lemma,axiom,
% 7.75/5.69 ! [D2: int,P: int > $o,K: int] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ D2 )
% 7.75/5.69 => ( ! [X3: int] :
% 7.75/5.69 ( ( P @ X3 )
% 7.75/5.69 => ( P @ ( plus_plus_int @ X3 @ D2 ) ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.69 => ! [X5: int] :
% 7.75/5.69 ( ( P @ X5 )
% 7.75/5.69 => ( P @ ( plus_plus_int @ X5 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % incr_mult_lemma
% 7.75/5.69 thf(fact_3247_zdiv__mono2__neg__lemma,axiom,
% 7.75/5.69 ! [B: int,Q3: int,R2: int,B6: int,Q7: int,R4: int] :
% 7.75/5.69 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ B6 @ Q7 ) @ R4 ) )
% 7.75/5.69 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q7 ) @ R4 ) @ zero_zero_int )
% 7.75/5.69 => ( ( ord_less_int @ R2 @ B )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 7.75/5.69 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 7.75/5.69 => ( ( ord_less_eq_int @ B6 @ B )
% 7.75/5.69 => ( ord_less_eq_int @ Q7 @ Q3 ) ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zdiv_mono2_neg_lemma
% 7.75/5.69 thf(fact_3248_unique__quotient__lemma,axiom,
% 7.75/5.69 ! [B: int,Q7: int,R4: int,Q3: int,R2: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q7 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 7.75/5.69 => ( ( ord_less_int @ R4 @ B )
% 7.75/5.69 => ( ( ord_less_int @ R2 @ B )
% 7.75/5.69 => ( ord_less_eq_int @ Q7 @ Q3 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % unique_quotient_lemma
% 7.75/5.69 thf(fact_3249_unique__quotient__lemma__neg,axiom,
% 7.75/5.69 ! [B: int,Q7: int,R4: int,Q3: int,R2: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q7 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 7.75/5.69 => ( ( ord_less_int @ B @ R2 )
% 7.75/5.69 => ( ( ord_less_int @ B @ R4 )
% 7.75/5.69 => ( ord_less_eq_int @ Q3 @ Q7 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % unique_quotient_lemma_neg
% 7.75/5.69 thf(fact_3250_mod__pos__neg__trivial,axiom,
% 7.75/5.69 ! [K: int,L: int] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.69 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 7.75/5.69 => ( ( modulo_modulo_int @ K @ L )
% 7.75/5.69 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mod_pos_neg_trivial
% 7.75/5.69 thf(fact_3251_int__mod__ge_H,axiom,
% 7.75/5.69 ! [B: int,N: int] :
% 7.75/5.69 ( ( ord_less_int @ B @ zero_zero_int )
% 7.75/5.69 => ( ( ord_less_int @ zero_zero_int @ N )
% 7.75/5.69 => ( ord_less_eq_int @ ( plus_plus_int @ B @ N ) @ ( modulo_modulo_int @ B @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % int_mod_ge'
% 7.75/5.69 thf(fact_3252_mod__int__pos__iff,axiom,
% 7.75/5.69 ! [K: int,L: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 7.75/5.69 = ( ( dvd_dvd_int @ L @ K )
% 7.75/5.69 | ( ( L = zero_zero_int )
% 7.75/5.69 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 7.75/5.69 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mod_int_pos_iff
% 7.75/5.69 thf(fact_3253_signed__take__bit__int__less__exp,axiom,
% 7.75/5.69 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_int_less_exp
% 7.75/5.69 thf(fact_3254_even__signed__take__bit__iff,axiom,
% 7.75/5.69 ! [M: nat,A: int] :
% 7.75/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 7.75/5.69 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % even_signed_take_bit_iff
% 7.75/5.69 thf(fact_3255_convex__bound__lt,axiom,
% 7.75/5.69 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ X @ A )
% 7.75/5.69 => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 7.75/5.69 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 7.75/5.69 = one_one_Code_integer )
% 7.75/5.69 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % convex_bound_lt
% 7.75/5.69 thf(fact_3256_convex__bound__lt,axiom,
% 7.75/5.69 ! [X: real,A: real,Y: real,U: real,V: real] :
% 7.75/5.69 ( ( ord_less_real @ X @ A )
% 7.75/5.69 => ( ( ord_less_real @ Y @ A )
% 7.75/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 7.75/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 7.75/5.69 => ( ( ( plus_plus_real @ U @ V )
% 7.75/5.69 = one_one_real )
% 7.75/5.69 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % convex_bound_lt
% 7.75/5.69 thf(fact_3257_convex__bound__lt,axiom,
% 7.75/5.69 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 7.75/5.69 ( ( ord_less_rat @ X @ A )
% 7.75/5.69 => ( ( ord_less_rat @ Y @ A )
% 7.75/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 7.75/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 7.75/5.69 => ( ( ( plus_plus_rat @ U @ V )
% 7.75/5.69 = one_one_rat )
% 7.75/5.69 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % convex_bound_lt
% 7.75/5.69 thf(fact_3258_convex__bound__lt,axiom,
% 7.75/5.69 ! [X: int,A: int,Y: int,U: int,V: int] :
% 7.75/5.69 ( ( ord_less_int @ X @ A )
% 7.75/5.69 => ( ( ord_less_int @ Y @ A )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 7.75/5.69 => ( ( ( plus_plus_int @ U @ V )
% 7.75/5.69 = one_one_int )
% 7.75/5.69 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % convex_bound_lt
% 7.75/5.69 thf(fact_3259_divide__le__eq__numeral_I1_J,axiom,
% 7.75/5.69 ! [B: real,C: real,W: num] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 7.75/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.69 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 7.75/5.69 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.69 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.69 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 7.75/5.69 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_le_eq_numeral(1)
% 7.75/5.69 thf(fact_3260_divide__le__eq__numeral_I1_J,axiom,
% 7.75/5.69 ! [B: rat,C: rat,W: num] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 7.75/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.69 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 7.75/5.69 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.69 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.69 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 7.75/5.69 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_le_eq_numeral(1)
% 7.75/5.69 thf(fact_3261_le__divide__eq__numeral_I1_J,axiom,
% 7.75/5.69 ! [W: num,B: real,C: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 7.75/5.69 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.69 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 7.75/5.69 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.69 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.69 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 7.75/5.69 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.69 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_divide_eq_numeral(1)
% 7.75/5.69 thf(fact_3262_le__divide__eq__numeral_I1_J,axiom,
% 7.75/5.69 ! [W: num,B: rat,C: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.69 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.69 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 7.75/5.69 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.69 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.69 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 7.75/5.69 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.69 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_divide_eq_numeral(1)
% 7.75/5.69 thf(fact_3263_zero__le__power2,axiom,
% 7.75/5.69 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_power2
% 7.75/5.69 thf(fact_3264_zero__le__power2,axiom,
% 7.75/5.69 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_power2
% 7.75/5.69 thf(fact_3265_zero__le__power2,axiom,
% 7.75/5.69 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_power2
% 7.75/5.69 thf(fact_3266_zero__le__power2,axiom,
% 7.75/5.69 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_power2
% 7.75/5.69 thf(fact_3267_power2__eq__imp__eq,axiom,
% 7.75/5.69 ! [X: real,Y: real] :
% 7.75/5.69 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.69 => ( X = Y ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_eq_imp_eq
% 7.75/5.69 thf(fact_3268_power2__eq__imp__eq,axiom,
% 7.75/5.69 ! [X: code_integer,Y: code_integer] :
% 7.75/5.69 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 7.75/5.69 => ( X = Y ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_eq_imp_eq
% 7.75/5.69 thf(fact_3269_power2__eq__imp__eq,axiom,
% 7.75/5.69 ! [X: rat,Y: rat] :
% 7.75/5.69 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.69 => ( X = Y ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_eq_imp_eq
% 7.75/5.69 thf(fact_3270_power2__eq__imp__eq,axiom,
% 7.75/5.69 ! [X: nat,Y: nat] :
% 7.75/5.69 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 7.75/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 7.75/5.69 => ( X = Y ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_eq_imp_eq
% 7.75/5.69 thf(fact_3271_power2__eq__imp__eq,axiom,
% 7.75/5.69 ! [X: int,Y: int] :
% 7.75/5.69 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.69 => ( X = Y ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_eq_imp_eq
% 7.75/5.69 thf(fact_3272_power2__le__imp__le,axiom,
% 7.75/5.69 ! [X: real,Y: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.69 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_le_imp_le
% 7.75/5.69 thf(fact_3273_power2__le__imp__le,axiom,
% 7.75/5.69 ! [X: code_integer,Y: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 7.75/5.69 => ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_le_imp_le
% 7.75/5.69 thf(fact_3274_power2__le__imp__le,axiom,
% 7.75/5.69 ! [X: rat,Y: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.69 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_le_imp_le
% 7.75/5.69 thf(fact_3275_power2__le__imp__le,axiom,
% 7.75/5.69 ! [X: nat,Y: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 7.75/5.69 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_le_imp_le
% 7.75/5.69 thf(fact_3276_power2__le__imp__le,axiom,
% 7.75/5.69 ! [X: int,Y: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.69 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_le_imp_le
% 7.75/5.69 thf(fact_3277_power__strict__mono,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer,N: nat] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.69 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_strict_mono
% 7.75/5.69 thf(fact_3278_power__strict__mono,axiom,
% 7.75/5.69 ! [A: real,B: real,N: nat] :
% 7.75/5.69 ( ( ord_less_real @ A @ B )
% 7.75/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.69 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_strict_mono
% 7.75/5.69 thf(fact_3279_power__strict__mono,axiom,
% 7.75/5.69 ! [A: rat,B: rat,N: nat] :
% 7.75/5.69 ( ( ord_less_rat @ A @ B )
% 7.75/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.69 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_strict_mono
% 7.75/5.69 thf(fact_3280_power__strict__mono,axiom,
% 7.75/5.69 ! [A: nat,B: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_nat @ A @ B )
% 7.75/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.69 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_strict_mono
% 7.75/5.69 thf(fact_3281_power__strict__mono,axiom,
% 7.75/5.69 ! [A: int,B: int,N: nat] :
% 7.75/5.69 ( ( ord_less_int @ A @ B )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.69 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_strict_mono
% 7.75/5.69 thf(fact_3282_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 7.75/5.69 ! [C: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 7.75/5.69 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 7.75/5.69 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 7.75/5.69 thf(fact_3283_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 7.75/5.69 ! [C: nat,A: nat,B: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 7.75/5.69 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 7.75/5.69 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 7.75/5.69 thf(fact_3284_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 7.75/5.69 ! [C: int,A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.69 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 7.75/5.69 thf(fact_3285_num_Osize__gen_I1_J,axiom,
% 7.75/5.69 ( ( size_num @ one )
% 7.75/5.69 = zero_zero_nat ) ).
% 7.75/5.69
% 7.75/5.69 % num.size_gen(1)
% 7.75/5.69 thf(fact_3286_power__mono__odd,axiom,
% 7.75/5.69 ! [N: nat,A: real,B: real] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( ord_less_eq_real @ A @ B )
% 7.75/5.69 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_mono_odd
% 7.75/5.69 thf(fact_3287_power__mono__odd,axiom,
% 7.75/5.69 ! [N: nat,A: code_integer,B: code_integer] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.69 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_mono_odd
% 7.75/5.69 thf(fact_3288_power__mono__odd,axiom,
% 7.75/5.69 ! [N: nat,A: rat,B: rat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.69 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_mono_odd
% 7.75/5.69 thf(fact_3289_power__mono__odd,axiom,
% 7.75/5.69 ! [N: nat,A: int,B: int] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( ord_less_eq_int @ A @ B )
% 7.75/5.69 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_mono_odd
% 7.75/5.69 thf(fact_3290_pos__mod__sign2,axiom,
% 7.75/5.69 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % pos_mod_sign2
% 7.75/5.69 thf(fact_3291_split__div_H,axiom,
% 7.75/5.69 ! [P: nat > $o,M: nat,N: nat] :
% 7.75/5.69 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 7.75/5.69 = ( ( ( N = zero_zero_nat )
% 7.75/5.69 & ( P @ zero_zero_nat ) )
% 7.75/5.69 | ? [Q6: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q6 ) @ M )
% 7.75/5.69 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q6 ) ) )
% 7.75/5.69 & ( P @ Q6 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % split_div'
% 7.75/5.69 thf(fact_3292_not__exp__less__eq__0__int,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % not_exp_less_eq_0_int
% 7.75/5.69 thf(fact_3293_dvd__power__iff__le,axiom,
% 7.75/5.69 ! [K: nat,M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 7.75/5.69 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dvd_power_iff_le
% 7.75/5.69 thf(fact_3294_two__realpow__ge__one,axiom,
% 7.75/5.69 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % two_realpow_ge_one
% 7.75/5.69 thf(fact_3295_split__zmod,axiom,
% 7.75/5.69 ! [P: int > $o,N: int,K: int] :
% 7.75/5.69 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 7.75/5.69 = ( ( ( K = zero_zero_int )
% 7.75/5.69 => ( P @ N ) )
% 7.75/5.69 & ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.69 => ! [I2: int,J2: int] :
% 7.75/5.69 ( ( ( ord_less_eq_int @ zero_zero_int @ J2 )
% 7.75/5.69 & ( ord_less_int @ J2 @ K )
% 7.75/5.69 & ( N
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J2 ) ) )
% 7.75/5.69 => ( P @ J2 ) ) )
% 7.75/5.69 & ( ( ord_less_int @ K @ zero_zero_int )
% 7.75/5.69 => ! [I2: int,J2: int] :
% 7.75/5.69 ( ( ( ord_less_int @ K @ J2 )
% 7.75/5.69 & ( ord_less_eq_int @ J2 @ zero_zero_int )
% 7.75/5.69 & ( N
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J2 ) ) )
% 7.75/5.69 => ( P @ J2 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % split_zmod
% 7.75/5.69 thf(fact_3296_int__mod__neg__eq,axiom,
% 7.75/5.69 ! [A: int,B: int,Q3: int,R2: int] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 7.75/5.69 => ( ( ord_less_int @ B @ R2 )
% 7.75/5.69 => ( ( modulo_modulo_int @ A @ B )
% 7.75/5.69 = R2 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % int_mod_neg_eq
% 7.75/5.69 thf(fact_3297_int__mod__pos__eq,axiom,
% 7.75/5.69 ! [A: int,B: int,Q3: int,R2: int] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 7.75/5.69 => ( ( ord_less_int @ R2 @ B )
% 7.75/5.69 => ( ( modulo_modulo_int @ A @ B )
% 7.75/5.69 = R2 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % int_mod_pos_eq
% 7.75/5.69 thf(fact_3298_int__div__pos__eq,axiom,
% 7.75/5.69 ! [A: int,B: int,Q3: int,R2: int] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 7.75/5.69 => ( ( ord_less_int @ R2 @ B )
% 7.75/5.69 => ( ( divide_divide_int @ A @ B )
% 7.75/5.69 = Q3 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % int_div_pos_eq
% 7.75/5.69 thf(fact_3299_int__div__neg__eq,axiom,
% 7.75/5.69 ! [A: int,B: int,Q3: int,R2: int] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 7.75/5.69 => ( ( ord_less_int @ B @ R2 )
% 7.75/5.69 => ( ( divide_divide_int @ A @ B )
% 7.75/5.69 = Q3 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % int_div_neg_eq
% 7.75/5.69 thf(fact_3300_split__zdiv,axiom,
% 7.75/5.69 ! [P: int > $o,N: int,K: int] :
% 7.75/5.69 ( ( P @ ( divide_divide_int @ N @ K ) )
% 7.75/5.69 = ( ( ( K = zero_zero_int )
% 7.75/5.69 => ( P @ zero_zero_int ) )
% 7.75/5.69 & ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.69 => ! [I2: int,J2: int] :
% 7.75/5.69 ( ( ( ord_less_eq_int @ zero_zero_int @ J2 )
% 7.75/5.69 & ( ord_less_int @ J2 @ K )
% 7.75/5.69 & ( N
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J2 ) ) )
% 7.75/5.69 => ( P @ I2 ) ) )
% 7.75/5.69 & ( ( ord_less_int @ K @ zero_zero_int )
% 7.75/5.69 => ! [I2: int,J2: int] :
% 7.75/5.69 ( ( ( ord_less_int @ K @ J2 )
% 7.75/5.69 & ( ord_less_eq_int @ J2 @ zero_zero_int )
% 7.75/5.69 & ( N
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J2 ) ) )
% 7.75/5.69 => ( P @ I2 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % split_zdiv
% 7.75/5.69 thf(fact_3301_mod__power__lem,axiom,
% 7.75/5.69 ! [A: int,M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_int @ one_one_int @ A )
% 7.75/5.69 => ( ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 => ( ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ M ) )
% 7.75/5.69 = zero_zero_int ) )
% 7.75/5.69 & ( ~ ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 => ( ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ M ) )
% 7.75/5.69 = ( power_power_int @ A @ N ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mod_power_lem
% 7.75/5.69 thf(fact_3302_zmod__zmult2__eq,axiom,
% 7.75/5.69 ! [C: int,A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 7.75/5.69 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zmod_zmult2_eq
% 7.75/5.69 thf(fact_3303_power2__less__imp__less,axiom,
% 7.75/5.69 ! [X: code_integer,Y: code_integer] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 7.75/5.69 => ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_less_imp_less
% 7.75/5.69 thf(fact_3304_power2__less__imp__less,axiom,
% 7.75/5.69 ! [X: real,Y: real] :
% 7.75/5.69 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.69 => ( ord_less_real @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_less_imp_less
% 7.75/5.69 thf(fact_3305_power2__less__imp__less,axiom,
% 7.75/5.69 ! [X: rat,Y: rat] :
% 7.75/5.69 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.69 => ( ord_less_rat @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_less_imp_less
% 7.75/5.69 thf(fact_3306_power2__less__imp__less,axiom,
% 7.75/5.69 ! [X: nat,Y: nat] :
% 7.75/5.69 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 7.75/5.69 => ( ord_less_nat @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_less_imp_less
% 7.75/5.69 thf(fact_3307_power2__less__imp__less,axiom,
% 7.75/5.69 ! [X: int,Y: int] :
% 7.75/5.69 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.69 => ( ord_less_int @ X @ Y ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_less_imp_less
% 7.75/5.69 thf(fact_3308_sum__power2__ge__zero,axiom,
% 7.75/5.69 ! [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 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_power2_ge_zero
% 7.75/5.69 thf(fact_3309_sum__power2__ge__zero,axiom,
% 7.75/5.69 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_power2_ge_zero
% 7.75/5.69 thf(fact_3310_sum__power2__ge__zero,axiom,
% 7.75/5.69 ! [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 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_power2_ge_zero
% 7.75/5.69 thf(fact_3311_sum__power2__ge__zero,axiom,
% 7.75/5.69 ! [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 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_power2_ge_zero
% 7.75/5.69 thf(fact_3312_sum__power2__le__zero__iff,axiom,
% 7.75/5.69 ! [X: real,Y: real] :
% 7.75/5.69 ( ( 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 )
% 7.75/5.69 = ( ( X = zero_zero_real )
% 7.75/5.69 & ( Y = zero_zero_real ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_power2_le_zero_iff
% 7.75/5.69 thf(fact_3313_sum__power2__le__zero__iff,axiom,
% 7.75/5.69 ! [X: code_integer,Y: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger )
% 7.75/5.69 = ( ( X = zero_z3403309356797280102nteger )
% 7.75/5.69 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_power2_le_zero_iff
% 7.75/5.69 thf(fact_3314_sum__power2__le__zero__iff,axiom,
% 7.75/5.69 ! [X: rat,Y: rat] :
% 7.75/5.69 ( ( 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 )
% 7.75/5.69 = ( ( X = zero_zero_rat )
% 7.75/5.69 & ( Y = zero_zero_rat ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_power2_le_zero_iff
% 7.75/5.69 thf(fact_3315_sum__power2__le__zero__iff,axiom,
% 7.75/5.69 ! [X: int,Y: int] :
% 7.75/5.69 ( ( 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 )
% 7.75/5.69 = ( ( X = zero_zero_int )
% 7.75/5.69 & ( Y = zero_zero_int ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_power2_le_zero_iff
% 7.75/5.69 thf(fact_3316_zero__le__even__power_H,axiom,
% 7.75/5.69 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_even_power'
% 7.75/5.69 thf(fact_3317_zero__le__even__power_H,axiom,
% 7.75/5.69 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_even_power'
% 7.75/5.69 thf(fact_3318_zero__le__even__power_H,axiom,
% 7.75/5.69 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_even_power'
% 7.75/5.69 thf(fact_3319_zero__le__even__power_H,axiom,
% 7.75/5.69 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_even_power'
% 7.75/5.69 thf(fact_3320_zero__le__power__eq,axiom,
% 7.75/5.69 ! [A: real,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 7.75/5.69 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_power_eq
% 7.75/5.69 thf(fact_3321_zero__le__power__eq,axiom,
% 7.75/5.69 ! [A: code_integer,N: nat] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.69 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_power_eq
% 7.75/5.69 thf(fact_3322_zero__le__power__eq,axiom,
% 7.75/5.69 ! [A: rat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 7.75/5.69 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_power_eq
% 7.75/5.69 thf(fact_3323_zero__le__power__eq,axiom,
% 7.75/5.69 ! [A: int,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 7.75/5.69 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_power_eq
% 7.75/5.69 thf(fact_3324_zero__le__odd__power,axiom,
% 7.75/5.69 ! [N: nat,A: real] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 7.75/5.69 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_odd_power
% 7.75/5.69 thf(fact_3325_zero__le__odd__power,axiom,
% 7.75/5.69 ! [N: nat,A: code_integer] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.69 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_odd_power
% 7.75/5.69 thf(fact_3326_zero__le__odd__power,axiom,
% 7.75/5.69 ! [N: nat,A: rat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 7.75/5.69 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_odd_power
% 7.75/5.69 thf(fact_3327_zero__le__odd__power,axiom,
% 7.75/5.69 ! [N: nat,A: int] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 7.75/5.69 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_odd_power
% 7.75/5.69 thf(fact_3328_zero__le__even__power,axiom,
% 7.75/5.69 ! [N: nat,A: real] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_even_power
% 7.75/5.69 thf(fact_3329_zero__le__even__power,axiom,
% 7.75/5.69 ! [N: nat,A: code_integer] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_even_power
% 7.75/5.69 thf(fact_3330_zero__le__even__power,axiom,
% 7.75/5.69 ! [N: nat,A: rat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_even_power
% 7.75/5.69 thf(fact_3331_zero__le__even__power,axiom,
% 7.75/5.69 ! [N: nat,A: int] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_le_even_power
% 7.75/5.69 thf(fact_3332_two__pow__div__gt__le,axiom,
% 7.75/5.69 ! [V: nat,N: nat,M: nat] :
% 7.75/5.69 ( ( ord_less_nat @ V @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) )
% 7.75/5.69 => ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % two_pow_div_gt_le
% 7.75/5.69 thf(fact_3333_L2__set__mult__ineq__lemma,axiom,
% 7.75/5.69 ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % L2_set_mult_ineq_lemma
% 7.75/5.69 thf(fact_3334_verit__le__mono__div,axiom,
% 7.75/5.69 ! [A2: nat,B3: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_nat @ A2 @ B3 )
% 7.75/5.69 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 => ( ord_less_eq_nat
% 7.75/5.69 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 7.75/5.69 @ ( if_nat
% 7.75/5.69 @ ( ( modulo_modulo_nat @ B3 @ N )
% 7.75/5.69 = zero_zero_nat )
% 7.75/5.69 @ one_one_nat
% 7.75/5.69 @ zero_zero_nat ) )
% 7.75/5.69 @ ( divide_divide_nat @ B3 @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_le_mono_div
% 7.75/5.69 thf(fact_3335_verit__le__mono__div__int,axiom,
% 7.75/5.69 ! [A2: int,B3: int,N: int] :
% 7.75/5.69 ( ( ord_less_int @ A2 @ B3 )
% 7.75/5.69 => ( ( ord_less_int @ zero_zero_int @ N )
% 7.75/5.69 => ( ord_less_eq_int
% 7.75/5.69 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 7.75/5.69 @ ( if_int
% 7.75/5.69 @ ( ( modulo_modulo_int @ B3 @ N )
% 7.75/5.69 = zero_zero_int )
% 7.75/5.69 @ one_one_int
% 7.75/5.69 @ zero_zero_int ) )
% 7.75/5.69 @ ( divide_divide_int @ B3 @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_le_mono_div_int
% 7.75/5.69 thf(fact_3336_split__pos__lemma,axiom,
% 7.75/5.69 ! [K: int,P: int > int > $o,N: int] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.69 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 7.75/5.69 = ( ! [I2: int,J2: int] :
% 7.75/5.69 ( ( ( ord_less_eq_int @ zero_zero_int @ J2 )
% 7.75/5.69 & ( ord_less_int @ J2 @ K )
% 7.75/5.69 & ( N
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J2 ) ) )
% 7.75/5.69 => ( P @ I2 @ J2 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % split_pos_lemma
% 7.75/5.69 thf(fact_3337_split__neg__lemma,axiom,
% 7.75/5.69 ! [K: int,P: int > int > $o,N: int] :
% 7.75/5.69 ( ( ord_less_int @ K @ zero_zero_int )
% 7.75/5.69 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 7.75/5.69 = ( ! [I2: int,J2: int] :
% 7.75/5.69 ( ( ( ord_less_int @ K @ J2 )
% 7.75/5.69 & ( ord_less_eq_int @ J2 @ zero_zero_int )
% 7.75/5.69 & ( N
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J2 ) ) )
% 7.75/5.69 => ( P @ I2 @ J2 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % split_neg_lemma
% 7.75/5.69 thf(fact_3338_sum__squares__bound,axiom,
% 7.75/5.69 ! [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 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_squares_bound
% 7.75/5.69 thf(fact_3339_sum__squares__bound,axiom,
% 7.75/5.69 ! [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 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sum_squares_bound
% 7.75/5.69 thf(fact_3340_odd__0__le__power__imp__0__le,axiom,
% 7.75/5.69 ! [A: real,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.69 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % odd_0_le_power_imp_0_le
% 7.75/5.69 thf(fact_3341_odd__0__le__power__imp__0__le,axiom,
% 7.75/5.69 ! [A: code_integer,N: nat] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.69 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % odd_0_le_power_imp_0_le
% 7.75/5.69 thf(fact_3342_odd__0__le__power__imp__0__le,axiom,
% 7.75/5.69 ! [A: rat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.69 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % odd_0_le_power_imp_0_le
% 7.75/5.69 thf(fact_3343_odd__0__le__power__imp__0__le,axiom,
% 7.75/5.69 ! [A: int,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.69 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % odd_0_le_power_imp_0_le
% 7.75/5.69 thf(fact_3344_ex__power__ivl1,axiom,
% 7.75/5.69 ! [B: nat,K: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 7.75/5.69 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 7.75/5.69 => ? [N2: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 7.75/5.69 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % ex_power_ivl1
% 7.75/5.69 thf(fact_3345_ex__power__ivl2,axiom,
% 7.75/5.69 ! [B: nat,K: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 7.75/5.69 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 7.75/5.69 => ? [N2: nat] :
% 7.75/5.69 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 7.75/5.69 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % ex_power_ivl2
% 7.75/5.69 thf(fact_3346_mod__double__modulus,axiom,
% 7.75/5.69 ! [M: code_integer,X: code_integer] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 7.75/5.69 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 7.75/5.69 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.69 = ( modulo364778990260209775nteger @ X @ M ) )
% 7.75/5.69 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.69 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mod_double_modulus
% 7.75/5.69 thf(fact_3347_mod__double__modulus,axiom,
% 7.75/5.69 ! [M: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.69 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 7.75/5.69 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.69 = ( modulo_modulo_nat @ X @ M ) )
% 7.75/5.69 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.69 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mod_double_modulus
% 7.75/5.69 thf(fact_3348_mod__double__modulus,axiom,
% 7.75/5.69 ! [M: int,X: int] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ M )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.69 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.69 = ( modulo_modulo_int @ X @ M ) )
% 7.75/5.69 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.69 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mod_double_modulus
% 7.75/5.69 thf(fact_3349_power__le__zero__eq,axiom,
% 7.75/5.69 ! [A: real,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 7.75/5.69 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 7.75/5.69 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( A = zero_zero_real ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_le_zero_eq
% 7.75/5.69 thf(fact_3350_power__le__zero__eq,axiom,
% 7.75/5.69 ! [A: code_integer,N: nat] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ zero_z3403309356797280102nteger )
% 7.75/5.69 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 7.75/5.69 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( A = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_le_zero_eq
% 7.75/5.69 thf(fact_3351_power__le__zero__eq,axiom,
% 7.75/5.69 ! [A: rat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 7.75/5.69 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 7.75/5.69 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( A = zero_zero_rat ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_le_zero_eq
% 7.75/5.69 thf(fact_3352_power__le__zero__eq,axiom,
% 7.75/5.69 ! [A: int,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 7.75/5.69 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 7.75/5.69 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 & ( A = zero_zero_int ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_le_zero_eq
% 7.75/5.69 thf(fact_3353_nat__div__eq__Suc__0__iff,axiom,
% 7.75/5.69 ! [N: nat,M: nat] :
% 7.75/5.69 ( ( ( divide_divide_nat @ N @ M )
% 7.75/5.69 = ( suc @ zero_zero_nat ) )
% 7.75/5.69 = ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 & ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % nat_div_eq_Suc_0_iff
% 7.75/5.69 thf(fact_3354_power__2__mult__step__le,axiom,
% 7.75/5.69 ! [N5: nat,N: nat,K4: nat,K: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ N5 @ N )
% 7.75/5.69 => ( ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) @ K4 ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) )
% 7.75/5.69 => ( ord_less_eq_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) @ ( plus_plus_nat @ K4 @ one_one_nat ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_2_mult_step_le
% 7.75/5.69 thf(fact_3355_pos__zmod__mult__2,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.69 => ( ( 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 ) )
% 7.75/5.69 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % pos_zmod_mult_2
% 7.75/5.69 thf(fact_3356_pos__zdiv__mult__2,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.69 => ( ( 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 ) )
% 7.75/5.69 = ( divide_divide_int @ B @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % pos_zdiv_mult_2
% 7.75/5.69 thf(fact_3357_neg__zdiv__mult__2,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.69 => ( ( 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 ) )
% 7.75/5.69 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_zdiv_mult_2
% 7.75/5.69 thf(fact_3358_eme1p,axiom,
% 7.75/5.69 ! [N: int,D2: int] :
% 7.75/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ D2 )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ D2 )
% 7.75/5.69 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ N ) @ D2 )
% 7.75/5.69 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ N @ D2 ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % eme1p
% 7.75/5.69 thf(fact_3359_emep1,axiom,
% 7.75/5.69 ! [N: int,D2: int] :
% 7.75/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ D2 )
% 7.75/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ D2 )
% 7.75/5.69 => ( ( modulo_modulo_int @ ( plus_plus_int @ N @ one_one_int ) @ D2 )
% 7.75/5.69 = ( plus_plus_int @ ( modulo_modulo_int @ N @ D2 ) @ one_one_int ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % emep1
% 7.75/5.69 thf(fact_3360_count__buildup,axiom,
% 7.75/5.69 ! [N: nat] : ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % count_buildup
% 7.75/5.69 thf(fact_3361_two__realpow__ge__two,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.69 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % two_realpow_ge_two
% 7.75/5.69 thf(fact_3362_cnt__non__neg,axiom,
% 7.75/5.69 ! [T: vEBT_VEBT] : ( ord_less_eq_real @ zero_zero_real @ ( vEBT_VEBT_cnt @ T ) ) ).
% 7.75/5.69
% 7.75/5.69 % cnt_non_neg
% 7.75/5.69 thf(fact_3363_sb__dec__lem,axiom,
% 7.75/5.69 ! [K: nat,A: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A ) )
% 7.75/5.69 => ( ord_less_eq_int @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sb_dec_lem
% 7.75/5.69 thf(fact_3364_sb__inc__lem_H,axiom,
% 7.75/5.69 ! [A: int,K: nat] :
% 7.75/5.69 ( ( ord_less_int @ A @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) )
% 7.75/5.69 => ( ord_less_eq_int @ ( plus_plus_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % sb_inc_lem'
% 7.75/5.69 thf(fact_3365_neg__zmod__mult__2,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.69 => ( ( 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 ) )
% 7.75/5.69 = ( 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 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_zmod_mult_2
% 7.75/5.69 thf(fact_3366_even__mult__exp__div__exp__iff,axiom,
% 7.75/5.69 ! [A: code_integer,M: nat,N: nat] :
% 7.75/5.69 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.69 = ( ( ord_less_nat @ N @ M )
% 7.75/5.69 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 = zero_z3403309356797280102nteger )
% 7.75/5.69 | ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % even_mult_exp_div_exp_iff
% 7.75/5.69 thf(fact_3367_even__mult__exp__div__exp__iff,axiom,
% 7.75/5.69 ! [A: nat,M: nat,N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.69 = ( ( ord_less_nat @ N @ M )
% 7.75/5.69 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 = zero_zero_nat )
% 7.75/5.69 | ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % even_mult_exp_div_exp_iff
% 7.75/5.69 thf(fact_3368_even__mult__exp__div__exp__iff,axiom,
% 7.75/5.69 ! [A: int,M: nat,N: nat] :
% 7.75/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.69 = ( ( ord_less_nat @ N @ M )
% 7.75/5.69 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 = zero_zero_int )
% 7.75/5.69 | ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % even_mult_exp_div_exp_iff
% 7.75/5.69 thf(fact_3369_zmod__numeral__Bit1,axiom,
% 7.75/5.69 ! [V: num,W: num] :
% 7.75/5.69 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 7.75/5.69 = ( 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 ) ) ).
% 7.75/5.69
% 7.75/5.69 % zmod_numeral_Bit1
% 7.75/5.69 thf(fact_3370_odd__two__times__div__two__nat,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.69 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % odd_two_times_div_two_nat
% 7.75/5.69 thf(fact_3371_neg__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ( uminus_uminus_int @ A )
% 7.75/5.69 = ( uminus_uminus_int @ B ) )
% 7.75/5.69 = ( A = B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_iff_equal
% 7.75/5.69 thf(fact_3372_neg__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( ( uminus_uminus_real @ A )
% 7.75/5.69 = ( uminus_uminus_real @ B ) )
% 7.75/5.69 = ( A = B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_iff_equal
% 7.75/5.69 thf(fact_3373_neg__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( ( uminus1351360451143612070nteger @ A )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.69 = ( A = B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_iff_equal
% 7.75/5.69 thf(fact_3374_neg__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( ( uminus1482373934393186551omplex @ A )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.69 = ( A = B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_iff_equal
% 7.75/5.69 thf(fact_3375_neg__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( ( uminus_uminus_rat @ A )
% 7.75/5.69 = ( uminus_uminus_rat @ B ) )
% 7.75/5.69 = ( A = B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_iff_equal
% 7.75/5.69 thf(fact_3376_add_Oinverse__inverse,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_inverse
% 7.75/5.69 thf(fact_3377_add_Oinverse__inverse,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_inverse
% 7.75/5.69 thf(fact_3378_add_Oinverse__inverse,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_inverse
% 7.75/5.69 thf(fact_3379_add_Oinverse__inverse,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_inverse
% 7.75/5.69 thf(fact_3380_add_Oinverse__inverse,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_inverse
% 7.75/5.69 thf(fact_3381_verit__minus__simplify_I4_J,axiom,
% 7.75/5.69 ! [B: int] :
% 7.75/5.69 ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(4)
% 7.75/5.69 thf(fact_3382_verit__minus__simplify_I4_J,axiom,
% 7.75/5.69 ! [B: real] :
% 7.75/5.69 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(4)
% 7.75/5.69 thf(fact_3383_verit__minus__simplify_I4_J,axiom,
% 7.75/5.69 ! [B: code_integer] :
% 7.75/5.69 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(4)
% 7.75/5.69 thf(fact_3384_verit__minus__simplify_I4_J,axiom,
% 7.75/5.69 ! [B: complex] :
% 7.75/5.69 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(4)
% 7.75/5.69 thf(fact_3385_verit__minus__simplify_I4_J,axiom,
% 7.75/5.69 ! [B: rat] :
% 7.75/5.69 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(4)
% 7.75/5.69 thf(fact_3386_verit__eq__simplify_I9_J,axiom,
% 7.75/5.69 ! [X32: num,Y32: num] :
% 7.75/5.69 ( ( ( bit1 @ X32 )
% 7.75/5.69 = ( bit1 @ Y32 ) )
% 7.75/5.69 = ( X32 = Y32 ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_eq_simplify(9)
% 7.75/5.69 thf(fact_3387_semiring__norm_I90_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ( bit1 @ M )
% 7.75/5.69 = ( bit1 @ N ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(90)
% 7.75/5.69 thf(fact_3388_of__nat__eq__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ( semiri5074537144036343181t_real @ M )
% 7.75/5.69 = ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_iff
% 7.75/5.69 thf(fact_3389_of__nat__eq__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ( semiri1314217659103216013at_int @ M )
% 7.75/5.69 = ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_iff
% 7.75/5.69 thf(fact_3390_of__nat__eq__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ( semiri1316708129612266289at_nat @ M )
% 7.75/5.69 = ( semiri1316708129612266289at_nat @ N ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_iff
% 7.75/5.69 thf(fact_3391_of__nat__eq__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ( semiri8010041392384452111omplex @ M )
% 7.75/5.69 = ( semiri8010041392384452111omplex @ N ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_iff
% 7.75/5.69 thf(fact_3392_diff__self,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ A @ A )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % diff_self
% 7.75/5.69 thf(fact_3393_diff__self,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ A @ A )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % diff_self
% 7.75/5.69 thf(fact_3394_diff__self,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( minus_minus_real @ A @ A )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % diff_self
% 7.75/5.69 thf(fact_3395_diff__self,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( minus_minus_int @ A @ A )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % diff_self
% 7.75/5.69 thf(fact_3396_diff__0__right,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0_right
% 7.75/5.69 thf(fact_3397_diff__0__right,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0_right
% 7.75/5.69 thf(fact_3398_diff__0__right,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( minus_minus_real @ A @ zero_zero_real )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0_right
% 7.75/5.69 thf(fact_3399_diff__0__right,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( minus_minus_int @ A @ zero_zero_int )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0_right
% 7.75/5.69 thf(fact_3400_zero__diff,axiom,
% 7.75/5.69 ! [A: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 7.75/5.69 = zero_zero_nat ) ).
% 7.75/5.69
% 7.75/5.69 % zero_diff
% 7.75/5.69 thf(fact_3401_diff__zero,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_zero
% 7.75/5.69 thf(fact_3402_diff__zero,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_zero
% 7.75/5.69 thf(fact_3403_diff__zero,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( minus_minus_real @ A @ zero_zero_real )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_zero
% 7.75/5.69 thf(fact_3404_diff__zero,axiom,
% 7.75/5.69 ! [A: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_zero
% 7.75/5.69 thf(fact_3405_diff__zero,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( minus_minus_int @ A @ zero_zero_int )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_zero
% 7.75/5.69 thf(fact_3406_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ A @ A )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % cancel_comm_monoid_add_class.diff_cancel
% 7.75/5.69 thf(fact_3407_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ A @ A )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % cancel_comm_monoid_add_class.diff_cancel
% 7.75/5.69 thf(fact_3408_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( minus_minus_real @ A @ A )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % cancel_comm_monoid_add_class.diff_cancel
% 7.75/5.69 thf(fact_3409_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 7.75/5.69 ! [A: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ A @ A )
% 7.75/5.69 = zero_zero_nat ) ).
% 7.75/5.69
% 7.75/5.69 % cancel_comm_monoid_add_class.diff_cancel
% 7.75/5.69 thf(fact_3410_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( minus_minus_int @ A @ A )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % cancel_comm_monoid_add_class.diff_cancel
% 7.75/5.69 thf(fact_3411_add_Oinverse__neutral,axiom,
% 7.75/5.69 ( ( uminus_uminus_int @ zero_zero_int )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_neutral
% 7.75/5.69 thf(fact_3412_add_Oinverse__neutral,axiom,
% 7.75/5.69 ( ( uminus_uminus_real @ zero_zero_real )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_neutral
% 7.75/5.69 thf(fact_3413_add_Oinverse__neutral,axiom,
% 7.75/5.69 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 7.75/5.69 = zero_z3403309356797280102nteger ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_neutral
% 7.75/5.69 thf(fact_3414_add_Oinverse__neutral,axiom,
% 7.75/5.69 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_neutral
% 7.75/5.69 thf(fact_3415_add_Oinverse__neutral,axiom,
% 7.75/5.69 ( ( uminus_uminus_rat @ zero_zero_rat )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % add.inverse_neutral
% 7.75/5.69 thf(fact_3416_neg__0__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( zero_zero_int
% 7.75/5.69 = ( uminus_uminus_int @ A ) )
% 7.75/5.69 = ( zero_zero_int = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_equal_iff_equal
% 7.75/5.69 thf(fact_3417_neg__0__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( zero_zero_real
% 7.75/5.69 = ( uminus_uminus_real @ A ) )
% 7.75/5.69 = ( zero_zero_real = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_equal_iff_equal
% 7.75/5.69 thf(fact_3418_neg__0__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( zero_z3403309356797280102nteger
% 7.75/5.69 = ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = ( zero_z3403309356797280102nteger = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_equal_iff_equal
% 7.75/5.69 thf(fact_3419_neg__0__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( zero_zero_complex
% 7.75/5.69 = ( uminus1482373934393186551omplex @ A ) )
% 7.75/5.69 = ( zero_zero_complex = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_equal_iff_equal
% 7.75/5.69 thf(fact_3420_neg__0__equal__iff__equal,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( zero_zero_rat
% 7.75/5.69 = ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = ( zero_zero_rat = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_equal_iff_equal
% 7.75/5.69 thf(fact_3421_neg__equal__0__iff__equal,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ( uminus_uminus_int @ A )
% 7.75/5.69 = zero_zero_int )
% 7.75/5.69 = ( A = zero_zero_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_0_iff_equal
% 7.75/5.69 thf(fact_3422_neg__equal__0__iff__equal,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ( uminus_uminus_real @ A )
% 7.75/5.69 = zero_zero_real )
% 7.75/5.69 = ( A = zero_zero_real ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_0_iff_equal
% 7.75/5.69 thf(fact_3423_neg__equal__0__iff__equal,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ( uminus1351360451143612070nteger @ A )
% 7.75/5.69 = zero_z3403309356797280102nteger )
% 7.75/5.69 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_0_iff_equal
% 7.75/5.69 thf(fact_3424_neg__equal__0__iff__equal,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( ( uminus1482373934393186551omplex @ A )
% 7.75/5.69 = zero_zero_complex )
% 7.75/5.69 = ( A = zero_zero_complex ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_0_iff_equal
% 7.75/5.69 thf(fact_3425_neg__equal__0__iff__equal,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ( uminus_uminus_rat @ A )
% 7.75/5.69 = zero_zero_rat )
% 7.75/5.69 = ( A = zero_zero_rat ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_0_iff_equal
% 7.75/5.69 thf(fact_3426_equal__neg__zero,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( uminus_uminus_int @ A ) )
% 7.75/5.69 = ( A = zero_zero_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % equal_neg_zero
% 7.75/5.69 thf(fact_3427_equal__neg__zero,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( uminus_uminus_real @ A ) )
% 7.75/5.69 = ( A = zero_zero_real ) ) ).
% 7.75/5.69
% 7.75/5.69 % equal_neg_zero
% 7.75/5.69 thf(fact_3428_equal__neg__zero,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.69
% 7.75/5.69 % equal_neg_zero
% 7.75/5.69 thf(fact_3429_equal__neg__zero,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = ( A = zero_zero_rat ) ) ).
% 7.75/5.69
% 7.75/5.69 % equal_neg_zero
% 7.75/5.69 thf(fact_3430_neg__equal__zero,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ( uminus_uminus_int @ A )
% 7.75/5.69 = A )
% 7.75/5.69 = ( A = zero_zero_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_zero
% 7.75/5.69 thf(fact_3431_neg__equal__zero,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ( uminus_uminus_real @ A )
% 7.75/5.69 = A )
% 7.75/5.69 = ( A = zero_zero_real ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_zero
% 7.75/5.69 thf(fact_3432_neg__equal__zero,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ( uminus1351360451143612070nteger @ A )
% 7.75/5.69 = A )
% 7.75/5.69 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_zero
% 7.75/5.69 thf(fact_3433_neg__equal__zero,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ( uminus_uminus_rat @ A )
% 7.75/5.69 = A )
% 7.75/5.69 = ( A = zero_zero_rat ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_equal_zero
% 7.75/5.69 thf(fact_3434_neg__le__iff__le,axiom,
% 7.75/5.69 ! [B: real,A: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 7.75/5.69 = ( ord_less_eq_real @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_le_iff_le
% 7.75/5.69 thf(fact_3435_neg__le__iff__le,axiom,
% 7.75/5.69 ! [B: code_integer,A: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_le_iff_le
% 7.75/5.69 thf(fact_3436_neg__le__iff__le,axiom,
% 7.75/5.69 ! [B: rat,A: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = ( ord_less_eq_rat @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_le_iff_le
% 7.75/5.69 thf(fact_3437_neg__le__iff__le,axiom,
% 7.75/5.69 ! [B: int,A: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 7.75/5.69 = ( ord_less_eq_int @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_le_iff_le
% 7.75/5.69 thf(fact_3438_add__diff__cancel,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel
% 7.75/5.69 thf(fact_3439_add__diff__cancel,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel
% 7.75/5.69 thf(fact_3440_add__diff__cancel,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel
% 7.75/5.69 thf(fact_3441_add__diff__cancel,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel
% 7.75/5.69 thf(fact_3442_diff__add__cancel,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_add_cancel
% 7.75/5.69 thf(fact_3443_diff__add__cancel,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_add_cancel
% 7.75/5.69 thf(fact_3444_diff__add__cancel,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_add_cancel
% 7.75/5.69 thf(fact_3445_diff__add__cancel,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % diff_add_cancel
% 7.75/5.69 thf(fact_3446_add__diff__cancel__left,axiom,
% 7.75/5.69 ! [C: rat,A: rat,B: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 7.75/5.69 = ( minus_minus_rat @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left
% 7.75/5.69 thf(fact_3447_add__diff__cancel__left,axiom,
% 7.75/5.69 ! [C: complex,A: complex,B: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ ( plus_plus_complex @ C @ A ) @ ( plus_plus_complex @ C @ B ) )
% 7.75/5.69 = ( minus_minus_complex @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left
% 7.75/5.69 thf(fact_3448_add__diff__cancel__left,axiom,
% 7.75/5.69 ! [C: real,A: real,B: real] :
% 7.75/5.69 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 7.75/5.69 = ( minus_minus_real @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left
% 7.75/5.69 thf(fact_3449_add__diff__cancel__left,axiom,
% 7.75/5.69 ! [C: nat,A: nat,B: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 7.75/5.69 = ( minus_minus_nat @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left
% 7.75/5.69 thf(fact_3450_add__diff__cancel__left,axiom,
% 7.75/5.69 ! [C: int,A: int,B: int] :
% 7.75/5.69 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 7.75/5.69 = ( minus_minus_int @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left
% 7.75/5.69 thf(fact_3451_add__diff__cancel__left_H,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left'
% 7.75/5.69 thf(fact_3452_add__diff__cancel__left_H,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ A )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left'
% 7.75/5.69 thf(fact_3453_add__diff__cancel__left_H,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left'
% 7.75/5.69 thf(fact_3454_add__diff__cancel__left_H,axiom,
% 7.75/5.69 ! [A: nat,B: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left'
% 7.75/5.69 thf(fact_3455_add__diff__cancel__left_H,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_left'
% 7.75/5.69 thf(fact_3456_add__diff__cancel__right,axiom,
% 7.75/5.69 ! [A: rat,C: rat,B: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.69 = ( minus_minus_rat @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right
% 7.75/5.69 thf(fact_3457_add__diff__cancel__right,axiom,
% 7.75/5.69 ! [A: complex,C: complex,B: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ C ) )
% 7.75/5.69 = ( minus_minus_complex @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right
% 7.75/5.69 thf(fact_3458_add__diff__cancel__right,axiom,
% 7.75/5.69 ! [A: real,C: real,B: real] :
% 7.75/5.69 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 7.75/5.69 = ( minus_minus_real @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right
% 7.75/5.69 thf(fact_3459_add__diff__cancel__right,axiom,
% 7.75/5.69 ! [A: nat,C: nat,B: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 7.75/5.69 = ( minus_minus_nat @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right
% 7.75/5.69 thf(fact_3460_add__diff__cancel__right,axiom,
% 7.75/5.69 ! [A: int,C: int,B: int] :
% 7.75/5.69 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 7.75/5.69 = ( minus_minus_int @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right
% 7.75/5.69 thf(fact_3461_add__diff__cancel__right_H,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right'
% 7.75/5.69 thf(fact_3462_add__diff__cancel__right_H,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right'
% 7.75/5.69 thf(fact_3463_add__diff__cancel__right_H,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right'
% 7.75/5.69 thf(fact_3464_add__diff__cancel__right_H,axiom,
% 7.75/5.69 ! [A: nat,B: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right'
% 7.75/5.69 thf(fact_3465_add__diff__cancel__right_H,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % add_diff_cancel_right'
% 7.75/5.69 thf(fact_3466_neg__less__iff__less,axiom,
% 7.75/5.69 ! [B: int,A: int] :
% 7.75/5.69 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 7.75/5.69 = ( ord_less_int @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_iff_less
% 7.75/5.69 thf(fact_3467_neg__less__iff__less,axiom,
% 7.75/5.69 ! [B: real,A: real] :
% 7.75/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 7.75/5.69 = ( ord_less_real @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_iff_less
% 7.75/5.69 thf(fact_3468_neg__less__iff__less,axiom,
% 7.75/5.69 ! [B: code_integer,A: code_integer] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_iff_less
% 7.75/5.69 thf(fact_3469_neg__less__iff__less,axiom,
% 7.75/5.69 ! [B: rat,A: rat] :
% 7.75/5.69 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = ( ord_less_rat @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_iff_less
% 7.75/5.69 thf(fact_3470_neg__numeral__eq__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_eq_iff
% 7.75/5.69 thf(fact_3471_neg__numeral__eq__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_eq_iff
% 7.75/5.69 thf(fact_3472_neg__numeral__eq__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_eq_iff
% 7.75/5.69 thf(fact_3473_neg__numeral__eq__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_eq_iff
% 7.75/5.69 thf(fact_3474_neg__numeral__eq__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.69 = ( M = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_eq_iff
% 7.75/5.69 thf(fact_3475_add__minus__cancel,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_minus_cancel
% 7.75/5.69 thf(fact_3476_add__minus__cancel,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_minus_cancel
% 7.75/5.69 thf(fact_3477_add__minus__cancel,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_minus_cancel
% 7.75/5.69 thf(fact_3478_add__minus__cancel,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_minus_cancel
% 7.75/5.69 thf(fact_3479_add__minus__cancel,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % add_minus_cancel
% 7.75/5.69 thf(fact_3480_minus__add__cancel,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_cancel
% 7.75/5.69 thf(fact_3481_minus__add__cancel,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_cancel
% 7.75/5.69 thf(fact_3482_minus__add__cancel,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_cancel
% 7.75/5.69 thf(fact_3483_minus__add__cancel,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_cancel
% 7.75/5.69 thf(fact_3484_minus__add__cancel,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.69 = B ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_cancel
% 7.75/5.69 thf(fact_3485_minus__add__distrib,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 7.75/5.69 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_distrib
% 7.75/5.69 thf(fact_3486_minus__add__distrib,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 7.75/5.69 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_distrib
% 7.75/5.69 thf(fact_3487_minus__add__distrib,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 7.75/5.69 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_distrib
% 7.75/5.69 thf(fact_3488_minus__add__distrib,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 7.75/5.69 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_distrib
% 7.75/5.69 thf(fact_3489_minus__add__distrib,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.69 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_add_distrib
% 7.75/5.69 thf(fact_3490_mult__minus__right,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_right
% 7.75/5.69 thf(fact_3491_mult__minus__right,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_right
% 7.75/5.69 thf(fact_3492_mult__minus__right,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_right
% 7.75/5.69 thf(fact_3493_mult__minus__right,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_right
% 7.75/5.69 thf(fact_3494_mult__minus__right,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_right
% 7.75/5.69 thf(fact_3495_minus__mult__minus,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 7.75/5.69 = ( times_times_int @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_mult_minus
% 7.75/5.69 thf(fact_3496_minus__mult__minus,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 7.75/5.69 = ( times_times_real @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_mult_minus
% 7.75/5.69 thf(fact_3497_minus__mult__minus,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.69 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_mult_minus
% 7.75/5.69 thf(fact_3498_minus__mult__minus,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.69 = ( times_times_complex @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_mult_minus
% 7.75/5.69 thf(fact_3499_minus__mult__minus,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 7.75/5.69 = ( times_times_rat @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_mult_minus
% 7.75/5.69 thf(fact_3500_mult__minus__left,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.69 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_left
% 7.75/5.69 thf(fact_3501_mult__minus__left,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 7.75/5.69 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_left
% 7.75/5.69 thf(fact_3502_mult__minus__left,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_left
% 7.75/5.69 thf(fact_3503_mult__minus__left,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_left
% 7.75/5.69 thf(fact_3504_mult__minus__left,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 7.75/5.69 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus_left
% 7.75/5.69 thf(fact_3505_minus__diff__eq,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 7.75/5.69 = ( minus_minus_int @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_eq
% 7.75/5.69 thf(fact_3506_minus__diff__eq,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 7.75/5.69 = ( minus_minus_real @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_eq
% 7.75/5.69 thf(fact_3507_minus__diff__eq,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 7.75/5.69 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_eq
% 7.75/5.69 thf(fact_3508_minus__diff__eq,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 7.75/5.69 = ( minus_minus_complex @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_eq
% 7.75/5.69 thf(fact_3509_minus__diff__eq,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 7.75/5.69 = ( minus_minus_rat @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_eq
% 7.75/5.69 thf(fact_3510_semiring__norm_I88_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( bit0 @ M )
% 7.75/5.69 != ( bit1 @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(88)
% 7.75/5.69 thf(fact_3511_semiring__norm_I89_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( bit1 @ M )
% 7.75/5.69 != ( bit0 @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(89)
% 7.75/5.69 thf(fact_3512_semiring__norm_I84_J,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( one
% 7.75/5.69 != ( bit1 @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(84)
% 7.75/5.69 thf(fact_3513_semiring__norm_I86_J,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( bit1 @ M )
% 7.75/5.69 != one ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(86)
% 7.75/5.69 thf(fact_3514_div__minus__minus,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 7.75/5.69 = ( divide_divide_int @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % div_minus_minus
% 7.75/5.69 thf(fact_3515_div__minus__minus,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.69 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % div_minus_minus
% 7.75/5.69 thf(fact_3516_dvd__minus__iff,axiom,
% 7.75/5.69 ! [X: int,Y: int] :
% 7.75/5.69 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 7.75/5.69 = ( dvd_dvd_int @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % dvd_minus_iff
% 7.75/5.69 thf(fact_3517_dvd__minus__iff,axiom,
% 7.75/5.69 ! [X: real,Y: real] :
% 7.75/5.69 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 7.75/5.69 = ( dvd_dvd_real @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % dvd_minus_iff
% 7.75/5.69 thf(fact_3518_dvd__minus__iff,axiom,
% 7.75/5.69 ! [X: code_integer,Y: code_integer] :
% 7.75/5.69 ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 7.75/5.69 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % dvd_minus_iff
% 7.75/5.69 thf(fact_3519_dvd__minus__iff,axiom,
% 7.75/5.69 ! [X: complex,Y: complex] :
% 7.75/5.69 ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 7.75/5.69 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % dvd_minus_iff
% 7.75/5.69 thf(fact_3520_dvd__minus__iff,axiom,
% 7.75/5.69 ! [X: rat,Y: rat] :
% 7.75/5.69 ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 7.75/5.69 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % dvd_minus_iff
% 7.75/5.69 thf(fact_3521_minus__dvd__iff,axiom,
% 7.75/5.69 ! [X: int,Y: int] :
% 7.75/5.69 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 7.75/5.69 = ( dvd_dvd_int @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_dvd_iff
% 7.75/5.69 thf(fact_3522_minus__dvd__iff,axiom,
% 7.75/5.69 ! [X: real,Y: real] :
% 7.75/5.69 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 7.75/5.69 = ( dvd_dvd_real @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_dvd_iff
% 7.75/5.69 thf(fact_3523_minus__dvd__iff,axiom,
% 7.75/5.69 ! [X: code_integer,Y: code_integer] :
% 7.75/5.69 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 7.75/5.69 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_dvd_iff
% 7.75/5.69 thf(fact_3524_minus__dvd__iff,axiom,
% 7.75/5.69 ! [X: complex,Y: complex] :
% 7.75/5.69 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 7.75/5.69 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_dvd_iff
% 7.75/5.69 thf(fact_3525_minus__dvd__iff,axiom,
% 7.75/5.69 ! [X: rat,Y: rat] :
% 7.75/5.69 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 7.75/5.69 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_dvd_iff
% 7.75/5.69 thf(fact_3526_Suc__diff__diff,axiom,
% 7.75/5.69 ! [M: nat,N: nat,K: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 7.75/5.69 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 7.75/5.69
% 7.75/5.69 % Suc_diff_diff
% 7.75/5.69 thf(fact_3527_diff__Suc__Suc,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 7.75/5.69 = ( minus_minus_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_Suc_Suc
% 7.75/5.69 thf(fact_3528_minus__mod__self2,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 7.75/5.69 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_mod_self2
% 7.75/5.69 thf(fact_3529_minus__mod__self2,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 7.75/5.69 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_mod_self2
% 7.75/5.69 thf(fact_3530_diff__self__eq__0,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ M @ M )
% 7.75/5.69 = zero_zero_nat ) ).
% 7.75/5.69
% 7.75/5.69 % diff_self_eq_0
% 7.75/5.69 thf(fact_3531_diff__0__eq__0,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 7.75/5.69 = zero_zero_nat ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0_eq_0
% 7.75/5.69 thf(fact_3532_mod__minus__minus,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mod_minus_minus
% 7.75/5.69 thf(fact_3533_mod__minus__minus,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mod_minus_minus
% 7.75/5.69 thf(fact_3534_diff__diff__left,axiom,
% 7.75/5.69 ! [I: nat,J: nat,K: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 7.75/5.69 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_diff_left
% 7.75/5.69 thf(fact_3535_diff__diff__cancel,axiom,
% 7.75/5.69 ! [I: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ I @ N )
% 7.75/5.69 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 7.75/5.69 = I ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_diff_cancel
% 7.75/5.69 thf(fact_3536_semiring__norm_I73_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 7.75/5.69 = ( ord_less_eq_num @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(73)
% 7.75/5.69 thf(fact_3537_semiring__norm_I80_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 7.75/5.69 = ( ord_less_num @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(80)
% 7.75/5.69 thf(fact_3538_count__buildup_H,axiom,
% 7.75/5.69 ! [N: nat] : ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( semiri5074537144036343181t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % count_buildup'
% 7.75/5.69 thf(fact_3539_diff__ge__0__iff__ge,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 7.75/5.69 = ( ord_less_eq_real @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_ge_0_iff_ge
% 7.75/5.69 thf(fact_3540_diff__ge__0__iff__ge,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 7.75/5.69 = ( ord_less_eq_rat @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_ge_0_iff_ge
% 7.75/5.69 thf(fact_3541_diff__ge__0__iff__ge,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 7.75/5.69 = ( ord_less_eq_int @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_ge_0_iff_ge
% 7.75/5.69 thf(fact_3542_zero__comp__diff__simps_I1_J,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 7.75/5.69 = ( ord_less_eq_real @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_comp_diff_simps(1)
% 7.75/5.69 thf(fact_3543_zero__comp__diff__simps_I1_J,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 7.75/5.69 = ( ord_less_eq_rat @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_comp_diff_simps(1)
% 7.75/5.69 thf(fact_3544_zero__comp__diff__simps_I1_J,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 7.75/5.69 = ( ord_less_eq_int @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_comp_diff_simps(1)
% 7.75/5.69 thf(fact_3545_diff__gt__0__iff__gt,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 7.75/5.69 = ( ord_less_real @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_gt_0_iff_gt
% 7.75/5.69 thf(fact_3546_diff__gt__0__iff__gt,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 7.75/5.69 = ( ord_less_rat @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_gt_0_iff_gt
% 7.75/5.69 thf(fact_3547_diff__gt__0__iff__gt,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 7.75/5.69 = ( ord_less_int @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_gt_0_iff_gt
% 7.75/5.69 thf(fact_3548_zero__comp__diff__simps_I2_J,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 7.75/5.69 = ( ord_less_real @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_comp_diff_simps(2)
% 7.75/5.69 thf(fact_3549_zero__comp__diff__simps_I2_J,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 7.75/5.69 = ( ord_less_rat @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_comp_diff_simps(2)
% 7.75/5.69 thf(fact_3550_zero__comp__diff__simps_I2_J,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 7.75/5.69 = ( ord_less_int @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_comp_diff_simps(2)
% 7.75/5.69 thf(fact_3551_neg__less__eq__nonneg,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 7.75/5.69 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_eq_nonneg
% 7.75/5.69 thf(fact_3552_neg__less__eq__nonneg,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 7.75/5.69 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_eq_nonneg
% 7.75/5.69 thf(fact_3553_neg__less__eq__nonneg,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 7.75/5.69 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_eq_nonneg
% 7.75/5.69 thf(fact_3554_neg__less__eq__nonneg,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 7.75/5.69 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_eq_nonneg
% 7.75/5.69 thf(fact_3555_less__eq__neg__nonpos,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 7.75/5.69 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_eq_neg_nonpos
% 7.75/5.69 thf(fact_3556_less__eq__neg__nonpos,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_eq_neg_nonpos
% 7.75/5.69 thf(fact_3557_less__eq__neg__nonpos,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_eq_neg_nonpos
% 7.75/5.69 thf(fact_3558_less__eq__neg__nonpos,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 7.75/5.69 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_eq_neg_nonpos
% 7.75/5.69 thf(fact_3559_neg__le__0__iff__le,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 7.75/5.69 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_le_0_iff_le
% 7.75/5.69 thf(fact_3560_neg__le__0__iff__le,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 7.75/5.69 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_le_0_iff_le
% 7.75/5.69 thf(fact_3561_neg__le__0__iff__le,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 7.75/5.69 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_le_0_iff_le
% 7.75/5.69 thf(fact_3562_neg__le__0__iff__le,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 7.75/5.69 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_le_0_iff_le
% 7.75/5.69 thf(fact_3563_neg__0__le__iff__le,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 7.75/5.69 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_le_iff_le
% 7.75/5.69 thf(fact_3564_neg__0__le__iff__le,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_le_iff_le
% 7.75/5.69 thf(fact_3565_neg__0__le__iff__le,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_le_iff_le
% 7.75/5.69 thf(fact_3566_neg__0__le__iff__le,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 7.75/5.69 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_le_iff_le
% 7.75/5.69 thf(fact_3567_diff__add__zero,axiom,
% 7.75/5.69 ! [A: nat,B: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 7.75/5.69 = zero_zero_nat ) ).
% 7.75/5.69
% 7.75/5.69 % diff_add_zero
% 7.75/5.69 thf(fact_3568_diff__numeral__special_I9_J,axiom,
% 7.75/5.69 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(9)
% 7.75/5.69 thf(fact_3569_diff__numeral__special_I9_J,axiom,
% 7.75/5.69 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(9)
% 7.75/5.69 thf(fact_3570_diff__numeral__special_I9_J,axiom,
% 7.75/5.69 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(9)
% 7.75/5.69 thf(fact_3571_diff__numeral__special_I9_J,axiom,
% 7.75/5.69 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(9)
% 7.75/5.69 thf(fact_3572_less__neg__neg,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 7.75/5.69 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_neg_neg
% 7.75/5.69 thf(fact_3573_less__neg__neg,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 7.75/5.69 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_neg_neg
% 7.75/5.69 thf(fact_3574_less__neg__neg,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_neg_neg
% 7.75/5.69 thf(fact_3575_less__neg__neg,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_neg_neg
% 7.75/5.69 thf(fact_3576_neg__less__pos,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 7.75/5.69 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_pos
% 7.75/5.69 thf(fact_3577_neg__less__pos,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 7.75/5.69 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_pos
% 7.75/5.69 thf(fact_3578_neg__less__pos,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 7.75/5.69 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_pos
% 7.75/5.69 thf(fact_3579_neg__less__pos,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 7.75/5.69 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_pos
% 7.75/5.69 thf(fact_3580_neg__0__less__iff__less,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 7.75/5.69 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_less_iff_less
% 7.75/5.69 thf(fact_3581_neg__0__less__iff__less,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 7.75/5.69 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_less_iff_less
% 7.75/5.69 thf(fact_3582_neg__0__less__iff__less,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_less_iff_less
% 7.75/5.69 thf(fact_3583_neg__0__less__iff__less,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_0_less_iff_less
% 7.75/5.69 thf(fact_3584_neg__less__0__iff__less,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 7.75/5.69 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_0_iff_less
% 7.75/5.69 thf(fact_3585_neg__less__0__iff__less,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 7.75/5.69 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_0_iff_less
% 7.75/5.69 thf(fact_3586_neg__less__0__iff__less,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 7.75/5.69 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_0_iff_less
% 7.75/5.69 thf(fact_3587_neg__less__0__iff__less,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 7.75/5.69 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_less_0_iff_less
% 7.75/5.69 thf(fact_3588_le__add__diff__inverse2,axiom,
% 7.75/5.69 ! [B: real,A: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ B @ A )
% 7.75/5.69 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_add_diff_inverse2
% 7.75/5.69 thf(fact_3589_le__add__diff__inverse2,axiom,
% 7.75/5.69 ! [B: rat,A: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ B @ A )
% 7.75/5.69 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_add_diff_inverse2
% 7.75/5.69 thf(fact_3590_le__add__diff__inverse2,axiom,
% 7.75/5.69 ! [B: nat,A: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ B @ A )
% 7.75/5.69 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_add_diff_inverse2
% 7.75/5.69 thf(fact_3591_le__add__diff__inverse2,axiom,
% 7.75/5.69 ! [B: int,A: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ B @ A )
% 7.75/5.69 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_add_diff_inverse2
% 7.75/5.69 thf(fact_3592_le__add__diff__inverse,axiom,
% 7.75/5.69 ! [B: real,A: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ B @ A )
% 7.75/5.69 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_add_diff_inverse
% 7.75/5.69 thf(fact_3593_le__add__diff__inverse,axiom,
% 7.75/5.69 ! [B: rat,A: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ B @ A )
% 7.75/5.69 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_add_diff_inverse
% 7.75/5.69 thf(fact_3594_le__add__diff__inverse,axiom,
% 7.75/5.69 ! [B: nat,A: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ B @ A )
% 7.75/5.69 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_add_diff_inverse
% 7.75/5.69 thf(fact_3595_le__add__diff__inverse,axiom,
% 7.75/5.69 ! [B: int,A: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ B @ A )
% 7.75/5.69 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_add_diff_inverse
% 7.75/5.69 thf(fact_3596_right__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [V: num,B: code_integer,C: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 7.75/5.69 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % right_diff_distrib_numeral
% 7.75/5.69 thf(fact_3597_right__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [V: num,B: complex,C: complex] :
% 7.75/5.69 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 7.75/5.69 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % right_diff_distrib_numeral
% 7.75/5.69 thf(fact_3598_right__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [V: num,B: real,C: real] :
% 7.75/5.69 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 7.75/5.69 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % right_diff_distrib_numeral
% 7.75/5.69 thf(fact_3599_right__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [V: num,B: rat,C: rat] :
% 7.75/5.69 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 7.75/5.69 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % right_diff_distrib_numeral
% 7.75/5.69 thf(fact_3600_right__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [V: num,B: int,C: int] :
% 7.75/5.69 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 7.75/5.69 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % right_diff_distrib_numeral
% 7.75/5.69 thf(fact_3601_left__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer,V: num] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 7.75/5.69 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % left_diff_distrib_numeral
% 7.75/5.69 thf(fact_3602_left__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [A: complex,B: complex,V: num] :
% 7.75/5.69 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 7.75/5.69 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % left_diff_distrib_numeral
% 7.75/5.69 thf(fact_3603_left__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [A: real,B: real,V: num] :
% 7.75/5.69 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.69 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % left_diff_distrib_numeral
% 7.75/5.69 thf(fact_3604_left__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [A: rat,B: rat,V: num] :
% 7.75/5.69 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.69 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % left_diff_distrib_numeral
% 7.75/5.69 thf(fact_3605_left__diff__distrib__numeral,axiom,
% 7.75/5.69 ! [A: int,B: int,V: num] :
% 7.75/5.69 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.69 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % left_diff_distrib_numeral
% 7.75/5.69 thf(fact_3606_add_Oright__inverse,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % add.right_inverse
% 7.75/5.69 thf(fact_3607_add_Oright__inverse,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % add.right_inverse
% 7.75/5.69 thf(fact_3608_add_Oright__inverse,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.69 = zero_z3403309356797280102nteger ) ).
% 7.75/5.69
% 7.75/5.69 % add.right_inverse
% 7.75/5.69 thf(fact_3609_add_Oright__inverse,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % add.right_inverse
% 7.75/5.69 thf(fact_3610_add_Oright__inverse,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % add.right_inverse
% 7.75/5.69 thf(fact_3611_ab__left__minus,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % ab_left_minus
% 7.75/5.69 thf(fact_3612_ab__left__minus,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % ab_left_minus
% 7.75/5.69 thf(fact_3613_ab__left__minus,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 7.75/5.69 = zero_z3403309356797280102nteger ) ).
% 7.75/5.69
% 7.75/5.69 % ab_left_minus
% 7.75/5.69 thf(fact_3614_ab__left__minus,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % ab_left_minus
% 7.75/5.69 thf(fact_3615_ab__left__minus,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % ab_left_minus
% 7.75/5.69 thf(fact_3616_verit__minus__simplify_I3_J,axiom,
% 7.75/5.69 ! [B: int] :
% 7.75/5.69 ( ( minus_minus_int @ zero_zero_int @ B )
% 7.75/5.69 = ( uminus_uminus_int @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(3)
% 7.75/5.69 thf(fact_3617_verit__minus__simplify_I3_J,axiom,
% 7.75/5.69 ! [B: real] :
% 7.75/5.69 ( ( minus_minus_real @ zero_zero_real @ B )
% 7.75/5.69 = ( uminus_uminus_real @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(3)
% 7.75/5.69 thf(fact_3618_verit__minus__simplify_I3_J,axiom,
% 7.75/5.69 ! [B: code_integer] :
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(3)
% 7.75/5.69 thf(fact_3619_verit__minus__simplify_I3_J,axiom,
% 7.75/5.69 ! [B: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(3)
% 7.75/5.69 thf(fact_3620_verit__minus__simplify_I3_J,axiom,
% 7.75/5.69 ! [B: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 7.75/5.69 = ( uminus_uminus_rat @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_minus_simplify(3)
% 7.75/5.69 thf(fact_3621_diff__0,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( minus_minus_int @ zero_zero_int @ A )
% 7.75/5.69 = ( uminus_uminus_int @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0
% 7.75/5.69 thf(fact_3622_diff__0,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( minus_minus_real @ zero_zero_real @ A )
% 7.75/5.69 = ( uminus_uminus_real @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0
% 7.75/5.69 thf(fact_3623_diff__0,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0
% 7.75/5.69 thf(fact_3624_diff__0,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0
% 7.75/5.69 thf(fact_3625_diff__0,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 7.75/5.69 = ( uminus_uminus_rat @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_0
% 7.75/5.69 thf(fact_3626_add__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3627_add__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3628_add__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3629_add__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3630_add__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3631_mult__minus1__right,axiom,
% 7.75/5.69 ! [Z: int] :
% 7.75/5.69 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = ( uminus_uminus_int @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1_right
% 7.75/5.69 thf(fact_3632_mult__minus1__right,axiom,
% 7.75/5.69 ! [Z: real] :
% 7.75/5.69 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.69 = ( uminus_uminus_real @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1_right
% 7.75/5.69 thf(fact_3633_mult__minus1__right,axiom,
% 7.75/5.69 ! [Z: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1_right
% 7.75/5.69 thf(fact_3634_mult__minus1__right,axiom,
% 7.75/5.69 ! [Z: complex] :
% 7.75/5.69 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1_right
% 7.75/5.69 thf(fact_3635_mult__minus1__right,axiom,
% 7.75/5.69 ! [Z: rat] :
% 7.75/5.69 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.69 = ( uminus_uminus_rat @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1_right
% 7.75/5.69 thf(fact_3636_mult__minus1,axiom,
% 7.75/5.69 ! [Z: int] :
% 7.75/5.69 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 7.75/5.69 = ( uminus_uminus_int @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1
% 7.75/5.69 thf(fact_3637_mult__minus1,axiom,
% 7.75/5.69 ! [Z: real] :
% 7.75/5.69 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 7.75/5.69 = ( uminus_uminus_real @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1
% 7.75/5.69 thf(fact_3638_mult__minus1,axiom,
% 7.75/5.69 ! [Z: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1
% 7.75/5.69 thf(fact_3639_mult__minus1,axiom,
% 7.75/5.69 ! [Z: complex] :
% 7.75/5.69 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1
% 7.75/5.69 thf(fact_3640_mult__minus1,axiom,
% 7.75/5.69 ! [Z: rat] :
% 7.75/5.69 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 7.75/5.69 = ( uminus_uminus_rat @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_minus1
% 7.75/5.69 thf(fact_3641_uminus__add__conv__diff,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.69 = ( minus_minus_int @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % uminus_add_conv_diff
% 7.75/5.69 thf(fact_3642_uminus__add__conv__diff,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 7.75/5.69 = ( minus_minus_real @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % uminus_add_conv_diff
% 7.75/5.69 thf(fact_3643_uminus__add__conv__diff,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 7.75/5.69 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % uminus_add_conv_diff
% 7.75/5.69 thf(fact_3644_uminus__add__conv__diff,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 7.75/5.69 = ( minus_minus_complex @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % uminus_add_conv_diff
% 7.75/5.69 thf(fact_3645_uminus__add__conv__diff,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 7.75/5.69 = ( minus_minus_rat @ B @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % uminus_add_conv_diff
% 7.75/5.69 thf(fact_3646_diff__minus__eq__add,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.69 = ( plus_plus_int @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_minus_eq_add
% 7.75/5.69 thf(fact_3647_diff__minus__eq__add,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 7.75/5.69 = ( plus_plus_real @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_minus_eq_add
% 7.75/5.69 thf(fact_3648_diff__minus__eq__add,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.69 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_minus_eq_add
% 7.75/5.69 thf(fact_3649_diff__minus__eq__add,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.69 = ( plus_plus_complex @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_minus_eq_add
% 7.75/5.69 thf(fact_3650_diff__minus__eq__add,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 7.75/5.69 = ( plus_plus_rat @ A @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_minus_eq_add
% 7.75/5.69 thf(fact_3651_divide__minus1,axiom,
% 7.75/5.69 ! [X: real] :
% 7.75/5.69 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.69 = ( uminus_uminus_real @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_minus1
% 7.75/5.69 thf(fact_3652_divide__minus1,axiom,
% 7.75/5.69 ! [X: complex] :
% 7.75/5.69 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_minus1
% 7.75/5.69 thf(fact_3653_divide__minus1,axiom,
% 7.75/5.69 ! [X: rat] :
% 7.75/5.69 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.69 = ( uminus_uminus_rat @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_minus1
% 7.75/5.69 thf(fact_3654_div__minus1__right,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = ( uminus_uminus_int @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % div_minus1_right
% 7.75/5.69 thf(fact_3655_div__minus1__right,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % div_minus1_right
% 7.75/5.69 thf(fact_3656_of__nat__eq__0__iff,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( ( semiri681578069525770553at_rat @ M )
% 7.75/5.69 = zero_zero_rat )
% 7.75/5.69 = ( M = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_0_iff
% 7.75/5.69 thf(fact_3657_of__nat__eq__0__iff,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( ( semiri5074537144036343181t_real @ M )
% 7.75/5.69 = zero_zero_real )
% 7.75/5.69 = ( M = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_0_iff
% 7.75/5.69 thf(fact_3658_of__nat__eq__0__iff,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( ( semiri1314217659103216013at_int @ M )
% 7.75/5.69 = zero_zero_int )
% 7.75/5.69 = ( M = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_0_iff
% 7.75/5.69 thf(fact_3659_of__nat__eq__0__iff,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( ( semiri1316708129612266289at_nat @ M )
% 7.75/5.69 = zero_zero_nat )
% 7.75/5.69 = ( M = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_0_iff
% 7.75/5.69 thf(fact_3660_of__nat__eq__0__iff,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( ( semiri8010041392384452111omplex @ M )
% 7.75/5.69 = zero_zero_complex )
% 7.75/5.69 = ( M = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_0_iff
% 7.75/5.69 thf(fact_3661_of__nat__0__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( zero_zero_rat
% 7.75/5.69 = ( semiri681578069525770553at_rat @ N ) )
% 7.75/5.69 = ( zero_zero_nat = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_0_eq_iff
% 7.75/5.69 thf(fact_3662_of__nat__0__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( zero_zero_real
% 7.75/5.69 = ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.69 = ( zero_zero_nat = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_0_eq_iff
% 7.75/5.69 thf(fact_3663_of__nat__0__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( zero_zero_int
% 7.75/5.69 = ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.69 = ( zero_zero_nat = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_0_eq_iff
% 7.75/5.69 thf(fact_3664_of__nat__0__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( zero_zero_nat
% 7.75/5.69 = ( semiri1316708129612266289at_nat @ N ) )
% 7.75/5.69 = ( zero_zero_nat = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_0_eq_iff
% 7.75/5.69 thf(fact_3665_of__nat__0__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( zero_zero_complex
% 7.75/5.69 = ( semiri8010041392384452111omplex @ N ) )
% 7.75/5.69 = ( zero_zero_nat = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_0_eq_iff
% 7.75/5.69 thf(fact_3666_semiring__1__class_Oof__nat__0,axiom,
% 7.75/5.69 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_0
% 7.75/5.69 thf(fact_3667_semiring__1__class_Oof__nat__0,axiom,
% 7.75/5.69 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_0
% 7.75/5.69 thf(fact_3668_semiring__1__class_Oof__nat__0,axiom,
% 7.75/5.69 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_0
% 7.75/5.69 thf(fact_3669_semiring__1__class_Oof__nat__0,axiom,
% 7.75/5.69 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 7.75/5.69 = zero_zero_nat ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_0
% 7.75/5.69 thf(fact_3670_semiring__1__class_Oof__nat__0,axiom,
% 7.75/5.69 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_0
% 7.75/5.69 thf(fact_3671_of__nat__numeral,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 7.75/5.69 = ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_numeral
% 7.75/5.69 thf(fact_3672_of__nat__numeral,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 7.75/5.69 = ( numeral_numeral_real @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_numeral
% 7.75/5.69 thf(fact_3673_of__nat__numeral,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 7.75/5.69 = ( numeral_numeral_int @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_numeral
% 7.75/5.69 thf(fact_3674_of__nat__numeral,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 7.75/5.69 = ( numeral_numeral_nat @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_numeral
% 7.75/5.69 thf(fact_3675_of__nat__numeral,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 7.75/5.69 = ( numera6690914467698888265omplex @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_numeral
% 7.75/5.69 thf(fact_3676_of__nat__less__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 7.75/5.69 = ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_iff
% 7.75/5.69 thf(fact_3677_of__nat__less__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.69 = ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_iff
% 7.75/5.69 thf(fact_3678_of__nat__less__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.69 = ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_iff
% 7.75/5.69 thf(fact_3679_of__nat__less__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 7.75/5.69 = ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_iff
% 7.75/5.69 thf(fact_3680_of__nat__le__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_iff
% 7.75/5.69 thf(fact_3681_of__nat__le__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_iff
% 7.75/5.69 thf(fact_3682_of__nat__le__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_iff
% 7.75/5.69 thf(fact_3683_of__nat__le__iff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_iff
% 7.75/5.69 thf(fact_3684_div__diff,axiom,
% 7.75/5.69 ! [C: int,A: int,B: int] :
% 7.75/5.69 ( ( dvd_dvd_int @ C @ A )
% 7.75/5.69 => ( ( dvd_dvd_int @ C @ B )
% 7.75/5.69 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 7.75/5.69 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % div_diff
% 7.75/5.69 thf(fact_3685_of__nat__add,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.69 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_add
% 7.75/5.69 thf(fact_3686_of__nat__add,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.69 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_add
% 7.75/5.69 thf(fact_3687_of__nat__add,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.69 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_add
% 7.75/5.69 thf(fact_3688_of__nat__add,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.69 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_add
% 7.75/5.69 thf(fact_3689_of__nat__add,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 7.75/5.69 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_add
% 7.75/5.69 thf(fact_3690_minus__mod__self1,axiom,
% 7.75/5.69 ! [B: int,A: int] :
% 7.75/5.69 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 7.75/5.69 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_mod_self1
% 7.75/5.69 thf(fact_3691_minus__mod__self1,axiom,
% 7.75/5.69 ! [B: code_integer,A: code_integer] :
% 7.75/5.69 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 7.75/5.69 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_mod_self1
% 7.75/5.69 thf(fact_3692_of__nat__eq__1__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ( semiri681578069525770553at_rat @ N )
% 7.75/5.69 = one_one_rat )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_1_iff
% 7.75/5.69 thf(fact_3693_of__nat__eq__1__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ( semiri5074537144036343181t_real @ N )
% 7.75/5.69 = one_one_real )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_1_iff
% 7.75/5.69 thf(fact_3694_of__nat__eq__1__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ( semiri1314217659103216013at_int @ N )
% 7.75/5.69 = one_one_int )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_1_iff
% 7.75/5.69 thf(fact_3695_of__nat__eq__1__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ( semiri1316708129612266289at_nat @ N )
% 7.75/5.69 = one_one_nat )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_1_iff
% 7.75/5.69 thf(fact_3696_of__nat__eq__1__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ( semiri8010041392384452111omplex @ N )
% 7.75/5.69 = one_one_complex )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_1_iff
% 7.75/5.69 thf(fact_3697_of__nat__1__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( one_one_rat
% 7.75/5.69 = ( semiri681578069525770553at_rat @ N ) )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1_eq_iff
% 7.75/5.69 thf(fact_3698_of__nat__1__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( one_one_real
% 7.75/5.69 = ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1_eq_iff
% 7.75/5.69 thf(fact_3699_of__nat__1__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( one_one_int
% 7.75/5.69 = ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1_eq_iff
% 7.75/5.69 thf(fact_3700_of__nat__1__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( one_one_nat
% 7.75/5.69 = ( semiri1316708129612266289at_nat @ N ) )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1_eq_iff
% 7.75/5.69 thf(fact_3701_of__nat__1__eq__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( one_one_complex
% 7.75/5.69 = ( semiri8010041392384452111omplex @ N ) )
% 7.75/5.69 = ( N = one_one_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1_eq_iff
% 7.75/5.69 thf(fact_3702_of__nat__1,axiom,
% 7.75/5.69 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 7.75/5.69 = one_one_rat ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1
% 7.75/5.69 thf(fact_3703_of__nat__1,axiom,
% 7.75/5.69 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 7.75/5.69 = one_one_real ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1
% 7.75/5.69 thf(fact_3704_of__nat__1,axiom,
% 7.75/5.69 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 7.75/5.69 = one_one_int ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1
% 7.75/5.69 thf(fact_3705_of__nat__1,axiom,
% 7.75/5.69 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 7.75/5.69 = one_one_nat ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1
% 7.75/5.69 thf(fact_3706_of__nat__1,axiom,
% 7.75/5.69 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 7.75/5.69 = one_one_complex ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_1
% 7.75/5.69 thf(fact_3707_zero__less__diff,axiom,
% 7.75/5.69 ! [N: nat,M: nat] :
% 7.75/5.69 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 7.75/5.69 = ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % zero_less_diff
% 7.75/5.69 thf(fact_3708_diff__Suc__1,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 7.75/5.69 = N ) ).
% 7.75/5.69
% 7.75/5.69 % diff_Suc_1
% 7.75/5.69 thf(fact_3709_diff__is__0__eq_H,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 => ( ( minus_minus_nat @ M @ N )
% 7.75/5.69 = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_is_0_eq'
% 7.75/5.69 thf(fact_3710_diff__is__0__eq,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ( minus_minus_nat @ M @ N )
% 7.75/5.69 = zero_zero_nat )
% 7.75/5.69 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_is_0_eq
% 7.75/5.69 thf(fact_3711_of__nat__mult,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N ) )
% 7.75/5.69 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_mult
% 7.75/5.69 thf(fact_3712_of__nat__mult,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 7.75/5.69 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_mult
% 7.75/5.69 thf(fact_3713_of__nat__mult,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 7.75/5.69 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_mult
% 7.75/5.69 thf(fact_3714_of__nat__mult,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 7.75/5.69 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_mult
% 7.75/5.69 thf(fact_3715_of__nat__mult,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 7.75/5.69 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_mult
% 7.75/5.69 thf(fact_3716_Nat_Odiff__diff__right,axiom,
% 7.75/5.69 ! [K: nat,J: nat,I: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ K @ J )
% 7.75/5.69 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 7.75/5.69 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Nat.diff_diff_right
% 7.75/5.69 thf(fact_3717_Nat_Oadd__diff__assoc2,axiom,
% 7.75/5.69 ! [K: nat,J: nat,I: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ K @ J )
% 7.75/5.69 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 7.75/5.69 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Nat.add_diff_assoc2
% 7.75/5.69 thf(fact_3718_Nat_Oadd__diff__assoc,axiom,
% 7.75/5.69 ! [K: nat,J: nat,I: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ K @ J )
% 7.75/5.69 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 7.75/5.69 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Nat.add_diff_assoc
% 7.75/5.69 thf(fact_3719_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ( semiri4939895301339042750nteger @ X )
% 7.75/5.69 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 7.75/5.69 = ( X
% 7.75/5.69 = ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3720_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ( semiri5074537144036343181t_real @ X )
% 7.75/5.69 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 7.75/5.69 = ( X
% 7.75/5.69 = ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3721_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ( semiri1314217659103216013at_int @ X )
% 7.75/5.69 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 7.75/5.69 = ( X
% 7.75/5.69 = ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3722_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ( semiri1316708129612266289at_nat @ X )
% 7.75/5.69 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 7.75/5.69 = ( X
% 7.75/5.69 = ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3723_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ( semiri8010041392384452111omplex @ X )
% 7.75/5.69 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 7.75/5.69 = ( X
% 7.75/5.69 = ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3724_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W )
% 7.75/5.69 = ( semiri4939895301339042750nteger @ X ) )
% 7.75/5.69 = ( ( power_power_nat @ B @ W )
% 7.75/5.69 = X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3725_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 7.75/5.69 = ( semiri5074537144036343181t_real @ X ) )
% 7.75/5.69 = ( ( power_power_nat @ B @ W )
% 7.75/5.69 = X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3726_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 7.75/5.69 = ( semiri1314217659103216013at_int @ X ) )
% 7.75/5.69 = ( ( power_power_nat @ B @ W )
% 7.75/5.69 = X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3727_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 7.75/5.69 = ( semiri1316708129612266289at_nat @ X ) )
% 7.75/5.69 = ( ( power_power_nat @ B @ W )
% 7.75/5.69 = X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3728_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 7.75/5.69 = ( semiri8010041392384452111omplex @ X ) )
% 7.75/5.69 = ( ( power_power_nat @ B @ W )
% 7.75/5.69 = X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_eq_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3729_semiring__1__class_Oof__nat__power,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri4939895301339042750nteger @ ( power_power_nat @ M @ N ) )
% 7.75/5.69 = ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ M ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_power
% 7.75/5.69 thf(fact_3730_semiring__1__class_Oof__nat__power,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 7.75/5.69 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_power
% 7.75/5.69 thf(fact_3731_semiring__1__class_Oof__nat__power,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 7.75/5.69 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_power
% 7.75/5.69 thf(fact_3732_semiring__1__class_Oof__nat__power,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 7.75/5.69 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_power
% 7.75/5.69 thf(fact_3733_semiring__1__class_Oof__nat__power,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 7.75/5.69 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_1_class.of_nat_power
% 7.75/5.69 thf(fact_3734_signed__take__bit__of__minus__1,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_of_minus_1
% 7.75/5.69 thf(fact_3735_signed__take__bit__of__minus__1,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_of_minus_1
% 7.75/5.69 thf(fact_3736_of__bool__not__iff,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 7.75/5.69 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_bool_not_iff
% 7.75/5.69 thf(fact_3737_of__bool__not__iff,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( zero_n1201886186963655149omplex @ ~ P )
% 7.75/5.69 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_bool_not_iff
% 7.75/5.69 thf(fact_3738_of__bool__not__iff,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( zero_n3304061248610475627l_real @ ~ P )
% 7.75/5.69 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_bool_not_iff
% 7.75/5.69 thf(fact_3739_of__bool__not__iff,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 7.75/5.69 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_bool_not_iff
% 7.75/5.69 thf(fact_3740_of__bool__not__iff,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( zero_n356916108424825756nteger @ ~ P )
% 7.75/5.69 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_bool_not_iff
% 7.75/5.69 thf(fact_3741_semiring__norm_I9_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 7.75/5.69 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(9)
% 7.75/5.69 thf(fact_3742_semiring__norm_I7_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 7.75/5.69 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(7)
% 7.75/5.69 thf(fact_3743_semiring__norm_I15_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 7.75/5.69 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(15)
% 7.75/5.69 thf(fact_3744_semiring__norm_I14_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 7.75/5.69 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(14)
% 7.75/5.69 thf(fact_3745_semiring__norm_I72_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 7.75/5.69 = ( ord_less_eq_num @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(72)
% 7.75/5.69 thf(fact_3746_semiring__norm_I81_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 7.75/5.69 = ( ord_less_num @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(81)
% 7.75/5.69 thf(fact_3747_semiring__norm_I70_J,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(70)
% 7.75/5.69 thf(fact_3748_semiring__norm_I77_J,axiom,
% 7.75/5.69 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(77)
% 7.75/5.69 thf(fact_3749_of__nat__of__bool,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 7.75/5.69 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_of_bool
% 7.75/5.69 thf(fact_3750_of__nat__of__bool,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 7.75/5.69 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_of_bool
% 7.75/5.69 thf(fact_3751_of__nat__of__bool,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 7.75/5.69 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_of_bool
% 7.75/5.69 thf(fact_3752_of__nat__of__bool,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 7.75/5.69 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_of_bool
% 7.75/5.69 thf(fact_3753_of__nat__of__bool,axiom,
% 7.75/5.69 ! [P: $o] :
% 7.75/5.69 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 7.75/5.69 = ( zero_n356916108424825756nteger @ P ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_of_bool
% 7.75/5.69 thf(fact_3754_dbl__simps_I1_J,axiom,
% 7.75/5.69 ! [K: num] :
% 7.75/5.69 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(1)
% 7.75/5.69 thf(fact_3755_dbl__simps_I1_J,axiom,
% 7.75/5.69 ! [K: num] :
% 7.75/5.69 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(1)
% 7.75/5.69 thf(fact_3756_dbl__simps_I1_J,axiom,
% 7.75/5.69 ! [K: num] :
% 7.75/5.69 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(1)
% 7.75/5.69 thf(fact_3757_dbl__simps_I1_J,axiom,
% 7.75/5.69 ! [K: num] :
% 7.75/5.69 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(1)
% 7.75/5.69 thf(fact_3758_dbl__simps_I1_J,axiom,
% 7.75/5.69 ! [K: num] :
% 7.75/5.69 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(1)
% 7.75/5.69 thf(fact_3759_add__neg__numeral__special_I8_J,axiom,
% 7.75/5.69 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(8)
% 7.75/5.69 thf(fact_3760_add__neg__numeral__special_I8_J,axiom,
% 7.75/5.69 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(8)
% 7.75/5.69 thf(fact_3761_add__neg__numeral__special_I8_J,axiom,
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 7.75/5.69 = zero_z3403309356797280102nteger ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(8)
% 7.75/5.69 thf(fact_3762_add__neg__numeral__special_I8_J,axiom,
% 7.75/5.69 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(8)
% 7.75/5.69 thf(fact_3763_add__neg__numeral__special_I8_J,axiom,
% 7.75/5.69 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(8)
% 7.75/5.69 thf(fact_3764_add__neg__numeral__special_I7_J,axiom,
% 7.75/5.69 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(7)
% 7.75/5.69 thf(fact_3765_add__neg__numeral__special_I7_J,axiom,
% 7.75/5.69 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(7)
% 7.75/5.69 thf(fact_3766_add__neg__numeral__special_I7_J,axiom,
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = zero_z3403309356797280102nteger ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(7)
% 7.75/5.69 thf(fact_3767_add__neg__numeral__special_I7_J,axiom,
% 7.75/5.69 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(7)
% 7.75/5.69 thf(fact_3768_add__neg__numeral__special_I7_J,axiom,
% 7.75/5.69 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(7)
% 7.75/5.69 thf(fact_3769_diff__numeral__special_I12_J,axiom,
% 7.75/5.69 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(12)
% 7.75/5.69 thf(fact_3770_diff__numeral__special_I12_J,axiom,
% 7.75/5.69 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.69 = zero_zero_real ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(12)
% 7.75/5.69 thf(fact_3771_diff__numeral__special_I12_J,axiom,
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = zero_z3403309356797280102nteger ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(12)
% 7.75/5.69 thf(fact_3772_diff__numeral__special_I12_J,axiom,
% 7.75/5.69 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.69 = zero_zero_complex ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(12)
% 7.75/5.69 thf(fact_3773_diff__numeral__special_I12_J,axiom,
% 7.75/5.69 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.69 = zero_zero_rat ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(12)
% 7.75/5.69 thf(fact_3774_numeral__eq__neg__one__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 7.75/5.69 = ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_eq_neg_one_iff
% 7.75/5.69 thf(fact_3775_numeral__eq__neg__one__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 7.75/5.69 = ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_eq_neg_one_iff
% 7.75/5.69 thf(fact_3776_numeral__eq__neg__one__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_eq_neg_one_iff
% 7.75/5.69 thf(fact_3777_numeral__eq__neg__one__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_eq_neg_one_iff
% 7.75/5.69 thf(fact_3778_numeral__eq__neg__one__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 7.75/5.69 = ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_eq_neg_one_iff
% 7.75/5.69 thf(fact_3779_neg__one__eq__numeral__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus_uminus_int @ one_one_int )
% 7.75/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_eq_numeral_iff
% 7.75/5.69 thf(fact_3780_neg__one__eq__numeral__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus_uminus_real @ one_one_real )
% 7.75/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_eq_numeral_iff
% 7.75/5.69 thf(fact_3781_neg__one__eq__numeral__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_eq_numeral_iff
% 7.75/5.69 thf(fact_3782_neg__one__eq__numeral__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_eq_numeral_iff
% 7.75/5.69 thf(fact_3783_neg__one__eq__numeral__iff,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( ( uminus_uminus_rat @ one_one_rat )
% 7.75/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.69 = ( N = one ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_eq_numeral_iff
% 7.75/5.69 thf(fact_3784_of__nat__le__0__iff,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 7.75/5.69 = ( M = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_0_iff
% 7.75/5.69 thf(fact_3785_of__nat__le__0__iff,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 7.75/5.69 = ( M = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_0_iff
% 7.75/5.69 thf(fact_3786_of__nat__le__0__iff,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 7.75/5.69 = ( M = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_0_iff
% 7.75/5.69 thf(fact_3787_of__nat__le__0__iff,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 7.75/5.69 = ( M = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_0_iff
% 7.75/5.69 thf(fact_3788_left__minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat,A: int] :
% 7.75/5.69 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % left_minus_one_mult_self
% 7.75/5.69 thf(fact_3789_left__minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat,A: real] :
% 7.75/5.69 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % left_minus_one_mult_self
% 7.75/5.69 thf(fact_3790_left__minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat,A: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % left_minus_one_mult_self
% 7.75/5.69 thf(fact_3791_left__minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat,A: complex] :
% 7.75/5.69 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % left_minus_one_mult_self
% 7.75/5.69 thf(fact_3792_left__minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat,A: rat] :
% 7.75/5.69 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 7.75/5.69 = A ) ).
% 7.75/5.69
% 7.75/5.69 % left_minus_one_mult_self
% 7.75/5.69 thf(fact_3793_minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 7.75/5.69 = one_one_int ) ).
% 7.75/5.69
% 7.75/5.69 % minus_one_mult_self
% 7.75/5.69 thf(fact_3794_minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 7.75/5.69 = one_one_real ) ).
% 7.75/5.69
% 7.75/5.69 % minus_one_mult_self
% 7.75/5.69 thf(fact_3795_minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 7.75/5.69 = one_one_Code_integer ) ).
% 7.75/5.69
% 7.75/5.69 % minus_one_mult_self
% 7.75/5.69 thf(fact_3796_minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 7.75/5.69 = one_one_complex ) ).
% 7.75/5.69
% 7.75/5.69 % minus_one_mult_self
% 7.75/5.69 thf(fact_3797_minus__one__mult__self,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 7.75/5.69 = one_one_rat ) ).
% 7.75/5.69
% 7.75/5.69 % minus_one_mult_self
% 7.75/5.69 thf(fact_3798_of__nat__Suc,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 7.75/5.69 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_Suc
% 7.75/5.69 thf(fact_3799_of__nat__Suc,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 7.75/5.69 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_Suc
% 7.75/5.69 thf(fact_3800_of__nat__Suc,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 7.75/5.69 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_Suc
% 7.75/5.69 thf(fact_3801_of__nat__Suc,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 7.75/5.69 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_Suc
% 7.75/5.69 thf(fact_3802_of__nat__Suc,axiom,
% 7.75/5.69 ! [M: nat] :
% 7.75/5.69 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 7.75/5.69 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_Suc
% 7.75/5.69 thf(fact_3803_mod__minus1__right,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = zero_zero_int ) ).
% 7.75/5.69
% 7.75/5.69 % mod_minus1_right
% 7.75/5.69 thf(fact_3804_mod__minus1__right,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = zero_z3403309356797280102nteger ) ).
% 7.75/5.69
% 7.75/5.69 % mod_minus1_right
% 7.75/5.69 thf(fact_3805_Suc__pred,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 7.75/5.69 = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % Suc_pred
% 7.75/5.69 thf(fact_3806_diff__Suc__diff__eq1,axiom,
% 7.75/5.69 ! [K: nat,J: nat,I: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ K @ J )
% 7.75/5.69 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 7.75/5.69 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_Suc_diff_eq1
% 7.75/5.69 thf(fact_3807_diff__Suc__diff__eq2,axiom,
% 7.75/5.69 ! [K: nat,J: nat,I: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ K @ J )
% 7.75/5.69 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 7.75/5.69 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_Suc_diff_eq2
% 7.75/5.69 thf(fact_3808_Suc__diff,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 7.75/5.69 => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 7.75/5.69 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Suc_diff
% 7.75/5.69 thf(fact_3809_zdiv__numeral__Bit1,axiom,
% 7.75/5.69 ! [V: num,W: num] :
% 7.75/5.69 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 7.75/5.69 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zdiv_numeral_Bit1
% 7.75/5.69 thf(fact_3810_semiring__norm_I168_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: int] :
% 7.75/5.69 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 7.75/5.69 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(168)
% 7.75/5.69 thf(fact_3811_semiring__norm_I168_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: real] :
% 7.75/5.69 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 7.75/5.69 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(168)
% 7.75/5.69 thf(fact_3812_semiring__norm_I168_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: code_integer] :
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 7.75/5.69 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(168)
% 7.75/5.69 thf(fact_3813_semiring__norm_I168_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: complex] :
% 7.75/5.69 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 7.75/5.69 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(168)
% 7.75/5.69 thf(fact_3814_semiring__norm_I168_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: rat] :
% 7.75/5.69 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 7.75/5.69 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(168)
% 7.75/5.69 thf(fact_3815_diff__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.69 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(2)
% 7.75/5.69 thf(fact_3816_diff__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.69 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(2)
% 7.75/5.69 thf(fact_3817_diff__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.69 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(2)
% 7.75/5.69 thf(fact_3818_diff__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 7.75/5.69 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(2)
% 7.75/5.69 thf(fact_3819_diff__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.69 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(2)
% 7.75/5.69 thf(fact_3820_diff__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(3)
% 7.75/5.69 thf(fact_3821_diff__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(3)
% 7.75/5.69 thf(fact_3822_diff__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(3)
% 7.75/5.69 thf(fact_3823_diff__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(3)
% 7.75/5.69 thf(fact_3824_diff__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_simps(3)
% 7.75/5.69 thf(fact_3825_semiring__norm_I3_J,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 7.75/5.69 = ( bit1 @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(3)
% 7.75/5.69 thf(fact_3826_semiring__norm_I4_J,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 7.75/5.69 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(4)
% 7.75/5.69 thf(fact_3827_semiring__norm_I5_J,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 7.75/5.69 = ( bit1 @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(5)
% 7.75/5.69 thf(fact_3828_semiring__norm_I8_J,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 7.75/5.69 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(8)
% 7.75/5.69 thf(fact_3829_semiring__norm_I10_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 7.75/5.69 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(10)
% 7.75/5.69 thf(fact_3830_mult__neg__numeral__simps_I1_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.69 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(1)
% 7.75/5.69 thf(fact_3831_mult__neg__numeral__simps_I1_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.69 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(1)
% 7.75/5.69 thf(fact_3832_mult__neg__numeral__simps_I1_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.69 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(1)
% 7.75/5.69 thf(fact_3833_mult__neg__numeral__simps_I1_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 7.75/5.69 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(1)
% 7.75/5.69 thf(fact_3834_mult__neg__numeral__simps_I1_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.69 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(1)
% 7.75/5.69 thf(fact_3835_mult__neg__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(2)
% 7.75/5.69 thf(fact_3836_mult__neg__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(2)
% 7.75/5.69 thf(fact_3837_mult__neg__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(2)
% 7.75/5.69 thf(fact_3838_mult__neg__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(2)
% 7.75/5.69 thf(fact_3839_mult__neg__numeral__simps_I2_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(2)
% 7.75/5.69 thf(fact_3840_mult__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3841_mult__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3842_mult__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3843_mult__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3844_mult__neg__numeral__simps_I3_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_neg_numeral_simps(3)
% 7.75/5.69 thf(fact_3845_semiring__norm_I170_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: int] :
% 7.75/5.69 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 7.75/5.69 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(170)
% 7.75/5.69 thf(fact_3846_semiring__norm_I170_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: real] :
% 7.75/5.69 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 7.75/5.69 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(170)
% 7.75/5.69 thf(fact_3847_semiring__norm_I170_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 7.75/5.69 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(170)
% 7.75/5.69 thf(fact_3848_semiring__norm_I170_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: complex] :
% 7.75/5.69 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 7.75/5.69 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(170)
% 7.75/5.69 thf(fact_3849_semiring__norm_I170_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: rat] :
% 7.75/5.69 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 7.75/5.69 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(170)
% 7.75/5.69 thf(fact_3850_semiring__norm_I171_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: int] :
% 7.75/5.69 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(171)
% 7.75/5.69 thf(fact_3851_semiring__norm_I171_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: real] :
% 7.75/5.69 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(171)
% 7.75/5.69 thf(fact_3852_semiring__norm_I171_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(171)
% 7.75/5.69 thf(fact_3853_semiring__norm_I171_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: complex] :
% 7.75/5.69 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(171)
% 7.75/5.69 thf(fact_3854_semiring__norm_I171_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: rat] :
% 7.75/5.69 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(171)
% 7.75/5.69 thf(fact_3855_semiring__norm_I172_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: int] :
% 7.75/5.69 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(172)
% 7.75/5.69 thf(fact_3856_semiring__norm_I172_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: real] :
% 7.75/5.69 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(172)
% 7.75/5.69 thf(fact_3857_semiring__norm_I172_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(172)
% 7.75/5.69 thf(fact_3858_semiring__norm_I172_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: complex] :
% 7.75/5.69 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(172)
% 7.75/5.69 thf(fact_3859_semiring__norm_I172_J,axiom,
% 7.75/5.69 ! [V: num,W: num,Y: rat] :
% 7.75/5.69 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 7.75/5.69 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(172)
% 7.75/5.69 thf(fact_3860_zle__diff1__eq,axiom,
% 7.75/5.69 ! [W: int,Z: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 7.75/5.69 = ( ord_less_int @ W @ Z ) ) ).
% 7.75/5.69
% 7.75/5.69 % zle_diff1_eq
% 7.75/5.69 thf(fact_3861_neg__numeral__le__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.69 = ( ord_less_eq_num @ N @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_le_iff
% 7.75/5.69 thf(fact_3862_neg__numeral__le__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.69 = ( ord_less_eq_num @ N @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_le_iff
% 7.75/5.69 thf(fact_3863_neg__numeral__le__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.69 = ( ord_less_eq_num @ N @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_le_iff
% 7.75/5.69 thf(fact_3864_neg__numeral__le__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.69 = ( ord_less_eq_num @ N @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_le_iff
% 7.75/5.69 thf(fact_3865_neg__numeral__less__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.69 = ( ord_less_num @ N @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_less_iff
% 7.75/5.69 thf(fact_3866_neg__numeral__less__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.69 = ( ord_less_num @ N @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_less_iff
% 7.75/5.69 thf(fact_3867_neg__numeral__less__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.69 = ( ord_less_num @ N @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_less_iff
% 7.75/5.69 thf(fact_3868_neg__numeral__less__iff,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.69 = ( ord_less_num @ N @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_less_iff
% 7.75/5.69 thf(fact_3869_semiring__norm_I16_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 7.75/5.69 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(16)
% 7.75/5.69 thf(fact_3870_semiring__norm_I79_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 7.75/5.69 = ( ord_less_eq_num @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(79)
% 7.75/5.69 thf(fact_3871_semiring__norm_I74_J,axiom,
% 7.75/5.69 ! [M: num,N: num] :
% 7.75/5.69 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 7.75/5.69 = ( ord_less_num @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_norm(74)
% 7.75/5.69 thf(fact_3872_not__neg__one__le__neg__numeral__iff,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 7.75/5.69 = ( M != one ) ) ).
% 7.75/5.69
% 7.75/5.69 % not_neg_one_le_neg_numeral_iff
% 7.75/5.69 thf(fact_3873_not__neg__one__le__neg__numeral__iff,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 7.75/5.69 = ( M != one ) ) ).
% 7.75/5.69
% 7.75/5.69 % not_neg_one_le_neg_numeral_iff
% 7.75/5.69 thf(fact_3874_not__neg__one__le__neg__numeral__iff,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 7.75/5.69 = ( M != one ) ) ).
% 7.75/5.69
% 7.75/5.69 % not_neg_one_le_neg_numeral_iff
% 7.75/5.69 thf(fact_3875_not__neg__one__le__neg__numeral__iff,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 7.75/5.69 = ( M != one ) ) ).
% 7.75/5.69
% 7.75/5.69 % not_neg_one_le_neg_numeral_iff
% 7.75/5.69 thf(fact_3876_neg__numeral__less__neg__one__iff,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = ( M != one ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_less_neg_one_iff
% 7.75/5.69 thf(fact_3877_neg__numeral__less__neg__one__iff,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.69 = ( M != one ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_less_neg_one_iff
% 7.75/5.69 thf(fact_3878_neg__numeral__less__neg__one__iff,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = ( M != one ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_less_neg_one_iff
% 7.75/5.69 thf(fact_3879_neg__numeral__less__neg__one__iff,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.69 = ( M != one ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_numeral_less_neg_one_iff
% 7.75/5.69 thf(fact_3880_eq__divide__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [A: real,B: real,W: num] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 7.75/5.69 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 7.75/5.69 != zero_zero_real )
% 7.75/5.69 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.69 = B ) )
% 7.75/5.69 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 7.75/5.69 = zero_zero_real )
% 7.75/5.69 => ( A = zero_zero_real ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % eq_divide_eq_numeral1(2)
% 7.75/5.69 thf(fact_3881_eq__divide__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [A: complex,B: complex,W: num] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 7.75/5.69 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.69 != zero_zero_complex )
% 7.75/5.69 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 7.75/5.69 = B ) )
% 7.75/5.69 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.69 = zero_zero_complex )
% 7.75/5.69 => ( A = zero_zero_complex ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % eq_divide_eq_numeral1(2)
% 7.75/5.69 thf(fact_3882_eq__divide__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [A: rat,B: rat,W: num] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 7.75/5.69 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 7.75/5.69 != zero_zero_rat )
% 7.75/5.69 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 7.75/5.69 = B ) )
% 7.75/5.69 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 7.75/5.69 = zero_zero_rat )
% 7.75/5.69 => ( A = zero_zero_rat ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % eq_divide_eq_numeral1(2)
% 7.75/5.69 thf(fact_3883_divide__eq__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [B: real,W: num,A: real] :
% 7.75/5.69 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.69 = A )
% 7.75/5.69 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 7.75/5.69 != zero_zero_real )
% 7.75/5.69 => ( B
% 7.75/5.69 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 7.75/5.69 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 7.75/5.69 = zero_zero_real )
% 7.75/5.69 => ( A = zero_zero_real ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_eq_eq_numeral1(2)
% 7.75/5.69 thf(fact_3884_divide__eq__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [B: complex,W: num,A: complex] :
% 7.75/5.69 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 7.75/5.69 = A )
% 7.75/5.69 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.69 != zero_zero_complex )
% 7.75/5.69 => ( B
% 7.75/5.69 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 7.75/5.69 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.69 = zero_zero_complex )
% 7.75/5.69 => ( A = zero_zero_complex ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_eq_eq_numeral1(2)
% 7.75/5.69 thf(fact_3885_divide__eq__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [B: rat,W: num,A: rat] :
% 7.75/5.69 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 7.75/5.69 = A )
% 7.75/5.69 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 7.75/5.69 != zero_zero_rat )
% 7.75/5.69 => ( B
% 7.75/5.69 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 7.75/5.69 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 7.75/5.69 = zero_zero_rat )
% 7.75/5.69 => ( A = zero_zero_rat ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_eq_eq_numeral1(2)
% 7.75/5.69 thf(fact_3886_le__divide__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [A: real,B: real,W: num] :
% 7.75/5.69 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 7.75/5.69 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_divide_eq_numeral1(2)
% 7.75/5.69 thf(fact_3887_le__divide__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [A: rat,B: rat,W: num] :
% 7.75/5.69 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 7.75/5.69 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_divide_eq_numeral1(2)
% 7.75/5.69 thf(fact_3888_divide__le__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [B: real,W: num,A: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 7.75/5.69 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_le_eq_numeral1(2)
% 7.75/5.69 thf(fact_3889_divide__le__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [B: rat,W: num,A: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 7.75/5.69 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_le_eq_numeral1(2)
% 7.75/5.69 thf(fact_3890_less__divide__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [A: real,B: real,W: num] :
% 7.75/5.69 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 7.75/5.69 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_divide_eq_numeral1(2)
% 7.75/5.69 thf(fact_3891_less__divide__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [A: rat,B: rat,W: num] :
% 7.75/5.69 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 7.75/5.69 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % less_divide_eq_numeral1(2)
% 7.75/5.69 thf(fact_3892_divide__less__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [B: real,W: num,A: real] :
% 7.75/5.69 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 7.75/5.69 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_less_eq_numeral1(2)
% 7.75/5.69 thf(fact_3893_divide__less__eq__numeral1_I2_J,axiom,
% 7.75/5.69 ! [B: rat,W: num,A: rat] :
% 7.75/5.69 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 7.75/5.69 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % divide_less_eq_numeral1(2)
% 7.75/5.69 thf(fact_3894_power2__minus,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_minus
% 7.75/5.69 thf(fact_3895_power2__minus,axiom,
% 7.75/5.69 ! [A: real] :
% 7.75/5.69 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_minus
% 7.75/5.69 thf(fact_3896_power2__minus,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_minus
% 7.75/5.69 thf(fact_3897_power2__minus,axiom,
% 7.75/5.69 ! [A: complex] :
% 7.75/5.69 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_minus
% 7.75/5.69 thf(fact_3898_power2__minus,axiom,
% 7.75/5.69 ! [A: rat] :
% 7.75/5.69 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power2_minus
% 7.75/5.69 thf(fact_3899_of__nat__0__less__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 7.75/5.69 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_0_less_iff
% 7.75/5.69 thf(fact_3900_of__nat__0__less__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.69 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_0_less_iff
% 7.75/5.69 thf(fact_3901_of__nat__0__less__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.69 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_0_less_iff
% 7.75/5.69 thf(fact_3902_of__nat__0__less__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 7.75/5.69 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_0_less_iff
% 7.75/5.69 thf(fact_3903_Suc__diff__1,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.69 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 7.75/5.69 = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % Suc_diff_1
% 7.75/5.69 thf(fact_3904_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [Y: nat,X: num,N: nat] :
% 7.75/5.69 ( ( ( semiri4939895301339042750nteger @ Y )
% 7.75/5.69 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) )
% 7.75/5.69 = ( Y
% 7.75/5.69 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % real_of_nat_eq_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_3905_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [Y: nat,X: num,N: nat] :
% 7.75/5.69 ( ( ( semiri681578069525770553at_rat @ Y )
% 7.75/5.69 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 7.75/5.69 = ( Y
% 7.75/5.69 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % real_of_nat_eq_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_3906_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [Y: nat,X: num,N: nat] :
% 7.75/5.69 ( ( ( semiri5074537144036343181t_real @ Y )
% 7.75/5.69 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 7.75/5.69 = ( Y
% 7.75/5.69 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % real_of_nat_eq_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_3907_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [Y: nat,X: num,N: nat] :
% 7.75/5.69 ( ( ( semiri1314217659103216013at_int @ Y )
% 7.75/5.69 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 7.75/5.69 = ( Y
% 7.75/5.69 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % real_of_nat_eq_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_3908_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [Y: nat,X: num,N: nat] :
% 7.75/5.69 ( ( ( semiri1316708129612266289at_nat @ Y )
% 7.75/5.69 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 7.75/5.69 = ( Y
% 7.75/5.69 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % real_of_nat_eq_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_3909_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [Y: nat,X: num,N: nat] :
% 7.75/5.69 ( ( ( semiri8010041392384452111omplex @ Y )
% 7.75/5.69 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 7.75/5.69 = ( Y
% 7.75/5.69 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % real_of_nat_eq_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_3910_numeral__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: num,N: nat,Y: nat] :
% 7.75/5.69 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N )
% 7.75/5.69 = ( semiri4939895301339042750nteger @ Y ) )
% 7.75/5.69 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 7.75/5.69 = Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3911_numeral__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: num,N: nat,Y: nat] :
% 7.75/5.69 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 7.75/5.69 = ( semiri681578069525770553at_rat @ Y ) )
% 7.75/5.69 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 7.75/5.69 = Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3912_numeral__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: num,N: nat,Y: nat] :
% 7.75/5.69 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 7.75/5.69 = ( semiri5074537144036343181t_real @ Y ) )
% 7.75/5.69 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 7.75/5.69 = Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3913_numeral__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: num,N: nat,Y: nat] :
% 7.75/5.69 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 7.75/5.69 = ( semiri1314217659103216013at_int @ Y ) )
% 7.75/5.69 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 7.75/5.69 = Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3914_numeral__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: num,N: nat,Y: nat] :
% 7.75/5.69 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 7.75/5.69 = ( semiri1316708129612266289at_nat @ Y ) )
% 7.75/5.69 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 7.75/5.69 = Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3915_numeral__power__eq__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: num,N: nat,Y: nat] :
% 7.75/5.69 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 7.75/5.69 = ( semiri8010041392384452111omplex @ Y ) )
% 7.75/5.69 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 7.75/5.69 = Y ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_eq_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3916_of__nat__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3917_of__nat__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3918_of__nat__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3919_of__nat__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3920_of__nat__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3921_of__nat__less__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) @ ( semiri4939895301339042750nteger @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3922_of__nat__less__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3923_of__nat__less__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3924_of__nat__less__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3925_of__nat__less__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3926_of__nat__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3927_of__nat__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3928_of__nat__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3929_of__nat__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3930_of__nat__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,B: nat,W: nat] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_3931_of__nat__le__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W ) @ ( semiri4939895301339042750nteger @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3932_of__nat__le__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3933_of__nat__le__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3934_of__nat__le__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3935_of__nat__le__of__nat__power__cancel__iff,axiom,
% 7.75/5.69 ! [B: nat,W: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_of_nat_power_cancel_iff
% 7.75/5.69 thf(fact_3936_real__of__nat__less__numeral__iff,axiom,
% 7.75/5.69 ! [N: nat,W: num] :
% 7.75/5.69 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 7.75/5.69 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % real_of_nat_less_numeral_iff
% 7.75/5.69 thf(fact_3937_numeral__less__real__of__nat__iff,axiom,
% 7.75/5.69 ! [W: num,N: nat] :
% 7.75/5.69 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.69 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_less_real_of_nat_iff
% 7.75/5.69 thf(fact_3938_numeral__le__real__of__nat__iff,axiom,
% 7.75/5.69 ! [N: num,M: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_le_real_of_nat_iff
% 7.75/5.69 thf(fact_3939_int__div__minus__is__minus1,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.69 => ( ( ( divide_divide_int @ A @ B )
% 7.75/5.69 = ( uminus_uminus_int @ A ) )
% 7.75/5.69 = ( B
% 7.75/5.69 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % int_div_minus_is_minus1
% 7.75/5.69 thf(fact_3940_add__neg__numeral__special_I9_J,axiom,
% 7.75/5.69 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(9)
% 7.75/5.69 thf(fact_3941_add__neg__numeral__special_I9_J,axiom,
% 7.75/5.69 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(9)
% 7.75/5.69 thf(fact_3942_add__neg__numeral__special_I9_J,axiom,
% 7.75/5.69 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(9)
% 7.75/5.69 thf(fact_3943_add__neg__numeral__special_I9_J,axiom,
% 7.75/5.69 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(9)
% 7.75/5.69 thf(fact_3944_add__neg__numeral__special_I9_J,axiom,
% 7.75/5.69 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % add_neg_numeral_special(9)
% 7.75/5.69 thf(fact_3945_diff__numeral__special_I10_J,axiom,
% 7.75/5.69 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 7.75/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(10)
% 7.75/5.69 thf(fact_3946_diff__numeral__special_I10_J,axiom,
% 7.75/5.69 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 7.75/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(10)
% 7.75/5.69 thf(fact_3947_diff__numeral__special_I10_J,axiom,
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(10)
% 7.75/5.69 thf(fact_3948_diff__numeral__special_I10_J,axiom,
% 7.75/5.69 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(10)
% 7.75/5.69 thf(fact_3949_diff__numeral__special_I10_J,axiom,
% 7.75/5.69 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 7.75/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(10)
% 7.75/5.69 thf(fact_3950_diff__numeral__special_I11_J,axiom,
% 7.75/5.69 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(11)
% 7.75/5.69 thf(fact_3951_diff__numeral__special_I11_J,axiom,
% 7.75/5.69 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.69 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(11)
% 7.75/5.69 thf(fact_3952_diff__numeral__special_I11_J,axiom,
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(11)
% 7.75/5.69 thf(fact_3953_diff__numeral__special_I11_J,axiom,
% 7.75/5.69 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.69 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(11)
% 7.75/5.69 thf(fact_3954_diff__numeral__special_I11_J,axiom,
% 7.75/5.69 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.69 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(11)
% 7.75/5.69 thf(fact_3955_minus__1__div__2__eq,axiom,
% 7.75/5.69 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_1_div_2_eq
% 7.75/5.69 thf(fact_3956_minus__1__div__2__eq,axiom,
% 7.75/5.69 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_1_div_2_eq
% 7.75/5.69 thf(fact_3957_even__diff,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 7.75/5.69 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % even_diff
% 7.75/5.69 thf(fact_3958_bits__minus__1__mod__2__eq,axiom,
% 7.75/5.69 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.69 = one_one_int ) ).
% 7.75/5.69
% 7.75/5.69 % bits_minus_1_mod_2_eq
% 7.75/5.69 thf(fact_3959_bits__minus__1__mod__2__eq,axiom,
% 7.75/5.69 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.69 = one_one_Code_integer ) ).
% 7.75/5.69
% 7.75/5.69 % bits_minus_1_mod_2_eq
% 7.75/5.69 thf(fact_3960_minus__1__mod__2__eq,axiom,
% 7.75/5.69 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.69 = one_one_int ) ).
% 7.75/5.69
% 7.75/5.69 % minus_1_mod_2_eq
% 7.75/5.69 thf(fact_3961_minus__1__mod__2__eq,axiom,
% 7.75/5.69 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.69 = one_one_Code_integer ) ).
% 7.75/5.69
% 7.75/5.69 % minus_1_mod_2_eq
% 7.75/5.69 thf(fact_3962_of__nat__zero__less__power__iff,axiom,
% 7.75/5.69 ! [X: nat,N: nat] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X ) @ N ) )
% 7.75/5.69 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 7.75/5.69 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_zero_less_power_iff
% 7.75/5.69 thf(fact_3963_of__nat__zero__less__power__iff,axiom,
% 7.75/5.69 ! [X: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 7.75/5.69 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 7.75/5.69 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_zero_less_power_iff
% 7.75/5.69 thf(fact_3964_of__nat__zero__less__power__iff,axiom,
% 7.75/5.69 ! [X: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 7.75/5.69 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 7.75/5.69 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_zero_less_power_iff
% 7.75/5.69 thf(fact_3965_of__nat__zero__less__power__iff,axiom,
% 7.75/5.69 ! [X: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 7.75/5.69 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 7.75/5.69 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_zero_less_power_iff
% 7.75/5.69 thf(fact_3966_of__nat__zero__less__power__iff,axiom,
% 7.75/5.69 ! [X: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 7.75/5.69 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 7.75/5.69 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_zero_less_power_iff
% 7.75/5.69 thf(fact_3967_Power_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [A: int,N: nat] :
% 7.75/5.69 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Power.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3968_Power_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [A: real,N: nat] :
% 7.75/5.69 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Power.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3969_Power_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [A: code_integer,N: nat] :
% 7.75/5.69 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Power.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3970_Power_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [A: complex,N: nat] :
% 7.75/5.69 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Power.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3971_Power_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [A: rat,N: nat] :
% 7.75/5.69 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Power.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3972_Parity_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [N: nat,A: int] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 7.75/5.69 = ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Parity.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3973_Parity_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [N: nat,A: real] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 7.75/5.69 = ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Parity.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3974_Parity_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [N: nat,A: code_integer] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 7.75/5.69 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Parity.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3975_Parity_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [N: nat,A: complex] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 7.75/5.69 = ( power_power_complex @ A @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Parity.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3976_Parity_Oring__1__class_Opower__minus__even,axiom,
% 7.75/5.69 ! [N: nat,A: rat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 7.75/5.69 = ( power_power_rat @ A @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Parity.ring_1_class.power_minus_even
% 7.75/5.69 thf(fact_3977_power__minus__odd,axiom,
% 7.75/5.69 ! [N: nat,A: int] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 7.75/5.69 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_odd
% 7.75/5.69 thf(fact_3978_power__minus__odd,axiom,
% 7.75/5.69 ! [N: nat,A: real] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 7.75/5.69 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_odd
% 7.75/5.69 thf(fact_3979_power__minus__odd,axiom,
% 7.75/5.69 ! [N: nat,A: code_integer] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_odd
% 7.75/5.69 thf(fact_3980_power__minus__odd,axiom,
% 7.75/5.69 ! [N: nat,A: complex] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_odd
% 7.75/5.69 thf(fact_3981_power__minus__odd,axiom,
% 7.75/5.69 ! [N: nat,A: rat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 7.75/5.69 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_odd
% 7.75/5.69 thf(fact_3982_Suc__div__eq__add3__div__numeral,axiom,
% 7.75/5.69 ! [M: nat,V: num] :
% 7.75/5.69 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 7.75/5.69 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Suc_div_eq_add3_div_numeral
% 7.75/5.69 thf(fact_3983_div__Suc__eq__div__add3,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 7.75/5.69 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % div_Suc_eq_div_add3
% 7.75/5.69 thf(fact_3984_Suc__mod__eq__add3__mod__numeral,axiom,
% 7.75/5.69 ! [M: nat,V: num] :
% 7.75/5.69 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 7.75/5.69 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Suc_mod_eq_add3_mod_numeral
% 7.75/5.69 thf(fact_3985_mod__Suc__eq__mod__add3,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 7.75/5.69 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mod_Suc_eq_mod_add3
% 7.75/5.69 thf(fact_3986_diff__numeral__special_I4_J,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 7.75/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(4)
% 7.75/5.69 thf(fact_3987_diff__numeral__special_I4_J,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 7.75/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(4)
% 7.75/5.69 thf(fact_3988_diff__numeral__special_I4_J,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(4)
% 7.75/5.69 thf(fact_3989_diff__numeral__special_I4_J,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(4)
% 7.75/5.69 thf(fact_3990_diff__numeral__special_I4_J,axiom,
% 7.75/5.69 ! [M: num] :
% 7.75/5.69 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 7.75/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(4)
% 7.75/5.69 thf(fact_3991_diff__numeral__special_I3_J,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.69 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(3)
% 7.75/5.69 thf(fact_3992_diff__numeral__special_I3_J,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.69 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(3)
% 7.75/5.69 thf(fact_3993_diff__numeral__special_I3_J,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.69 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(3)
% 7.75/5.69 thf(fact_3994_diff__numeral__special_I3_J,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 7.75/5.69 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(3)
% 7.75/5.69 thf(fact_3995_diff__numeral__special_I3_J,axiom,
% 7.75/5.69 ! [N: num] :
% 7.75/5.69 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.69 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_numeral_special(3)
% 7.75/5.69 thf(fact_3996_dbl__simps_I4_J,axiom,
% 7.75/5.69 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(4)
% 7.75/5.69 thf(fact_3997_dbl__simps_I4_J,axiom,
% 7.75/5.69 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(4)
% 7.75/5.69 thf(fact_3998_dbl__simps_I4_J,axiom,
% 7.75/5.69 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(4)
% 7.75/5.69 thf(fact_3999_dbl__simps_I4_J,axiom,
% 7.75/5.69 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(4)
% 7.75/5.69 thf(fact_4000_dbl__simps_I4_J,axiom,
% 7.75/5.69 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % dbl_simps(4)
% 7.75/5.69 thf(fact_4001_power__minus1__even,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = one_one_int ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus1_even
% 7.75/5.69 thf(fact_4002_power__minus1__even,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = one_one_real ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus1_even
% 7.75/5.69 thf(fact_4003_power__minus1__even,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = one_one_Code_integer ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus1_even
% 7.75/5.69 thf(fact_4004_power__minus1__even,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = one_one_complex ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus1_even
% 7.75/5.69 thf(fact_4005_power__minus1__even,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.69 = one_one_rat ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus1_even
% 7.75/5.69 thf(fact_4006_neg__one__even__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 7.75/5.69 = one_one_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_even_power
% 7.75/5.69 thf(fact_4007_neg__one__even__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 7.75/5.69 = one_one_real ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_even_power
% 7.75/5.69 thf(fact_4008_neg__one__even__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 7.75/5.69 = one_one_Code_integer ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_even_power
% 7.75/5.69 thf(fact_4009_neg__one__even__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 7.75/5.69 = one_one_complex ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_even_power
% 7.75/5.69 thf(fact_4010_neg__one__even__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 7.75/5.69 = one_one_rat ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_even_power
% 7.75/5.69 thf(fact_4011_neg__one__odd__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 7.75/5.69 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_odd_power
% 7.75/5.69 thf(fact_4012_neg__one__odd__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 7.75/5.69 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_odd_power
% 7.75/5.69 thf(fact_4013_neg__one__odd__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_odd_power
% 7.75/5.69 thf(fact_4014_neg__one__odd__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_odd_power
% 7.75/5.69 thf(fact_4015_neg__one__odd__power,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 7.75/5.69 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % neg_one_odd_power
% 7.75/5.69 thf(fact_4016_of__nat__less__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4017_of__nat__less__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4018_of__nat__less__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4019_of__nat__less__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4020_of__nat__less__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_less_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4021_numeral__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4022_numeral__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4023_numeral__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4024_numeral__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4025_numeral__power__less__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 7.75/5.69 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_less_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4026_of__nat__le__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4027_of__nat__le__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4028_of__nat__le__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4029_of__nat__le__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4030_of__nat__le__numeral__power__cancel__iff,axiom,
% 7.75/5.69 ! [X: nat,I: num,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 7.75/5.69 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_le_numeral_power_cancel_iff
% 7.75/5.69 thf(fact_4031_numeral__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I ) @ N ) @ ( semiri4939895301339042750nteger @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4032_numeral__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4033_numeral__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4034_numeral__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4035_numeral__power__le__of__nat__cancel__iff,axiom,
% 7.75/5.69 ! [I: num,N: nat,X: nat] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 7.75/5.69 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 7.75/5.69
% 7.75/5.69 % numeral_power_le_of_nat_cancel_iff
% 7.75/5.69 thf(fact_4036_even__of__nat,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.69 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % even_of_nat
% 7.75/5.69 thf(fact_4037_even__of__nat,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 7.75/5.69 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % even_of_nat
% 7.75/5.69 thf(fact_4038_odd__Suc__minus__one,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.69 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 7.75/5.69 = N ) ) ).
% 7.75/5.69
% 7.75/5.69 % odd_Suc_minus_one
% 7.75/5.69 thf(fact_4039_signed__take__bit__0,axiom,
% 7.75/5.69 ! [A: code_integer] :
% 7.75/5.69 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_0
% 7.75/5.69 thf(fact_4040_signed__take__bit__0,axiom,
% 7.75/5.69 ! [A: int] :
% 7.75/5.69 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 7.75/5.69 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_0
% 7.75/5.69 thf(fact_4041_even__diff__nat,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.69 = ( ( ord_less_nat @ M @ N )
% 7.75/5.69 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % even_diff_nat
% 7.75/5.69 thf(fact_4042_signed__take__bit__Suc__minus__bit0,axiom,
% 7.75/5.69 ! [N: nat,K: num] :
% 7.75/5.69 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 7.75/5.69 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_Suc_minus_bit0
% 7.75/5.69 thf(fact_4043_semiring__parity__class_Oeven__mask__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 7.75/5.69 = ( N = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_parity_class.even_mask_iff
% 7.75/5.69 thf(fact_4044_semiring__parity__class_Oeven__mask__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 7.75/5.69 = ( N = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_parity_class.even_mask_iff
% 7.75/5.69 thf(fact_4045_semiring__parity__class_Oeven__mask__iff,axiom,
% 7.75/5.69 ! [N: nat] :
% 7.75/5.69 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 7.75/5.69 = ( N = zero_zero_nat ) ) ).
% 7.75/5.69
% 7.75/5.69 % semiring_parity_class.even_mask_iff
% 7.75/5.69 thf(fact_4046_signed__take__bit__Suc__bit1,axiom,
% 7.75/5.69 ! [N: nat,K: num] :
% 7.75/5.69 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_Suc_bit1
% 7.75/5.69 thf(fact_4047_signed__take__bit__Suc__minus__bit1,axiom,
% 7.75/5.69 ! [N: nat,K: num] :
% 7.75/5.69 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 7.75/5.69 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_Suc_minus_bit1
% 7.75/5.69 thf(fact_4048_cnt__cnt__eq,axiom,
% 7.75/5.69 ( vEBT_VEBT_cnt
% 7.75/5.69 = ( ^ [T2: vEBT_VEBT] : ( semiri5074537144036343181t_real @ ( vEBT_VEBT_cnt2 @ T2 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % cnt_cnt_eq
% 7.75/5.69 thf(fact_4049_minus__int__code_I2_J,axiom,
% 7.75/5.69 ! [L: int] :
% 7.75/5.69 ( ( minus_minus_int @ zero_zero_int @ L )
% 7.75/5.69 = ( uminus_uminus_int @ L ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_int_code(2)
% 7.75/5.69 thf(fact_4050_of__nat__diff,axiom,
% 7.75/5.69 ! [N: nat,M: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.69 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.69 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_diff
% 7.75/5.69 thf(fact_4051_of__nat__diff,axiom,
% 7.75/5.69 ! [N: nat,M: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.69 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.69 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_diff
% 7.75/5.69 thf(fact_4052_of__nat__diff,axiom,
% 7.75/5.69 ! [N: nat,M: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.69 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.69 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_diff
% 7.75/5.69 thf(fact_4053_of__nat__diff,axiom,
% 7.75/5.69 ! [N: nat,M: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.69 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.69 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_diff
% 7.75/5.69 thf(fact_4054_le__refl,axiom,
% 7.75/5.69 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 7.75/5.69
% 7.75/5.69 % le_refl
% 7.75/5.69 thf(fact_4055_le__trans,axiom,
% 7.75/5.69 ! [I: nat,J: nat,K: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.69 => ( ( ord_less_eq_nat @ J @ K )
% 7.75/5.69 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_trans
% 7.75/5.69 thf(fact_4056_eq__imp__le,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( M = N )
% 7.75/5.69 => ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.69
% 7.75/5.69 % eq_imp_le
% 7.75/5.69 thf(fact_4057_le__antisym,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.69 => ( M = N ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_antisym
% 7.75/5.69 thf(fact_4058_eq__diff__iff,axiom,
% 7.75/5.69 ! [K: nat,M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ K @ M )
% 7.75/5.69 => ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.69 => ( ( ( minus_minus_nat @ M @ K )
% 7.75/5.69 = ( minus_minus_nat @ N @ K ) )
% 7.75/5.69 = ( M = N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % eq_diff_iff
% 7.75/5.69 thf(fact_4059_le__diff__iff,axiom,
% 7.75/5.69 ! [K: nat,M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ K @ M )
% 7.75/5.69 => ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.69 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 7.75/5.69 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_diff_iff
% 7.75/5.69 thf(fact_4060_Nat_Odiff__diff__eq,axiom,
% 7.75/5.69 ! [K: nat,M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ K @ M )
% 7.75/5.69 => ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.69 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 7.75/5.69 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Nat.diff_diff_eq
% 7.75/5.69 thf(fact_4061_diff__le__mono,axiom,
% 7.75/5.69 ! [M: nat,N: nat,L: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_le_mono
% 7.75/5.69 thf(fact_4062_diff__le__self,axiom,
% 7.75/5.69 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 7.75/5.69
% 7.75/5.69 % diff_le_self
% 7.75/5.69 thf(fact_4063_le__diff__iff_H,axiom,
% 7.75/5.69 ! [A: nat,C: nat,B: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ A @ C )
% 7.75/5.69 => ( ( ord_less_eq_nat @ B @ C )
% 7.75/5.69 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 7.75/5.69 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_diff_iff'
% 7.75/5.69 thf(fact_4064_diff__le__mono2,axiom,
% 7.75/5.69 ! [M: nat,N: nat,L: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_le_mono2
% 7.75/5.69 thf(fact_4065_nat__le__linear,axiom,
% 7.75/5.69 ! [M: nat,N: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.69 | ( ord_less_eq_nat @ N @ M ) ) ).
% 7.75/5.69
% 7.75/5.69 % nat_le_linear
% 7.75/5.69 thf(fact_4066_complete__real,axiom,
% 7.75/5.69 ! [S3: set_real] :
% 7.75/5.69 ( ? [X5: real] : ( member_real @ X5 @ S3 )
% 7.75/5.69 => ( ? [Z4: real] :
% 7.75/5.69 ! [X3: real] :
% 7.75/5.69 ( ( member_real @ X3 @ S3 )
% 7.75/5.69 => ( ord_less_eq_real @ X3 @ Z4 ) )
% 7.75/5.69 => ? [Y3: real] :
% 7.75/5.69 ( ! [X5: real] :
% 7.75/5.69 ( ( member_real @ X5 @ S3 )
% 7.75/5.69 => ( ord_less_eq_real @ X5 @ Y3 ) )
% 7.75/5.69 & ! [Z4: real] :
% 7.75/5.69 ( ! [X3: real] :
% 7.75/5.69 ( ( member_real @ X3 @ S3 )
% 7.75/5.69 => ( ord_less_eq_real @ X3 @ Z4 ) )
% 7.75/5.69 => ( ord_less_eq_real @ Y3 @ Z4 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % complete_real
% 7.75/5.69 thf(fact_4067_Nat_Oex__has__greatest__nat,axiom,
% 7.75/5.69 ! [P: nat > $o,K: nat,B: nat] :
% 7.75/5.69 ( ( P @ K )
% 7.75/5.69 => ( ! [Y3: nat] :
% 7.75/5.69 ( ( P @ Y3 )
% 7.75/5.69 => ( ord_less_eq_nat @ Y3 @ B ) )
% 7.75/5.69 => ? [X3: nat] :
% 7.75/5.69 ( ( P @ X3 )
% 7.75/5.69 & ! [Y4: nat] :
% 7.75/5.69 ( ( P @ Y4 )
% 7.75/5.69 => ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % Nat.ex_has_greatest_nat
% 7.75/5.69 thf(fact_4068_signed__take__bit__diff,axiom,
% 7.75/5.69 ! [N: nat,K: int,L: int] :
% 7.75/5.69 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 7.75/5.69 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_diff
% 7.75/5.69 thf(fact_4069_signed__take__bit__minus,axiom,
% 7.75/5.69 ! [N: nat,K: int] :
% 7.75/5.69 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 7.75/5.69 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % signed_take_bit_minus
% 7.75/5.69 thf(fact_4070_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_minus_int
% 7.75/5.69 = ( ^ [A3: int,B4: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % ab_group_add_class.ab_diff_conv_add_uminus
% 7.75/5.69 thf(fact_4071_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_minus_real
% 7.75/5.69 = ( ^ [A3: real,B4: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % ab_group_add_class.ab_diff_conv_add_uminus
% 7.75/5.69 thf(fact_4072_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_8373710615458151222nteger
% 7.75/5.69 = ( ^ [A3: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % ab_group_add_class.ab_diff_conv_add_uminus
% 7.75/5.69 thf(fact_4073_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_minus_complex
% 7.75/5.69 = ( ^ [A3: complex,B4: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % ab_group_add_class.ab_diff_conv_add_uminus
% 7.75/5.69 thf(fact_4074_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_minus_rat
% 7.75/5.69 = ( ^ [A3: rat,B4: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % ab_group_add_class.ab_diff_conv_add_uminus
% 7.75/5.69 thf(fact_4075_diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_minus_int
% 7.75/5.69 = ( ^ [A3: int,B4: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_conv_add_uminus
% 7.75/5.69 thf(fact_4076_diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_minus_real
% 7.75/5.69 = ( ^ [A3: real,B4: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_conv_add_uminus
% 7.75/5.69 thf(fact_4077_diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_8373710615458151222nteger
% 7.75/5.69 = ( ^ [A3: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_conv_add_uminus
% 7.75/5.69 thf(fact_4078_diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_minus_complex
% 7.75/5.69 = ( ^ [A3: complex,B4: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_conv_add_uminus
% 7.75/5.69 thf(fact_4079_diff__conv__add__uminus,axiom,
% 7.75/5.69 ( minus_minus_rat
% 7.75/5.69 = ( ^ [A3: rat,B4: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_conv_add_uminus
% 7.75/5.69 thf(fact_4080_group__cancel_Osub2,axiom,
% 7.75/5.69 ! [B3: int,K: int,B: int,A: int] :
% 7.75/5.69 ( ( B3
% 7.75/5.69 = ( plus_plus_int @ K @ B ) )
% 7.75/5.69 => ( ( minus_minus_int @ A @ B3 )
% 7.75/5.69 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % group_cancel.sub2
% 7.75/5.69 thf(fact_4081_group__cancel_Osub2,axiom,
% 7.75/5.69 ! [B3: real,K: real,B: real,A: real] :
% 7.75/5.69 ( ( B3
% 7.75/5.69 = ( plus_plus_real @ K @ B ) )
% 7.75/5.69 => ( ( minus_minus_real @ A @ B3 )
% 7.75/5.69 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % group_cancel.sub2
% 7.75/5.69 thf(fact_4082_group__cancel_Osub2,axiom,
% 7.75/5.69 ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 7.75/5.69 ( ( B3
% 7.75/5.69 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 7.75/5.69 => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 7.75/5.69 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % group_cancel.sub2
% 7.75/5.69 thf(fact_4083_group__cancel_Osub2,axiom,
% 7.75/5.69 ! [B3: complex,K: complex,B: complex,A: complex] :
% 7.75/5.69 ( ( B3
% 7.75/5.69 = ( plus_plus_complex @ K @ B ) )
% 7.75/5.69 => ( ( minus_minus_complex @ A @ B3 )
% 7.75/5.69 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % group_cancel.sub2
% 7.75/5.69 thf(fact_4084_group__cancel_Osub2,axiom,
% 7.75/5.69 ! [B3: rat,K: rat,B: rat,A: rat] :
% 7.75/5.69 ( ( B3
% 7.75/5.69 = ( plus_plus_rat @ K @ B ) )
% 7.75/5.69 => ( ( minus_minus_rat @ A @ B3 )
% 7.75/5.69 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % group_cancel.sub2
% 7.75/5.69 thf(fact_4085_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 7.75/5.69 ! [A: complex,C: complex,B: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B )
% 7.75/5.69 = ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C ) ) ).
% 7.75/5.69
% 7.75/5.69 % cancel_ab_semigroup_add_class.diff_right_commute
% 7.75/5.69 thf(fact_4086_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 7.75/5.69 ! [A: real,C: real,B: real] :
% 7.75/5.69 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 7.75/5.69 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 7.75/5.69
% 7.75/5.69 % cancel_ab_semigroup_add_class.diff_right_commute
% 7.75/5.69 thf(fact_4087_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 7.75/5.69 ! [A: nat,C: nat,B: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 7.75/5.69 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 7.75/5.69
% 7.75/5.69 % cancel_ab_semigroup_add_class.diff_right_commute
% 7.75/5.69 thf(fact_4088_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 7.75/5.69 ! [A: int,C: int,B: int] :
% 7.75/5.69 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 7.75/5.69 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 7.75/5.69
% 7.75/5.69 % cancel_ab_semigroup_add_class.diff_right_commute
% 7.75/5.69 thf(fact_4089_minus__diff__commute,axiom,
% 7.75/5.69 ! [B: int,A: int] :
% 7.75/5.69 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 7.75/5.69 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_commute
% 7.75/5.69 thf(fact_4090_minus__diff__commute,axiom,
% 7.75/5.69 ! [B: real,A: real] :
% 7.75/5.69 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 7.75/5.69 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_commute
% 7.75/5.69 thf(fact_4091_minus__diff__commute,axiom,
% 7.75/5.69 ! [B: code_integer,A: code_integer] :
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 7.75/5.69 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_commute
% 7.75/5.69 thf(fact_4092_minus__diff__commute,axiom,
% 7.75/5.69 ! [B: complex,A: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 7.75/5.69 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_commute
% 7.75/5.69 thf(fact_4093_minus__diff__commute,axiom,
% 7.75/5.69 ! [B: rat,A: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 7.75/5.69 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_commute
% 7.75/5.69 thf(fact_4094_minus__equation__iff,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ( uminus_uminus_int @ A )
% 7.75/5.69 = B )
% 7.75/5.69 = ( ( uminus_uminus_int @ B )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_equation_iff
% 7.75/5.69 thf(fact_4095_minus__equation__iff,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( ( uminus_uminus_real @ A )
% 7.75/5.69 = B )
% 7.75/5.69 = ( ( uminus_uminus_real @ B )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_equation_iff
% 7.75/5.69 thf(fact_4096_minus__equation__iff,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( ( uminus1351360451143612070nteger @ A )
% 7.75/5.69 = B )
% 7.75/5.69 = ( ( uminus1351360451143612070nteger @ B )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_equation_iff
% 7.75/5.69 thf(fact_4097_minus__equation__iff,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( ( uminus1482373934393186551omplex @ A )
% 7.75/5.69 = B )
% 7.75/5.69 = ( ( uminus1482373934393186551omplex @ B )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_equation_iff
% 7.75/5.69 thf(fact_4098_minus__equation__iff,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( ( uminus_uminus_rat @ A )
% 7.75/5.69 = B )
% 7.75/5.69 = ( ( uminus_uminus_rat @ B )
% 7.75/5.69 = A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_equation_iff
% 7.75/5.69 thf(fact_4099_equation__minus__iff,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( uminus_uminus_int @ B ) )
% 7.75/5.69 = ( B
% 7.75/5.69 = ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % equation_minus_iff
% 7.75/5.69 thf(fact_4100_equation__minus__iff,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( uminus_uminus_real @ B ) )
% 7.75/5.69 = ( B
% 7.75/5.69 = ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % equation_minus_iff
% 7.75/5.69 thf(fact_4101_equation__minus__iff,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.69 = ( B
% 7.75/5.69 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % equation_minus_iff
% 7.75/5.69 thf(fact_4102_equation__minus__iff,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.69 = ( B
% 7.75/5.69 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % equation_minus_iff
% 7.75/5.69 thf(fact_4103_equation__minus__iff,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( A
% 7.75/5.69 = ( uminus_uminus_rat @ B ) )
% 7.75/5.69 = ( B
% 7.75/5.69 = ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % equation_minus_iff
% 7.75/5.69 thf(fact_4104_diff__eq__diff__eq,axiom,
% 7.75/5.69 ! [A: complex,B: complex,C: complex,D2: complex] :
% 7.75/5.69 ( ( ( minus_minus_complex @ A @ B )
% 7.75/5.69 = ( minus_minus_complex @ C @ D2 ) )
% 7.75/5.69 => ( ( A = B )
% 7.75/5.69 = ( C = D2 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_eq_diff_eq
% 7.75/5.69 thf(fact_4105_diff__eq__diff__eq,axiom,
% 7.75/5.69 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.69 ( ( ( minus_minus_real @ A @ B )
% 7.75/5.69 = ( minus_minus_real @ C @ D2 ) )
% 7.75/5.69 => ( ( A = B )
% 7.75/5.69 = ( C = D2 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_eq_diff_eq
% 7.75/5.69 thf(fact_4106_diff__eq__diff__eq,axiom,
% 7.75/5.69 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.69 ( ( ( minus_minus_int @ A @ B )
% 7.75/5.69 = ( minus_minus_int @ C @ D2 ) )
% 7.75/5.69 => ( ( A = B )
% 7.75/5.69 = ( C = D2 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_eq_diff_eq
% 7.75/5.69 thf(fact_4107_verit__negate__coefficient_I3_J,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( A = B )
% 7.75/5.69 => ( ( uminus_uminus_int @ A )
% 7.75/5.69 = ( uminus_uminus_int @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_negate_coefficient(3)
% 7.75/5.69 thf(fact_4108_verit__negate__coefficient_I3_J,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( A = B )
% 7.75/5.69 => ( ( uminus_uminus_real @ A )
% 7.75/5.69 = ( uminus_uminus_real @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_negate_coefficient(3)
% 7.75/5.69 thf(fact_4109_verit__negate__coefficient_I3_J,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( A = B )
% 7.75/5.69 => ( ( uminus1351360451143612070nteger @ A )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_negate_coefficient(3)
% 7.75/5.69 thf(fact_4110_verit__negate__coefficient_I3_J,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( A = B )
% 7.75/5.69 => ( ( uminus_uminus_rat @ A )
% 7.75/5.69 = ( uminus_uminus_rat @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % verit_negate_coefficient(3)
% 7.75/5.69 thf(fact_4111_minus__diff__minus,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_minus
% 7.75/5.69 thf(fact_4112_minus__diff__minus,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_minus
% 7.75/5.69 thf(fact_4113_minus__diff__minus,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_minus
% 7.75/5.69 thf(fact_4114_minus__diff__minus,axiom,
% 7.75/5.69 ! [A: complex,B: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_minus
% 7.75/5.69 thf(fact_4115_minus__diff__minus,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_diff_minus
% 7.75/5.69 thf(fact_4116_diff__commute,axiom,
% 7.75/5.69 ! [I: nat,J: nat,K: nat] :
% 7.75/5.69 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 7.75/5.69 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_commute
% 7.75/5.69 thf(fact_4117_power__minus__Bit1,axiom,
% 7.75/5.69 ! [X: int,K: num] :
% 7.75/5.69 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 7.75/5.69 = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_Bit1
% 7.75/5.69 thf(fact_4118_power__minus__Bit1,axiom,
% 7.75/5.69 ! [X: real,K: num] :
% 7.75/5.69 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 7.75/5.69 = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_Bit1
% 7.75/5.69 thf(fact_4119_power__minus__Bit1,axiom,
% 7.75/5.69 ! [X: code_integer,K: num] :
% 7.75/5.69 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 7.75/5.69 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_Bit1
% 7.75/5.69 thf(fact_4120_power__minus__Bit1,axiom,
% 7.75/5.69 ! [X: complex,K: num] :
% 7.75/5.69 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 7.75/5.69 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_Bit1
% 7.75/5.69 thf(fact_4121_power__minus__Bit1,axiom,
% 7.75/5.69 ! [X: rat,K: num] :
% 7.75/5.69 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 7.75/5.69 = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % power_minus_Bit1
% 7.75/5.69 thf(fact_4122_zmod__zminus1__eq__if,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.69 = zero_zero_int )
% 7.75/5.69 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.69 = zero_zero_int ) )
% 7.75/5.69 & ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.69 != zero_zero_int )
% 7.75/5.69 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.69 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zmod_zminus1_eq_if
% 7.75/5.69 thf(fact_4123_zmod__zminus2__eq__if,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.69 = zero_zero_int )
% 7.75/5.69 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.69 = zero_zero_int ) )
% 7.75/5.69 & ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.69 != zero_zero_int )
% 7.75/5.69 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.69 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % zmod_zminus2_eq_if
% 7.75/5.69 thf(fact_4124_of__nat__mono,axiom,
% 7.75/5.69 ! [I: nat,J: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.69 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_mono
% 7.75/5.69 thf(fact_4125_of__nat__mono,axiom,
% 7.75/5.69 ! [I: nat,J: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.69 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_mono
% 7.75/5.69 thf(fact_4126_of__nat__mono,axiom,
% 7.75/5.69 ! [I: nat,J: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.69 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_mono
% 7.75/5.69 thf(fact_4127_of__nat__mono,axiom,
% 7.75/5.69 ! [I: nat,J: nat] :
% 7.75/5.69 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.69 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % of_nat_mono
% 7.75/5.69 thf(fact_4128_mult__of__nat__commute,axiom,
% 7.75/5.69 ! [X: nat,Y: code_integer] :
% 7.75/5.69 ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 7.75/5.69 = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_of_nat_commute
% 7.75/5.69 thf(fact_4129_mult__of__nat__commute,axiom,
% 7.75/5.69 ! [X: nat,Y: real] :
% 7.75/5.69 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 7.75/5.69 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_of_nat_commute
% 7.75/5.69 thf(fact_4130_mult__of__nat__commute,axiom,
% 7.75/5.69 ! [X: nat,Y: int] :
% 7.75/5.69 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 7.75/5.69 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_of_nat_commute
% 7.75/5.69 thf(fact_4131_mult__of__nat__commute,axiom,
% 7.75/5.69 ! [X: nat,Y: nat] :
% 7.75/5.69 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 7.75/5.69 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_of_nat_commute
% 7.75/5.69 thf(fact_4132_mult__of__nat__commute,axiom,
% 7.75/5.69 ! [X: nat,Y: complex] :
% 7.75/5.69 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y )
% 7.75/5.69 = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % mult_of_nat_commute
% 7.75/5.69 thf(fact_4133_eq__iff__diff__eq__0,axiom,
% 7.75/5.69 ( ( ^ [Y2: rat,Z2: rat] : ( Y2 = Z2 ) )
% 7.75/5.69 = ( ^ [A3: rat,B4: rat] :
% 7.75/5.69 ( ( minus_minus_rat @ A3 @ B4 )
% 7.75/5.69 = zero_zero_rat ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % eq_iff_diff_eq_0
% 7.75/5.69 thf(fact_4134_eq__iff__diff__eq__0,axiom,
% 7.75/5.69 ( ( ^ [Y2: complex,Z2: complex] : ( Y2 = Z2 ) )
% 7.75/5.69 = ( ^ [A3: complex,B4: complex] :
% 7.75/5.69 ( ( minus_minus_complex @ A3 @ B4 )
% 7.75/5.69 = zero_zero_complex ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % eq_iff_diff_eq_0
% 7.75/5.69 thf(fact_4135_eq__iff__diff__eq__0,axiom,
% 7.75/5.69 ( ( ^ [Y2: real,Z2: real] : ( Y2 = Z2 ) )
% 7.75/5.69 = ( ^ [A3: real,B4: real] :
% 7.75/5.69 ( ( minus_minus_real @ A3 @ B4 )
% 7.75/5.69 = zero_zero_real ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % eq_iff_diff_eq_0
% 7.75/5.69 thf(fact_4136_eq__iff__diff__eq__0,axiom,
% 7.75/5.69 ( ( ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
% 7.75/5.69 = ( ^ [A3: int,B4: int] :
% 7.75/5.69 ( ( minus_minus_int @ A3 @ B4 )
% 7.75/5.69 = zero_zero_int ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % eq_iff_diff_eq_0
% 7.75/5.69 thf(fact_4137_diff__eq__diff__less__eq,axiom,
% 7.75/5.69 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.69 ( ( ( minus_minus_real @ A @ B )
% 7.75/5.69 = ( minus_minus_real @ C @ D2 ) )
% 7.75/5.69 => ( ( ord_less_eq_real @ A @ B )
% 7.75/5.69 = ( ord_less_eq_real @ C @ D2 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_eq_diff_less_eq
% 7.75/5.69 thf(fact_4138_diff__eq__diff__less__eq,axiom,
% 7.75/5.69 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.69 ( ( ( minus_minus_rat @ A @ B )
% 7.75/5.69 = ( minus_minus_rat @ C @ D2 ) )
% 7.75/5.69 => ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.69 = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_eq_diff_less_eq
% 7.75/5.69 thf(fact_4139_diff__eq__diff__less__eq,axiom,
% 7.75/5.69 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.69 ( ( ( minus_minus_int @ A @ B )
% 7.75/5.69 = ( minus_minus_int @ C @ D2 ) )
% 7.75/5.69 => ( ( ord_less_eq_int @ A @ B )
% 7.75/5.69 = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_eq_diff_less_eq
% 7.75/5.69 thf(fact_4140_diff__right__mono,axiom,
% 7.75/5.69 ! [A: real,B: real,C: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.69 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_right_mono
% 7.75/5.69 thf(fact_4141_diff__right__mono,axiom,
% 7.75/5.69 ! [A: rat,B: rat,C: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.69 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_right_mono
% 7.75/5.69 thf(fact_4142_diff__right__mono,axiom,
% 7.75/5.69 ! [A: int,B: int,C: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.69 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_right_mono
% 7.75/5.69 thf(fact_4143_diff__left__mono,axiom,
% 7.75/5.69 ! [B: real,A: real,C: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ B @ A )
% 7.75/5.69 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_left_mono
% 7.75/5.69 thf(fact_4144_diff__left__mono,axiom,
% 7.75/5.69 ! [B: rat,A: rat,C: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ B @ A )
% 7.75/5.69 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_left_mono
% 7.75/5.69 thf(fact_4145_diff__left__mono,axiom,
% 7.75/5.69 ! [B: int,A: int,C: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ B @ A )
% 7.75/5.69 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_left_mono
% 7.75/5.69 thf(fact_4146_diff__mono,axiom,
% 7.75/5.69 ! [A: real,B: real,D2: real,C: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.69 => ( ( ord_less_eq_real @ D2 @ C )
% 7.75/5.69 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_mono
% 7.75/5.69 thf(fact_4147_diff__mono,axiom,
% 7.75/5.69 ! [A: rat,B: rat,D2: rat,C: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.69 => ( ( ord_less_eq_rat @ D2 @ C )
% 7.75/5.69 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_mono
% 7.75/5.69 thf(fact_4148_diff__mono,axiom,
% 7.75/5.69 ! [A: int,B: int,D2: int,C: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.69 => ( ( ord_less_eq_int @ D2 @ C )
% 7.75/5.69 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_mono
% 7.75/5.69 thf(fact_4149_diff__strict__mono,axiom,
% 7.75/5.69 ! [A: real,B: real,D2: real,C: real] :
% 7.75/5.69 ( ( ord_less_real @ A @ B )
% 7.75/5.69 => ( ( ord_less_real @ D2 @ C )
% 7.75/5.69 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_strict_mono
% 7.75/5.69 thf(fact_4150_diff__strict__mono,axiom,
% 7.75/5.69 ! [A: rat,B: rat,D2: rat,C: rat] :
% 7.75/5.69 ( ( ord_less_rat @ A @ B )
% 7.75/5.69 => ( ( ord_less_rat @ D2 @ C )
% 7.75/5.69 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_strict_mono
% 7.75/5.69 thf(fact_4151_diff__strict__mono,axiom,
% 7.75/5.69 ! [A: int,B: int,D2: int,C: int] :
% 7.75/5.69 ( ( ord_less_int @ A @ B )
% 7.75/5.69 => ( ( ord_less_int @ D2 @ C )
% 7.75/5.69 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_strict_mono
% 7.75/5.69 thf(fact_4152_diff__eq__diff__less,axiom,
% 7.75/5.69 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.69 ( ( ( minus_minus_real @ A @ B )
% 7.75/5.69 = ( minus_minus_real @ C @ D2 ) )
% 7.75/5.69 => ( ( ord_less_real @ A @ B )
% 7.75/5.69 = ( ord_less_real @ C @ D2 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_eq_diff_less
% 7.75/5.69 thf(fact_4153_diff__eq__diff__less,axiom,
% 7.75/5.69 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.69 ( ( ( minus_minus_rat @ A @ B )
% 7.75/5.69 = ( minus_minus_rat @ C @ D2 ) )
% 7.75/5.69 => ( ( ord_less_rat @ A @ B )
% 7.75/5.69 = ( ord_less_rat @ C @ D2 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_eq_diff_less
% 7.75/5.69 thf(fact_4154_diff__eq__diff__less,axiom,
% 7.75/5.69 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.69 ( ( ( minus_minus_int @ A @ B )
% 7.75/5.69 = ( minus_minus_int @ C @ D2 ) )
% 7.75/5.69 => ( ( ord_less_int @ A @ B )
% 7.75/5.69 = ( ord_less_int @ C @ D2 ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_eq_diff_less
% 7.75/5.69 thf(fact_4155_diff__strict__left__mono,axiom,
% 7.75/5.69 ! [B: real,A: real,C: real] :
% 7.75/5.69 ( ( ord_less_real @ B @ A )
% 7.75/5.69 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_strict_left_mono
% 7.75/5.69 thf(fact_4156_diff__strict__left__mono,axiom,
% 7.75/5.69 ! [B: rat,A: rat,C: rat] :
% 7.75/5.69 ( ( ord_less_rat @ B @ A )
% 7.75/5.69 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_strict_left_mono
% 7.75/5.69 thf(fact_4157_diff__strict__left__mono,axiom,
% 7.75/5.69 ! [B: int,A: int,C: int] :
% 7.75/5.69 ( ( ord_less_int @ B @ A )
% 7.75/5.69 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_strict_left_mono
% 7.75/5.69 thf(fact_4158_diff__strict__right__mono,axiom,
% 7.75/5.69 ! [A: real,B: real,C: real] :
% 7.75/5.69 ( ( ord_less_real @ A @ B )
% 7.75/5.69 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_strict_right_mono
% 7.75/5.69 thf(fact_4159_diff__strict__right__mono,axiom,
% 7.75/5.69 ! [A: rat,B: rat,C: rat] :
% 7.75/5.69 ( ( ord_less_rat @ A @ B )
% 7.75/5.69 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_strict_right_mono
% 7.75/5.69 thf(fact_4160_diff__strict__right__mono,axiom,
% 7.75/5.69 ! [A: int,B: int,C: int] :
% 7.75/5.69 ( ( ord_less_int @ A @ B )
% 7.75/5.69 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % diff_strict_right_mono
% 7.75/5.69 thf(fact_4161_le__imp__neg__le,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.69 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_imp_neg_le
% 7.75/5.69 thf(fact_4162_le__imp__neg__le,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.69 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_imp_neg_le
% 7.75/5.69 thf(fact_4163_le__imp__neg__le,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.69 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_imp_neg_le
% 7.75/5.69 thf(fact_4164_le__imp__neg__le,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.69 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.69
% 7.75/5.69 % le_imp_neg_le
% 7.75/5.69 thf(fact_4165_minus__le__iff,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 7.75/5.69 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_le_iff
% 7.75/5.69 thf(fact_4166_minus__le__iff,axiom,
% 7.75/5.69 ! [A: code_integer,B: code_integer] :
% 7.75/5.69 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 7.75/5.69 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_le_iff
% 7.75/5.69 thf(fact_4167_minus__le__iff,axiom,
% 7.75/5.69 ! [A: rat,B: rat] :
% 7.75/5.69 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 7.75/5.69 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_le_iff
% 7.75/5.69 thf(fact_4168_minus__le__iff,axiom,
% 7.75/5.69 ! [A: int,B: int] :
% 7.75/5.69 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.69 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 7.75/5.69
% 7.75/5.69 % minus_le_iff
% 7.75/5.69 thf(fact_4169_le__minus__iff,axiom,
% 7.75/5.69 ! [A: real,B: real] :
% 7.75/5.69 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 7.75/5.69 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_iff
% 7.75/5.70 thf(fact_4170_le__minus__iff,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.70 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_iff
% 7.75/5.70 thf(fact_4171_le__minus__iff,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 7.75/5.70 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_iff
% 7.75/5.70 thf(fact_4172_le__minus__iff,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.70 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_iff
% 7.75/5.70 thf(fact_4173_add__diff__add,axiom,
% 7.75/5.70 ! [A: rat,C: rat,B: rat,D2: rat] :
% 7.75/5.70 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) )
% 7.75/5.70 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_diff_add
% 7.75/5.70 thf(fact_4174_add__diff__add,axiom,
% 7.75/5.70 ! [A: complex,C: complex,B: complex,D2: complex] :
% 7.75/5.70 ( ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ ( plus_plus_complex @ B @ D2 ) )
% 7.75/5.70 = ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ ( minus_minus_complex @ C @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_diff_add
% 7.75/5.70 thf(fact_4175_add__diff__add,axiom,
% 7.75/5.70 ! [A: real,C: real,B: real,D2: real] :
% 7.75/5.70 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D2 ) )
% 7.75/5.70 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_diff_add
% 7.75/5.70 thf(fact_4176_add__diff__add,axiom,
% 7.75/5.70 ! [A: int,C: int,B: int,D2: int] :
% 7.75/5.70 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) )
% 7.75/5.70 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_diff_add
% 7.75/5.70 thf(fact_4177_group__cancel_Osub1,axiom,
% 7.75/5.70 ! [A2: rat,K: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( A2
% 7.75/5.70 = ( plus_plus_rat @ K @ A ) )
% 7.75/5.70 => ( ( minus_minus_rat @ A2 @ B )
% 7.75/5.70 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % group_cancel.sub1
% 7.75/5.70 thf(fact_4178_group__cancel_Osub1,axiom,
% 7.75/5.70 ! [A2: complex,K: complex,A: complex,B: complex] :
% 7.75/5.70 ( ( A2
% 7.75/5.70 = ( plus_plus_complex @ K @ A ) )
% 7.75/5.70 => ( ( minus_minus_complex @ A2 @ B )
% 7.75/5.70 = ( plus_plus_complex @ K @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % group_cancel.sub1
% 7.75/5.70 thf(fact_4179_group__cancel_Osub1,axiom,
% 7.75/5.70 ! [A2: real,K: real,A: real,B: real] :
% 7.75/5.70 ( ( A2
% 7.75/5.70 = ( plus_plus_real @ K @ A ) )
% 7.75/5.70 => ( ( minus_minus_real @ A2 @ B )
% 7.75/5.70 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % group_cancel.sub1
% 7.75/5.70 thf(fact_4180_group__cancel_Osub1,axiom,
% 7.75/5.70 ! [A2: int,K: int,A: int,B: int] :
% 7.75/5.70 ( ( A2
% 7.75/5.70 = ( plus_plus_int @ K @ A ) )
% 7.75/5.70 => ( ( minus_minus_int @ A2 @ B )
% 7.75/5.70 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % group_cancel.sub1
% 7.75/5.70 thf(fact_4181_diff__eq__eq,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( ( minus_minus_rat @ A @ B )
% 7.75/5.70 = C )
% 7.75/5.70 = ( A
% 7.75/5.70 = ( plus_plus_rat @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_eq_eq
% 7.75/5.70 thf(fact_4182_diff__eq__eq,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( ( minus_minus_complex @ A @ B )
% 7.75/5.70 = C )
% 7.75/5.70 = ( A
% 7.75/5.70 = ( plus_plus_complex @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_eq_eq
% 7.75/5.70 thf(fact_4183_diff__eq__eq,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( ( minus_minus_real @ A @ B )
% 7.75/5.70 = C )
% 7.75/5.70 = ( A
% 7.75/5.70 = ( plus_plus_real @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_eq_eq
% 7.75/5.70 thf(fact_4184_diff__eq__eq,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( ( minus_minus_int @ A @ B )
% 7.75/5.70 = C )
% 7.75/5.70 = ( A
% 7.75/5.70 = ( plus_plus_int @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_eq_eq
% 7.75/5.70 thf(fact_4185_eq__diff__eq,axiom,
% 7.75/5.70 ! [A: rat,C: rat,B: rat] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( minus_minus_rat @ C @ B ) )
% 7.75/5.70 = ( ( plus_plus_rat @ A @ B )
% 7.75/5.70 = C ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_diff_eq
% 7.75/5.70 thf(fact_4186_eq__diff__eq,axiom,
% 7.75/5.70 ! [A: complex,C: complex,B: complex] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( minus_minus_complex @ C @ B ) )
% 7.75/5.70 = ( ( plus_plus_complex @ A @ B )
% 7.75/5.70 = C ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_diff_eq
% 7.75/5.70 thf(fact_4187_eq__diff__eq,axiom,
% 7.75/5.70 ! [A: real,C: real,B: real] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( minus_minus_real @ C @ B ) )
% 7.75/5.70 = ( ( plus_plus_real @ A @ B )
% 7.75/5.70 = C ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_diff_eq
% 7.75/5.70 thf(fact_4188_eq__diff__eq,axiom,
% 7.75/5.70 ! [A: int,C: int,B: int] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( minus_minus_int @ C @ B ) )
% 7.75/5.70 = ( ( plus_plus_int @ A @ B )
% 7.75/5.70 = C ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_diff_eq
% 7.75/5.70 thf(fact_4189_add__diff__eq,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 7.75/5.70 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_diff_eq
% 7.75/5.70 thf(fact_4190_add__diff__eq,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( plus_plus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 7.75/5.70 = ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_diff_eq
% 7.75/5.70 thf(fact_4191_add__diff__eq,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 7.75/5.70 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_diff_eq
% 7.75/5.70 thf(fact_4192_add__diff__eq,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 7.75/5.70 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_diff_eq
% 7.75/5.70 thf(fact_4193_diff__diff__eq2,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 7.75/5.70 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_eq2
% 7.75/5.70 thf(fact_4194_diff__diff__eq2,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( minus_minus_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 7.75/5.70 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_eq2
% 7.75/5.70 thf(fact_4195_diff__diff__eq2,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 7.75/5.70 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_eq2
% 7.75/5.70 thf(fact_4196_diff__diff__eq2,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 7.75/5.70 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_eq2
% 7.75/5.70 thf(fact_4197_diff__add__eq,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_eq
% 7.75/5.70 thf(fact_4198_diff__add__eq,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( plus_plus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_complex @ ( plus_plus_complex @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_eq
% 7.75/5.70 thf(fact_4199_diff__add__eq,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_eq
% 7.75/5.70 thf(fact_4200_diff__add__eq,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_eq
% 7.75/5.70 thf(fact_4201_diff__add__eq__diff__diff__swap,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 7.75/5.70 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_eq_diff_diff_swap
% 7.75/5.70 thf(fact_4202_diff__add__eq__diff__diff__swap,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 7.75/5.70 = ( minus_minus_complex @ ( minus_minus_complex @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_eq_diff_diff_swap
% 7.75/5.70 thf(fact_4203_diff__add__eq__diff__diff__swap,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 7.75/5.70 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_eq_diff_diff_swap
% 7.75/5.70 thf(fact_4204_diff__add__eq__diff__diff__swap,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 7.75/5.70 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_eq_diff_diff_swap
% 7.75/5.70 thf(fact_4205_add__implies__diff,axiom,
% 7.75/5.70 ! [C: rat,B: rat,A: rat] :
% 7.75/5.70 ( ( ( plus_plus_rat @ C @ B )
% 7.75/5.70 = A )
% 7.75/5.70 => ( C
% 7.75/5.70 = ( minus_minus_rat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_implies_diff
% 7.75/5.70 thf(fact_4206_add__implies__diff,axiom,
% 7.75/5.70 ! [C: complex,B: complex,A: complex] :
% 7.75/5.70 ( ( ( plus_plus_complex @ C @ B )
% 7.75/5.70 = A )
% 7.75/5.70 => ( C
% 7.75/5.70 = ( minus_minus_complex @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_implies_diff
% 7.75/5.70 thf(fact_4207_add__implies__diff,axiom,
% 7.75/5.70 ! [C: real,B: real,A: real] :
% 7.75/5.70 ( ( ( plus_plus_real @ C @ B )
% 7.75/5.70 = A )
% 7.75/5.70 => ( C
% 7.75/5.70 = ( minus_minus_real @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_implies_diff
% 7.75/5.70 thf(fact_4208_add__implies__diff,axiom,
% 7.75/5.70 ! [C: nat,B: nat,A: nat] :
% 7.75/5.70 ( ( ( plus_plus_nat @ C @ B )
% 7.75/5.70 = A )
% 7.75/5.70 => ( C
% 7.75/5.70 = ( minus_minus_nat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_implies_diff
% 7.75/5.70 thf(fact_4209_add__implies__diff,axiom,
% 7.75/5.70 ! [C: int,B: int,A: int] :
% 7.75/5.70 ( ( ( plus_plus_int @ C @ B )
% 7.75/5.70 = A )
% 7.75/5.70 => ( C
% 7.75/5.70 = ( minus_minus_int @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_implies_diff
% 7.75/5.70 thf(fact_4210_diff__diff__eq,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_eq
% 7.75/5.70 thf(fact_4211_diff__diff__eq,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( minus_minus_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_complex @ A @ ( plus_plus_complex @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_eq
% 7.75/5.70 thf(fact_4212_diff__diff__eq,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_eq
% 7.75/5.70 thf(fact_4213_diff__diff__eq,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_eq
% 7.75/5.70 thf(fact_4214_diff__diff__eq,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_eq
% 7.75/5.70 thf(fact_4215_inf__period_I1_J,axiom,
% 7.75/5.70 ! [P: real > $o,D4: real,Q: real > $o] :
% 7.75/5.70 ( ! [X3: real,K2: real] :
% 7.75/5.70 ( ( P @ X3 )
% 7.75/5.70 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ( ! [X3: real,K2: real] :
% 7.75/5.70 ( ( Q @ X3 )
% 7.75/5.70 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ! [X5: real,K5: real] :
% 7.75/5.70 ( ( ( P @ X5 )
% 7.75/5.70 & ( Q @ X5 ) )
% 7.75/5.70 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K5 @ D4 ) ) )
% 7.75/5.70 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(1)
% 7.75/5.70 thf(fact_4216_inf__period_I1_J,axiom,
% 7.75/5.70 ! [P: int > $o,D4: int,Q: int > $o] :
% 7.75/5.70 ( ! [X3: int,K2: int] :
% 7.75/5.70 ( ( P @ X3 )
% 7.75/5.70 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ( ! [X3: int,K2: int] :
% 7.75/5.70 ( ( Q @ X3 )
% 7.75/5.70 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ! [X5: int,K5: int] :
% 7.75/5.70 ( ( ( P @ X5 )
% 7.75/5.70 & ( Q @ X5 ) )
% 7.75/5.70 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K5 @ D4 ) ) )
% 7.75/5.70 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(1)
% 7.75/5.70 thf(fact_4217_inf__period_I1_J,axiom,
% 7.75/5.70 ! [P: code_integer > $o,D4: code_integer,Q: code_integer > $o] :
% 7.75/5.70 ( ! [X3: code_integer,K2: code_integer] :
% 7.75/5.70 ( ( P @ X3 )
% 7.75/5.70 = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ( ! [X3: code_integer,K2: code_integer] :
% 7.75/5.70 ( ( Q @ X3 )
% 7.75/5.70 = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ! [X5: code_integer,K5: code_integer] :
% 7.75/5.70 ( ( ( P @ X5 )
% 7.75/5.70 & ( Q @ X5 ) )
% 7.75/5.70 = ( ( P @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K5 @ D4 ) ) )
% 7.75/5.70 & ( Q @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(1)
% 7.75/5.70 thf(fact_4218_inf__period_I1_J,axiom,
% 7.75/5.70 ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 7.75/5.70 ( ! [X3: complex,K2: complex] :
% 7.75/5.70 ( ( P @ X3 )
% 7.75/5.70 = ( P @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ( ! [X3: complex,K2: complex] :
% 7.75/5.70 ( ( Q @ X3 )
% 7.75/5.70 = ( Q @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ! [X5: complex,K5: complex] :
% 7.75/5.70 ( ( ( P @ X5 )
% 7.75/5.70 & ( Q @ X5 ) )
% 7.75/5.70 = ( ( P @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K5 @ D4 ) ) )
% 7.75/5.70 & ( Q @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(1)
% 7.75/5.70 thf(fact_4219_inf__period_I2_J,axiom,
% 7.75/5.70 ! [P: real > $o,D4: real,Q: real > $o] :
% 7.75/5.70 ( ! [X3: real,K2: real] :
% 7.75/5.70 ( ( P @ X3 )
% 7.75/5.70 = ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ( ! [X3: real,K2: real] :
% 7.75/5.70 ( ( Q @ X3 )
% 7.75/5.70 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ! [X5: real,K5: real] :
% 7.75/5.70 ( ( ( P @ X5 )
% 7.75/5.70 | ( Q @ X5 ) )
% 7.75/5.70 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K5 @ D4 ) ) )
% 7.75/5.70 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(2)
% 7.75/5.70 thf(fact_4220_inf__period_I2_J,axiom,
% 7.75/5.70 ! [P: int > $o,D4: int,Q: int > $o] :
% 7.75/5.70 ( ! [X3: int,K2: int] :
% 7.75/5.70 ( ( P @ X3 )
% 7.75/5.70 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ( ! [X3: int,K2: int] :
% 7.75/5.70 ( ( Q @ X3 )
% 7.75/5.70 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ! [X5: int,K5: int] :
% 7.75/5.70 ( ( ( P @ X5 )
% 7.75/5.70 | ( Q @ X5 ) )
% 7.75/5.70 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K5 @ D4 ) ) )
% 7.75/5.70 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(2)
% 7.75/5.70 thf(fact_4221_inf__period_I2_J,axiom,
% 7.75/5.70 ! [P: code_integer > $o,D4: code_integer,Q: code_integer > $o] :
% 7.75/5.70 ( ! [X3: code_integer,K2: code_integer] :
% 7.75/5.70 ( ( P @ X3 )
% 7.75/5.70 = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ( ! [X3: code_integer,K2: code_integer] :
% 7.75/5.70 ( ( Q @ X3 )
% 7.75/5.70 = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ! [X5: code_integer,K5: code_integer] :
% 7.75/5.70 ( ( ( P @ X5 )
% 7.75/5.70 | ( Q @ X5 ) )
% 7.75/5.70 = ( ( P @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K5 @ D4 ) ) )
% 7.75/5.70 | ( Q @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(2)
% 7.75/5.70 thf(fact_4222_inf__period_I2_J,axiom,
% 7.75/5.70 ! [P: complex > $o,D4: complex,Q: complex > $o] :
% 7.75/5.70 ( ! [X3: complex,K2: complex] :
% 7.75/5.70 ( ( P @ X3 )
% 7.75/5.70 = ( P @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ( ! [X3: complex,K2: complex] :
% 7.75/5.70 ( ( Q @ X3 )
% 7.75/5.70 = ( Q @ ( minus_minus_complex @ X3 @ ( times_times_complex @ K2 @ D4 ) ) ) )
% 7.75/5.70 => ! [X5: complex,K5: complex] :
% 7.75/5.70 ( ( ( P @ X5 )
% 7.75/5.70 | ( Q @ X5 ) )
% 7.75/5.70 = ( ( P @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K5 @ D4 ) ) )
% 7.75/5.70 | ( Q @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(2)
% 7.75/5.70 thf(fact_4223_right__diff__distrib_H,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 7.75/5.70 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % right_diff_distrib'
% 7.75/5.70 thf(fact_4224_right__diff__distrib_H,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 7.75/5.70 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % right_diff_distrib'
% 7.75/5.70 thf(fact_4225_right__diff__distrib_H,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 7.75/5.70 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % right_diff_distrib'
% 7.75/5.70 thf(fact_4226_right__diff__distrib_H,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 7.75/5.70 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % right_diff_distrib'
% 7.75/5.70 thf(fact_4227_right__diff__distrib_H,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 7.75/5.70 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % right_diff_distrib'
% 7.75/5.70 thf(fact_4228_left__diff__distrib_H,axiom,
% 7.75/5.70 ! [B: real,C: real,A: real] :
% 7.75/5.70 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 7.75/5.70 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % left_diff_distrib'
% 7.75/5.70 thf(fact_4229_left__diff__distrib_H,axiom,
% 7.75/5.70 ! [B: nat,C: nat,A: nat] :
% 7.75/5.70 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 7.75/5.70 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % left_diff_distrib'
% 7.75/5.70 thf(fact_4230_left__diff__distrib_H,axiom,
% 7.75/5.70 ! [B: int,C: int,A: int] :
% 7.75/5.70 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 7.75/5.70 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % left_diff_distrib'
% 7.75/5.70 thf(fact_4231_left__diff__distrib_H,axiom,
% 7.75/5.70 ! [B: code_integer,C: code_integer,A: code_integer] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ C ) @ A )
% 7.75/5.70 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % left_diff_distrib'
% 7.75/5.70 thf(fact_4232_left__diff__distrib_H,axiom,
% 7.75/5.70 ! [B: complex,C: complex,A: complex] :
% 7.75/5.70 ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
% 7.75/5.70 = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % left_diff_distrib'
% 7.75/5.70 thf(fact_4233_right__diff__distrib,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 7.75/5.70 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % right_diff_distrib
% 7.75/5.70 thf(fact_4234_right__diff__distrib,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 7.75/5.70 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % right_diff_distrib
% 7.75/5.70 thf(fact_4235_right__diff__distrib,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 7.75/5.70 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % right_diff_distrib
% 7.75/5.70 thf(fact_4236_right__diff__distrib,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 7.75/5.70 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % right_diff_distrib
% 7.75/5.70 thf(fact_4237_left__diff__distrib,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % left_diff_distrib
% 7.75/5.70 thf(fact_4238_left__diff__distrib,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % left_diff_distrib
% 7.75/5.70 thf(fact_4239_left__diff__distrib,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 7.75/5.70 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % left_diff_distrib
% 7.75/5.70 thf(fact_4240_left__diff__distrib,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % left_diff_distrib
% 7.75/5.70 thf(fact_4241_verit__negate__coefficient_I2_J,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( ord_less_int @ A @ B )
% 7.75/5.70 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % verit_negate_coefficient(2)
% 7.75/5.70 thf(fact_4242_verit__negate__coefficient_I2_J,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( ord_less_real @ A @ B )
% 7.75/5.70 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % verit_negate_coefficient(2)
% 7.75/5.70 thf(fact_4243_verit__negate__coefficient_I2_J,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.70 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % verit_negate_coefficient(2)
% 7.75/5.70 thf(fact_4244_verit__negate__coefficient_I2_J,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_rat @ A @ B )
% 7.75/5.70 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % verit_negate_coefficient(2)
% 7.75/5.70 thf(fact_4245_less__minus__iff,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.70 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_iff
% 7.75/5.70 thf(fact_4246_less__minus__iff,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 7.75/5.70 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_iff
% 7.75/5.70 thf(fact_4247_less__minus__iff,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.70 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_iff
% 7.75/5.70 thf(fact_4248_less__minus__iff,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 7.75/5.70 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_iff
% 7.75/5.70 thf(fact_4249_minus__less__iff,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.70 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_less_iff
% 7.75/5.70 thf(fact_4250_minus__less__iff,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 7.75/5.70 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_less_iff
% 7.75/5.70 thf(fact_4251_minus__less__iff,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 7.75/5.70 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_less_iff
% 7.75/5.70 thf(fact_4252_minus__less__iff,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 7.75/5.70 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_less_iff
% 7.75/5.70 thf(fact_4253_numeral__neq__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( numeral_numeral_int @ M )
% 7.75/5.70 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_numeral
% 7.75/5.70 thf(fact_4254_numeral__neq__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( numeral_numeral_real @ M )
% 7.75/5.70 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_numeral
% 7.75/5.70 thf(fact_4255_numeral__neq__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( numera6620942414471956472nteger @ M )
% 7.75/5.70 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_numeral
% 7.75/5.70 thf(fact_4256_numeral__neq__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( numera6690914467698888265omplex @ M )
% 7.75/5.70 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_numeral
% 7.75/5.70 thf(fact_4257_numeral__neq__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( numeral_numeral_rat @ M )
% 7.75/5.70 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_numeral
% 7.75/5.70 thf(fact_4258_neg__numeral__neq__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 7.75/5.70 != ( numeral_numeral_int @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_neq_numeral
% 7.75/5.70 thf(fact_4259_neg__numeral__neq__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 7.75/5.70 != ( numeral_numeral_real @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_neq_numeral
% 7.75/5.70 thf(fact_4260_neg__numeral__neq__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 7.75/5.70 != ( numera6620942414471956472nteger @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_neq_numeral
% 7.75/5.70 thf(fact_4261_neg__numeral__neq__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 7.75/5.70 != ( numera6690914467698888265omplex @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_neq_numeral
% 7.75/5.70 thf(fact_4262_neg__numeral__neq__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 7.75/5.70 != ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_neq_numeral
% 7.75/5.70 thf(fact_4263_is__num__normalize_I8_J,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 7.75/5.70 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % is_num_normalize(8)
% 7.75/5.70 thf(fact_4264_is__num__normalize_I8_J,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 7.75/5.70 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % is_num_normalize(8)
% 7.75/5.70 thf(fact_4265_is__num__normalize_I8_J,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 7.75/5.70 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % is_num_normalize(8)
% 7.75/5.70 thf(fact_4266_is__num__normalize_I8_J,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 7.75/5.70 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % is_num_normalize(8)
% 7.75/5.70 thf(fact_4267_is__num__normalize_I8_J,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.70 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % is_num_normalize(8)
% 7.75/5.70 thf(fact_4268_group__cancel_Oneg1,axiom,
% 7.75/5.70 ! [A2: int,K: int,A: int] :
% 7.75/5.70 ( ( A2
% 7.75/5.70 = ( plus_plus_int @ K @ A ) )
% 7.75/5.70 => ( ( uminus_uminus_int @ A2 )
% 7.75/5.70 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % group_cancel.neg1
% 7.75/5.70 thf(fact_4269_group__cancel_Oneg1,axiom,
% 7.75/5.70 ! [A2: real,K: real,A: real] :
% 7.75/5.70 ( ( A2
% 7.75/5.70 = ( plus_plus_real @ K @ A ) )
% 7.75/5.70 => ( ( uminus_uminus_real @ A2 )
% 7.75/5.70 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % group_cancel.neg1
% 7.75/5.70 thf(fact_4270_group__cancel_Oneg1,axiom,
% 7.75/5.70 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 7.75/5.70 ( ( A2
% 7.75/5.70 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 7.75/5.70 => ( ( uminus1351360451143612070nteger @ A2 )
% 7.75/5.70 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % group_cancel.neg1
% 7.75/5.70 thf(fact_4271_group__cancel_Oneg1,axiom,
% 7.75/5.70 ! [A2: complex,K: complex,A: complex] :
% 7.75/5.70 ( ( A2
% 7.75/5.70 = ( plus_plus_complex @ K @ A ) )
% 7.75/5.70 => ( ( uminus1482373934393186551omplex @ A2 )
% 7.75/5.70 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % group_cancel.neg1
% 7.75/5.70 thf(fact_4272_group__cancel_Oneg1,axiom,
% 7.75/5.70 ! [A2: rat,K: rat,A: rat] :
% 7.75/5.70 ( ( A2
% 7.75/5.70 = ( plus_plus_rat @ K @ A ) )
% 7.75/5.70 => ( ( uminus_uminus_rat @ A2 )
% 7.75/5.70 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % group_cancel.neg1
% 7.75/5.70 thf(fact_4273_add_Oinverse__distrib__swap,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 7.75/5.70 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_distrib_swap
% 7.75/5.70 thf(fact_4274_add_Oinverse__distrib__swap,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 7.75/5.70 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_distrib_swap
% 7.75/5.70 thf(fact_4275_add_Oinverse__distrib__swap,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 7.75/5.70 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_distrib_swap
% 7.75/5.70 thf(fact_4276_add_Oinverse__distrib__swap,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 7.75/5.70 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_distrib_swap
% 7.75/5.70 thf(fact_4277_add_Oinverse__distrib__swap,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.70 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_distrib_swap
% 7.75/5.70 thf(fact_4278_one__neq__neg__one,axiom,
% 7.75/5.70 ( one_one_int
% 7.75/5.70 != ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_one
% 7.75/5.70 thf(fact_4279_one__neq__neg__one,axiom,
% 7.75/5.70 ( one_one_real
% 7.75/5.70 != ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_one
% 7.75/5.70 thf(fact_4280_one__neq__neg__one,axiom,
% 7.75/5.70 ( one_one_Code_integer
% 7.75/5.70 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_one
% 7.75/5.70 thf(fact_4281_one__neq__neg__one,axiom,
% 7.75/5.70 ( one_one_complex
% 7.75/5.70 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_one
% 7.75/5.70 thf(fact_4282_one__neq__neg__one,axiom,
% 7.75/5.70 ( one_one_rat
% 7.75/5.70 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_one
% 7.75/5.70 thf(fact_4283_minus__mult__commute,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.70 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mult_commute
% 7.75/5.70 thf(fact_4284_minus__mult__commute,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 7.75/5.70 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mult_commute
% 7.75/5.70 thf(fact_4285_minus__mult__commute,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 7.75/5.70 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mult_commute
% 7.75/5.70 thf(fact_4286_minus__mult__commute,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 7.75/5.70 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mult_commute
% 7.75/5.70 thf(fact_4287_minus__mult__commute,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 7.75/5.70 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mult_commute
% 7.75/5.70 thf(fact_4288_square__eq__iff,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( ( times_times_int @ A @ A )
% 7.75/5.70 = ( times_times_int @ B @ B ) )
% 7.75/5.70 = ( ( A = B )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus_uminus_int @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_iff
% 7.75/5.70 thf(fact_4289_square__eq__iff,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( ( times_times_real @ A @ A )
% 7.75/5.70 = ( times_times_real @ B @ B ) )
% 7.75/5.70 = ( ( A = B )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus_uminus_real @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_iff
% 7.75/5.70 thf(fact_4290_square__eq__iff,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ( times_3573771949741848930nteger @ A @ A )
% 7.75/5.70 = ( times_3573771949741848930nteger @ B @ B ) )
% 7.75/5.70 = ( ( A = B )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_iff
% 7.75/5.70 thf(fact_4291_square__eq__iff,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( ( times_times_complex @ A @ A )
% 7.75/5.70 = ( times_times_complex @ B @ B ) )
% 7.75/5.70 = ( ( A = B )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_iff
% 7.75/5.70 thf(fact_4292_square__eq__iff,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( ( times_times_rat @ A @ A )
% 7.75/5.70 = ( times_times_rat @ B @ B ) )
% 7.75/5.70 = ( ( A = B )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_iff
% 7.75/5.70 thf(fact_4293_diff__divide__distrib,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_divide_distrib
% 7.75/5.70 thf(fact_4294_diff__divide__distrib,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_divide_distrib
% 7.75/5.70 thf(fact_4295_diff__divide__distrib,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 7.75/5.70 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_divide_distrib
% 7.75/5.70 thf(fact_4296_div__minus__right,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.70 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_minus_right
% 7.75/5.70 thf(fact_4297_div__minus__right,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.70 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_minus_right
% 7.75/5.70 thf(fact_4298_minus__divide__left,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.70 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_left
% 7.75/5.70 thf(fact_4299_minus__divide__left,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_left
% 7.75/5.70 thf(fact_4300_minus__divide__left,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 7.75/5.70 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_left
% 7.75/5.70 thf(fact_4301_minus__divide__divide,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 7.75/5.70 = ( divide_divide_real @ A @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_divide
% 7.75/5.70 thf(fact_4302_minus__divide__divide,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_divide
% 7.75/5.70 thf(fact_4303_minus__divide__divide,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 7.75/5.70 = ( divide_divide_rat @ A @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_divide
% 7.75/5.70 thf(fact_4304_minus__divide__right,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.70 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_right
% 7.75/5.70 thf(fact_4305_minus__divide__right,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_right
% 7.75/5.70 thf(fact_4306_minus__divide__right,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 7.75/5.70 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_right
% 7.75/5.70 thf(fact_4307_verit__eq__simplify_I14_J,axiom,
% 7.75/5.70 ! [X22: num,X32: num] :
% 7.75/5.70 ( ( bit0 @ X22 )
% 7.75/5.70 != ( bit1 @ X32 ) ) ).
% 7.75/5.70
% 7.75/5.70 % verit_eq_simplify(14)
% 7.75/5.70 thf(fact_4308_verit__eq__simplify_I12_J,axiom,
% 7.75/5.70 ! [X32: num] :
% 7.75/5.70 ( one
% 7.75/5.70 != ( bit1 @ X32 ) ) ).
% 7.75/5.70
% 7.75/5.70 % verit_eq_simplify(12)
% 7.75/5.70 thf(fact_4309_dvd__diff__commute,axiom,
% 7.75/5.70 ! [A: int,C: int,B: int] :
% 7.75/5.70 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 7.75/5.70 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_diff_commute
% 7.75/5.70 thf(fact_4310_dvd__diff,axiom,
% 7.75/5.70 ! [X: complex,Y: complex,Z: complex] :
% 7.75/5.70 ( ( dvd_dvd_complex @ X @ Y )
% 7.75/5.70 => ( ( dvd_dvd_complex @ X @ Z )
% 7.75/5.70 => ( dvd_dvd_complex @ X @ ( minus_minus_complex @ Y @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_diff
% 7.75/5.70 thf(fact_4311_dvd__diff,axiom,
% 7.75/5.70 ! [X: real,Y: real,Z: real] :
% 7.75/5.70 ( ( dvd_dvd_real @ X @ Y )
% 7.75/5.70 => ( ( dvd_dvd_real @ X @ Z )
% 7.75/5.70 => ( dvd_dvd_real @ X @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_diff
% 7.75/5.70 thf(fact_4312_dvd__diff,axiom,
% 7.75/5.70 ! [X: int,Y: int,Z: int] :
% 7.75/5.70 ( ( dvd_dvd_int @ X @ Y )
% 7.75/5.70 => ( ( dvd_dvd_int @ X @ Z )
% 7.75/5.70 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_diff
% 7.75/5.70 thf(fact_4313_zero__induct__lemma,axiom,
% 7.75/5.70 ! [P: nat > $o,K: nat,I: nat] :
% 7.75/5.70 ( ( P @ K )
% 7.75/5.70 => ( ! [N2: nat] :
% 7.75/5.70 ( ( P @ ( suc @ N2 ) )
% 7.75/5.70 => ( P @ N2 ) )
% 7.75/5.70 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_induct_lemma
% 7.75/5.70 thf(fact_4314_Suc__diff__le,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 7.75/5.70 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Suc_diff_le
% 7.75/5.70 thf(fact_4315_mod__diff__right__eq,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 7.75/5.70 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_diff_right_eq
% 7.75/5.70 thf(fact_4316_mod__diff__right__eq,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.70 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_diff_right_eq
% 7.75/5.70 thf(fact_4317_mod__diff__left__eq,axiom,
% 7.75/5.70 ! [A: int,C: int,B: int] :
% 7.75/5.70 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 7.75/5.70 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_diff_left_eq
% 7.75/5.70 thf(fact_4318_mod__diff__left__eq,axiom,
% 7.75/5.70 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.70 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_diff_left_eq
% 7.75/5.70 thf(fact_4319_mod__diff__cong,axiom,
% 7.75/5.70 ! [A: int,C: int,A4: int,B: int,B6: int] :
% 7.75/5.70 ( ( ( modulo_modulo_int @ A @ C )
% 7.75/5.70 = ( modulo_modulo_int @ A4 @ C ) )
% 7.75/5.70 => ( ( ( modulo_modulo_int @ B @ C )
% 7.75/5.70 = ( modulo_modulo_int @ B6 @ C ) )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 7.75/5.70 = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B6 ) @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_diff_cong
% 7.75/5.70 thf(fact_4320_mod__diff__cong,axiom,
% 7.75/5.70 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B6: code_integer] :
% 7.75/5.70 ( ( ( modulo364778990260209775nteger @ A @ C )
% 7.75/5.70 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 7.75/5.70 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 7.75/5.70 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 7.75/5.70 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B6 ) @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_diff_cong
% 7.75/5.70 thf(fact_4321_mod__diff__eq,axiom,
% 7.75/5.70 ! [A: int,C: int,B: int] :
% 7.75/5.70 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 7.75/5.70 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_diff_eq
% 7.75/5.70 thf(fact_4322_mod__diff__eq,axiom,
% 7.75/5.70 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.70 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_diff_eq
% 7.75/5.70 thf(fact_4323_diffs0__imp__equal,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ( minus_minus_nat @ M @ N )
% 7.75/5.70 = zero_zero_nat )
% 7.75/5.70 => ( ( ( minus_minus_nat @ N @ M )
% 7.75/5.70 = zero_zero_nat )
% 7.75/5.70 => ( M = N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diffs0_imp_equal
% 7.75/5.70 thf(fact_4324_minus__nat_Odiff__0,axiom,
% 7.75/5.70 ! [M: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 7.75/5.70 = M ) ).
% 7.75/5.70
% 7.75/5.70 % minus_nat.diff_0
% 7.75/5.70 thf(fact_4325_mod__minus__right,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.70 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_minus_right
% 7.75/5.70 thf(fact_4326_mod__minus__right,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.70 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_minus_right
% 7.75/5.70 thf(fact_4327_euclidean__ring__cancel__class_Omod__minus__cong,axiom,
% 7.75/5.70 ! [A: int,B: int,A4: int] :
% 7.75/5.70 ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.70 = ( modulo_modulo_int @ A4 @ B ) )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.70 = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % euclidean_ring_cancel_class.mod_minus_cong
% 7.75/5.70 thf(fact_4328_euclidean__ring__cancel__class_Omod__minus__cong,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer,A4: code_integer] :
% 7.75/5.70 ( ( ( modulo364778990260209775nteger @ A @ B )
% 7.75/5.70 = ( modulo364778990260209775nteger @ A4 @ B ) )
% 7.75/5.70 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % euclidean_ring_cancel_class.mod_minus_cong
% 7.75/5.70 thf(fact_4329_mod__minus__eq,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 7.75/5.70 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_minus_eq
% 7.75/5.70 thf(fact_4330_mod__minus__eq,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_minus_eq
% 7.75/5.70 thf(fact_4331_diff__diff__less,axiom,
% 7.75/5.70 ! [I: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_nat @ I @ ( minus_minus_nat @ M @ ( minus_minus_nat @ M @ N ) ) )
% 7.75/5.70 = ( ( ord_less_nat @ I @ M )
% 7.75/5.70 & ( ord_less_nat @ I @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_diff_less
% 7.75/5.70 thf(fact_4332_less__imp__diff__less,axiom,
% 7.75/5.70 ! [J: nat,K: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_nat @ J @ K )
% 7.75/5.70 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_imp_diff_less
% 7.75/5.70 thf(fact_4333_diff__less__mono2,axiom,
% 7.75/5.70 ! [M: nat,N: nat,L: nat] :
% 7.75/5.70 ( ( ord_less_nat @ M @ N )
% 7.75/5.70 => ( ( ord_less_nat @ M @ L )
% 7.75/5.70 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_less_mono2
% 7.75/5.70 thf(fact_4334_diff__less__mono,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( ord_less_nat @ A @ B )
% 7.75/5.70 => ( ( ord_less_eq_nat @ C @ A )
% 7.75/5.70 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_less_mono
% 7.75/5.70 thf(fact_4335_less__diff__iff,axiom,
% 7.75/5.70 ! [K: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ M )
% 7.75/5.70 => ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.70 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 7.75/5.70 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_diff_iff
% 7.75/5.70 thf(fact_4336_minus__int__code_I1_J,axiom,
% 7.75/5.70 ! [K: int] :
% 7.75/5.70 ( ( minus_minus_int @ K @ zero_zero_int )
% 7.75/5.70 = K ) ).
% 7.75/5.70
% 7.75/5.70 % minus_int_code(1)
% 7.75/5.70 thf(fact_4337_Nat_Odiff__cancel,axiom,
% 7.75/5.70 ! [K: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 7.75/5.70 = ( minus_minus_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % Nat.diff_cancel
% 7.75/5.70 thf(fact_4338_diff__cancel2,axiom,
% 7.75/5.70 ! [M: nat,K: nat,N: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 7.75/5.70 = ( minus_minus_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_cancel2
% 7.75/5.70 thf(fact_4339_diff__add__inverse,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 7.75/5.70 = M ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_inverse
% 7.75/5.70 thf(fact_4340_diff__add__inverse2,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 7.75/5.70 = M ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_inverse2
% 7.75/5.70 thf(fact_4341_Nat_Ole__imp__diff__is__add,axiom,
% 7.75/5.70 ! [I: nat,J: nat,K: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.70 => ( ( ( minus_minus_nat @ J @ I )
% 7.75/5.70 = K )
% 7.75/5.70 = ( J
% 7.75/5.70 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Nat.le_imp_diff_is_add
% 7.75/5.70 thf(fact_4342_Nat_Odiff__add__assoc2,axiom,
% 7.75/5.70 ! [K: nat,J: nat,I: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ J )
% 7.75/5.70 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 7.75/5.70 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Nat.diff_add_assoc2
% 7.75/5.70 thf(fact_4343_Nat_Odiff__add__assoc,axiom,
% 7.75/5.70 ! [K: nat,J: nat,I: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ J )
% 7.75/5.70 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 7.75/5.70 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Nat.diff_add_assoc
% 7.75/5.70 thf(fact_4344_Nat_Ole__diff__conv2,axiom,
% 7.75/5.70 ! [K: nat,J: nat,I: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ J )
% 7.75/5.70 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 7.75/5.70 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Nat.le_diff_conv2
% 7.75/5.70 thf(fact_4345_le__diff__conv,axiom,
% 7.75/5.70 ! [J: nat,K: nat,I: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 7.75/5.70 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_diff_conv
% 7.75/5.70 thf(fact_4346_uminus__int__code_I1_J,axiom,
% 7.75/5.70 ( ( uminus_uminus_int @ zero_zero_int )
% 7.75/5.70 = zero_zero_int ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_int_code(1)
% 7.75/5.70 thf(fact_4347_diff__mult__distrib2,axiom,
% 7.75/5.70 ! [K: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_mult_distrib2
% 7.75/5.70 thf(fact_4348_diff__mult__distrib,axiom,
% 7.75/5.70 ! [M: nat,N: nat,K: nat] :
% 7.75/5.70 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 7.75/5.70 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_mult_distrib
% 7.75/5.70 thf(fact_4349_Word_Omod__minus__cong,axiom,
% 7.75/5.70 ! [B: int,B6: int,X: int,X6: int,Y: int,Y5: int,Z5: int] :
% 7.75/5.70 ( ( B = B6 )
% 7.75/5.70 => ( ( ( modulo_modulo_int @ X @ B6 )
% 7.75/5.70 = ( modulo_modulo_int @ X6 @ B6 ) )
% 7.75/5.70 => ( ( ( modulo_modulo_int @ Y @ B6 )
% 7.75/5.70 = ( modulo_modulo_int @ Y5 @ B6 ) )
% 7.75/5.70 => ( ( ( minus_minus_int @ X6 @ Y5 )
% 7.75/5.70 = Z5 )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( minus_minus_int @ X @ Y ) @ B )
% 7.75/5.70 = ( modulo_modulo_int @ Z5 @ B6 ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Word.mod_minus_cong
% 7.75/5.70 thf(fact_4350_dvd__diff__nat,axiom,
% 7.75/5.70 ! [K: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_nat @ K @ M )
% 7.75/5.70 => ( ( dvd_dvd_nat @ K @ N )
% 7.75/5.70 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_diff_nat
% 7.75/5.70 thf(fact_4351_dvd__diffD,axiom,
% 7.75/5.70 ! [K: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 => ( ( dvd_dvd_nat @ K @ N )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_diffD
% 7.75/5.70 thf(fact_4352_dvd__diffD1,axiom,
% 7.75/5.70 ! [K: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 => ( ( dvd_dvd_nat @ K @ M )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_diffD1
% 7.75/5.70 thf(fact_4353_less__eq__dvd__minus,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.70 => ( ( dvd_dvd_nat @ M @ N )
% 7.75/5.70 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_eq_dvd_minus
% 7.75/5.70 thf(fact_4354_le__mod__geq,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( modulo_modulo_nat @ M @ N )
% 7.75/5.70 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_mod_geq
% 7.75/5.70 thf(fact_4355_uminus__dvd__conv_I1_J,axiom,
% 7.75/5.70 ( dvd_dvd_int
% 7.75/5.70 = ( ^ [D: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_dvd_conv(1)
% 7.75/5.70 thf(fact_4356_uminus__dvd__conv_I2_J,axiom,
% 7.75/5.70 ( dvd_dvd_int
% 7.75/5.70 = ( ^ [D: int,T2: int] : ( dvd_dvd_int @ D @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_dvd_conv(2)
% 7.75/5.70 thf(fact_4357_minus__divide__diff__eq__iff,axiom,
% 7.75/5.70 ! [Z: real,X: real,Y: real] :
% 7.75/5.70 ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 7.75/5.70 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_diff_eq_iff
% 7.75/5.70 thf(fact_4358_minus__divide__diff__eq__iff,axiom,
% 7.75/5.70 ! [Z: complex,X: complex,Y: complex] :
% 7.75/5.70 ( ( Z != zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_diff_eq_iff
% 7.75/5.70 thf(fact_4359_minus__divide__diff__eq__iff,axiom,
% 7.75/5.70 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.70 ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 7.75/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_diff_eq_iff
% 7.75/5.70 thf(fact_4360_add__divide__eq__if__simps_I5_J,axiom,
% 7.75/5.70 ! [Z: real,A: real,B: real] :
% 7.75/5.70 ( ( ( Z = zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 7.75/5.70 = ( uminus_uminus_real @ B ) ) )
% 7.75/5.70 & ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 7.75/5.70 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(5)
% 7.75/5.70 thf(fact_4361_add__divide__eq__if__simps_I5_J,axiom,
% 7.75/5.70 ! [Z: complex,A: complex,B: complex] :
% 7.75/5.70 ( ( ( Z = zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ B ) ) )
% 7.75/5.70 & ( ( Z != zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(5)
% 7.75/5.70 thf(fact_4362_add__divide__eq__if__simps_I5_J,axiom,
% 7.75/5.70 ! [Z: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( ( Z = zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 7.75/5.70 = ( uminus_uminus_rat @ B ) ) )
% 7.75/5.70 & ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 7.75/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(5)
% 7.75/5.70 thf(fact_4363_add__divide__eq__if__simps_I6_J,axiom,
% 7.75/5.70 ! [Z: real,A: real,B: real] :
% 7.75/5.70 ( ( ( Z = zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 7.75/5.70 = ( uminus_uminus_real @ B ) ) )
% 7.75/5.70 & ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 7.75/5.70 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(6)
% 7.75/5.70 thf(fact_4364_add__divide__eq__if__simps_I6_J,axiom,
% 7.75/5.70 ! [Z: complex,A: complex,B: complex] :
% 7.75/5.70 ( ( ( Z = zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ B ) ) )
% 7.75/5.70 & ( ( Z != zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(6)
% 7.75/5.70 thf(fact_4365_add__divide__eq__if__simps_I6_J,axiom,
% 7.75/5.70 ! [Z: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( ( Z = zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 7.75/5.70 = ( uminus_uminus_rat @ B ) ) )
% 7.75/5.70 & ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 7.75/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(6)
% 7.75/5.70 thf(fact_4366_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 7.75/5.70 ! [K: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.70 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 7.75/5.70 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_power_add_eq_neg_one_power_diff
% 7.75/5.70 thf(fact_4367_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 7.75/5.70 ! [K: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.70 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 7.75/5.70 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_power_add_eq_neg_one_power_diff
% 7.75/5.70 thf(fact_4368_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 7.75/5.70 ! [K: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.70 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 7.75/5.70 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_power_add_eq_neg_one_power_diff
% 7.75/5.70 thf(fact_4369_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 7.75/5.70 ! [K: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.70 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 7.75/5.70 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_power_add_eq_neg_one_power_diff
% 7.75/5.70 thf(fact_4370_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 7.75/5.70 ! [K: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.70 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 7.75/5.70 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_power_add_eq_neg_one_power_diff
% 7.75/5.70 thf(fact_4371_field__char__0__class_Oof__nat__div,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 7.75/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % field_char_0_class.of_nat_div
% 7.75/5.70 thf(fact_4372_field__char__0__class_Oof__nat__div,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 7.75/5.70 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % field_char_0_class.of_nat_div
% 7.75/5.70 thf(fact_4373_field__char__0__class_Oof__nat__div,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % field_char_0_class.of_nat_div
% 7.75/5.70 thf(fact_4374_of__nat__0__le__iff,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_0_le_iff
% 7.75/5.70 thf(fact_4375_of__nat__0__le__iff,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_0_le_iff
% 7.75/5.70 thf(fact_4376_of__nat__0__le__iff,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_0_le_iff
% 7.75/5.70 thf(fact_4377_of__nat__0__le__iff,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_0_le_iff
% 7.75/5.70 thf(fact_4378_of__nat__less__0__iff,axiom,
% 7.75/5.70 ! [M: nat] :
% 7.75/5.70 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_0_iff
% 7.75/5.70 thf(fact_4379_of__nat__less__0__iff,axiom,
% 7.75/5.70 ! [M: nat] :
% 7.75/5.70 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_0_iff
% 7.75/5.70 thf(fact_4380_of__nat__less__0__iff,axiom,
% 7.75/5.70 ! [M: nat] :
% 7.75/5.70 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_0_iff
% 7.75/5.70 thf(fact_4381_of__nat__less__0__iff,axiom,
% 7.75/5.70 ! [M: nat] :
% 7.75/5.70 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_0_iff
% 7.75/5.70 thf(fact_4382_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 7.75/5.70 != zero_zero_rat ) ).
% 7.75/5.70
% 7.75/5.70 % semiring_char_0_class.of_nat_neq_0
% 7.75/5.70 thf(fact_4383_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 7.75/5.70 != zero_zero_real ) ).
% 7.75/5.70
% 7.75/5.70 % semiring_char_0_class.of_nat_neq_0
% 7.75/5.70 thf(fact_4384_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 7.75/5.70 != zero_zero_int ) ).
% 7.75/5.70
% 7.75/5.70 % semiring_char_0_class.of_nat_neq_0
% 7.75/5.70 thf(fact_4385_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 7.75/5.70 != zero_zero_nat ) ).
% 7.75/5.70
% 7.75/5.70 % semiring_char_0_class.of_nat_neq_0
% 7.75/5.70 thf(fact_4386_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 7.75/5.70 != zero_zero_complex ) ).
% 7.75/5.70
% 7.75/5.70 % semiring_char_0_class.of_nat_neq_0
% 7.75/5.70 thf(fact_4387_of__nat__less__imp__less,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 7.75/5.70 => ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_imp_less
% 7.75/5.70 thf(fact_4388_of__nat__less__imp__less,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.70 => ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_imp_less
% 7.75/5.70 thf(fact_4389_of__nat__less__imp__less,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.70 => ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_imp_less
% 7.75/5.70 thf(fact_4390_of__nat__less__imp__less,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 7.75/5.70 => ( ord_less_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_imp_less
% 7.75/5.70 thf(fact_4391_less__imp__of__nat__less,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_nat @ M @ N )
% 7.75/5.70 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_imp_of_nat_less
% 7.75/5.70 thf(fact_4392_less__imp__of__nat__less,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_nat @ M @ N )
% 7.75/5.70 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_imp_of_nat_less
% 7.75/5.70 thf(fact_4393_less__imp__of__nat__less,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_nat @ M @ N )
% 7.75/5.70 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_imp_of_nat_less
% 7.75/5.70 thf(fact_4394_less__imp__of__nat__less,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_nat @ M @ N )
% 7.75/5.70 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_imp_of_nat_less
% 7.75/5.70 thf(fact_4395_div__mult2__eq_H,axiom,
% 7.75/5.70 ! [A: code_integer,M: nat,N: nat] :
% 7.75/5.70 ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 7.75/5.70 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_mult2_eq'
% 7.75/5.70 thf(fact_4396_div__mult2__eq_H,axiom,
% 7.75/5.70 ! [A: int,M: nat,N: nat] :
% 7.75/5.70 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 7.75/5.70 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_mult2_eq'
% 7.75/5.70 thf(fact_4397_div__mult2__eq_H,axiom,
% 7.75/5.70 ! [A: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 7.75/5.70 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_mult2_eq'
% 7.75/5.70 thf(fact_4398_minus__mod__int__eq,axiom,
% 7.75/5.70 ! [L: int,K: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 7.75/5.70 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mod_int_eq
% 7.75/5.70 thf(fact_4399_zmod__minus1,axiom,
% 7.75/5.70 ! [B: int] :
% 7.75/5.70 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 7.75/5.70 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zmod_minus1
% 7.75/5.70 thf(fact_4400_Abs__fnat__hom__add,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( plus_plus_rat @ ( semiri681578069525770553at_rat @ A ) @ ( semiri681578069525770553at_rat @ B ) )
% 7.75/5.70 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Abs_fnat_hom_add
% 7.75/5.70 thf(fact_4401_Abs__fnat__hom__add,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( plus_plus_real @ ( semiri5074537144036343181t_real @ A ) @ ( semiri5074537144036343181t_real @ B ) )
% 7.75/5.70 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Abs_fnat_hom_add
% 7.75/5.70 thf(fact_4402_Abs__fnat__hom__add,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 7.75/5.70 = ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Abs_fnat_hom_add
% 7.75/5.70 thf(fact_4403_Abs__fnat__hom__add,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ A ) @ ( semiri1316708129612266289at_nat @ B ) )
% 7.75/5.70 = ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Abs_fnat_hom_add
% 7.75/5.70 thf(fact_4404_Abs__fnat__hom__add,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( plus_plus_complex @ ( semiri8010041392384452111omplex @ A ) @ ( semiri8010041392384452111omplex @ B ) )
% 7.75/5.70 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Abs_fnat_hom_add
% 7.75/5.70 thf(fact_4405_le__iff__diff__le__0,axiom,
% 7.75/5.70 ( ord_less_eq_real
% 7.75/5.70 = ( ^ [A3: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B4 ) @ zero_zero_real ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_iff_diff_le_0
% 7.75/5.70 thf(fact_4406_le__iff__diff__le__0,axiom,
% 7.75/5.70 ( ord_less_eq_rat
% 7.75/5.70 = ( ^ [A3: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B4 ) @ zero_zero_rat ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_iff_diff_le_0
% 7.75/5.70 thf(fact_4407_le__iff__diff__le__0,axiom,
% 7.75/5.70 ( ord_less_eq_int
% 7.75/5.70 = ( ^ [A3: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B4 ) @ zero_zero_int ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_iff_diff_le_0
% 7.75/5.70 thf(fact_4408_less__iff__diff__less__0,axiom,
% 7.75/5.70 ( ord_less_real
% 7.75/5.70 = ( ^ [A3: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B4 ) @ zero_zero_real ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_iff_diff_less_0
% 7.75/5.70 thf(fact_4409_less__iff__diff__less__0,axiom,
% 7.75/5.70 ( ord_less_rat
% 7.75/5.70 = ( ^ [A3: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B4 ) @ zero_zero_rat ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_iff_diff_less_0
% 7.75/5.70 thf(fact_4410_less__iff__diff__less__0,axiom,
% 7.75/5.70 ( ord_less_int
% 7.75/5.70 = ( ^ [A3: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B4 ) @ zero_zero_int ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_iff_diff_less_0
% 7.75/5.70 thf(fact_4411_add__le__imp__le__diff,axiom,
% 7.75/5.70 ! [I: real,K: real,N: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 7.75/5.70 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_le_imp_le_diff
% 7.75/5.70 thf(fact_4412_add__le__imp__le__diff,axiom,
% 7.75/5.70 ! [I: rat,K: rat,N: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 7.75/5.70 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_le_imp_le_diff
% 7.75/5.70 thf(fact_4413_add__le__imp__le__diff,axiom,
% 7.75/5.70 ! [I: nat,K: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 7.75/5.70 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_le_imp_le_diff
% 7.75/5.70 thf(fact_4414_add__le__imp__le__diff,axiom,
% 7.75/5.70 ! [I: int,K: int,N: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 7.75/5.70 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_le_imp_le_diff
% 7.75/5.70 thf(fact_4415_add__le__add__imp__diff__le,axiom,
% 7.75/5.70 ! [I: real,K: real,N: real,J: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 7.75/5.70 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 7.75/5.70 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 7.75/5.70 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 7.75/5.70 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_le_add_imp_diff_le
% 7.75/5.70 thf(fact_4416_add__le__add__imp__diff__le,axiom,
% 7.75/5.70 ! [I: rat,K: rat,N: rat,J: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 7.75/5.70 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 7.75/5.70 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 7.75/5.70 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 7.75/5.70 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_le_add_imp_diff_le
% 7.75/5.70 thf(fact_4417_add__le__add__imp__diff__le,axiom,
% 7.75/5.70 ! [I: nat,K: nat,N: nat,J: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 7.75/5.70 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 7.75/5.70 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_le_add_imp_diff_le
% 7.75/5.70 thf(fact_4418_add__le__add__imp__diff__le,axiom,
% 7.75/5.70 ! [I: int,K: int,N: int,J: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 7.75/5.70 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 7.75/5.70 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 7.75/5.70 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 7.75/5.70 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_le_add_imp_diff_le
% 7.75/5.70 thf(fact_4419_diff__le__eq,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 7.75/5.70 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_le_eq
% 7.75/5.70 thf(fact_4420_diff__le__eq,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 7.75/5.70 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_le_eq
% 7.75/5.70 thf(fact_4421_diff__le__eq,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 7.75/5.70 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_le_eq
% 7.75/5.70 thf(fact_4422_le__diff__eq,axiom,
% 7.75/5.70 ! [A: real,C: real,B: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 7.75/5.70 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_diff_eq
% 7.75/5.70 thf(fact_4423_le__diff__eq,axiom,
% 7.75/5.70 ! [A: rat,C: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 7.75/5.70 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_diff_eq
% 7.75/5.70 thf(fact_4424_le__diff__eq,axiom,
% 7.75/5.70 ! [A: int,C: int,B: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 7.75/5.70 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_diff_eq
% 7.75/5.70 thf(fact_4425_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 7.75/5.70 = B ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_cancel_comm_monoid_diff_class.diff_add
% 7.75/5.70 thf(fact_4426_le__add__diff,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_add_diff
% 7.75/5.70 thf(fact_4427_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 7.75/5.70 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 7.75/5.70 thf(fact_4428_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 7.75/5.70 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 7.75/5.70 thf(fact_4429_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 7.75/5.70 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 7.75/5.70 thf(fact_4430_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 7.75/5.70 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 7.75/5.70 thf(fact_4431_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 7.75/5.70 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 7.75/5.70 thf(fact_4432_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 7.75/5.70 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 7.75/5.70 thf(fact_4433_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 7.75/5.70 = B ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 7.75/5.70 thf(fact_4434_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 7.75/5.70 ! [A: nat,B: nat,C: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( ord_less_eq_nat @ A @ B )
% 7.75/5.70 => ( ( ( minus_minus_nat @ B @ A )
% 7.75/5.70 = C )
% 7.75/5.70 = ( B
% 7.75/5.70 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 7.75/5.70 thf(fact_4435_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ~ ( ord_less_real @ A @ B )
% 7.75/5.70 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 7.75/5.70 = A ) ) ).
% 7.75/5.70
% 7.75/5.70 % linordered_semidom_class.add_diff_inverse
% 7.75/5.70 thf(fact_4436_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ~ ( ord_less_rat @ A @ B )
% 7.75/5.70 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 7.75/5.70 = A ) ) ).
% 7.75/5.70
% 7.75/5.70 % linordered_semidom_class.add_diff_inverse
% 7.75/5.70 thf(fact_4437_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ~ ( ord_less_nat @ A @ B )
% 7.75/5.70 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 7.75/5.70 = A ) ) ).
% 7.75/5.70
% 7.75/5.70 % linordered_semidom_class.add_diff_inverse
% 7.75/5.70 thf(fact_4438_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ~ ( ord_less_int @ A @ B )
% 7.75/5.70 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 7.75/5.70 = A ) ) ).
% 7.75/5.70
% 7.75/5.70 % linordered_semidom_class.add_diff_inverse
% 7.75/5.70 thf(fact_4439_diff__less__eq,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 7.75/5.70 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_less_eq
% 7.75/5.70 thf(fact_4440_diff__less__eq,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 7.75/5.70 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_less_eq
% 7.75/5.70 thf(fact_4441_diff__less__eq,axiom,
% 7.75/5.70 ! [A: int,B: int,C: int] :
% 7.75/5.70 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 7.75/5.70 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_less_eq
% 7.75/5.70 thf(fact_4442_less__diff__eq,axiom,
% 7.75/5.70 ! [A: real,C: real,B: real] :
% 7.75/5.70 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 7.75/5.70 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_diff_eq
% 7.75/5.70 thf(fact_4443_less__diff__eq,axiom,
% 7.75/5.70 ! [A: rat,C: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 7.75/5.70 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_diff_eq
% 7.75/5.70 thf(fact_4444_less__diff__eq,axiom,
% 7.75/5.70 ! [A: int,C: int,B: int] :
% 7.75/5.70 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 7.75/5.70 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_diff_eq
% 7.75/5.70 thf(fact_4445_zdiv__zminus2__eq__if,axiom,
% 7.75/5.70 ! [B: int,A: int] :
% 7.75/5.70 ( ( B != zero_zero_int )
% 7.75/5.70 => ( ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.70 = zero_zero_int )
% 7.75/5.70 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.70 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 7.75/5.70 & ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.70 != zero_zero_int )
% 7.75/5.70 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.70 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zdiv_zminus2_eq_if
% 7.75/5.70 thf(fact_4446_zdiv__zminus1__eq__if,axiom,
% 7.75/5.70 ! [B: int,A: int] :
% 7.75/5.70 ( ( B != zero_zero_int )
% 7.75/5.70 => ( ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.70 = zero_zero_int )
% 7.75/5.70 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.70 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 7.75/5.70 & ( ( ( modulo_modulo_int @ A @ B )
% 7.75/5.70 != zero_zero_int )
% 7.75/5.70 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.70 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zdiv_zminus1_eq_if
% 7.75/5.70 thf(fact_4447_zero__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( zero_zero_int
% 7.75/5.70 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_numeral
% 7.75/5.70 thf(fact_4448_zero__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( zero_zero_real
% 7.75/5.70 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_numeral
% 7.75/5.70 thf(fact_4449_zero__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( zero_z3403309356797280102nteger
% 7.75/5.70 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_numeral
% 7.75/5.70 thf(fact_4450_zero__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( zero_zero_complex
% 7.75/5.70 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_numeral
% 7.75/5.70 thf(fact_4451_zero__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( zero_zero_rat
% 7.75/5.70 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_numeral
% 7.75/5.70 thf(fact_4452_not__numeral__le__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_le_neg_numeral
% 7.75/5.70 thf(fact_4453_not__numeral__le__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_le_neg_numeral
% 7.75/5.70 thf(fact_4454_not__numeral__le__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_le_neg_numeral
% 7.75/5.70 thf(fact_4455_not__numeral__le__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_le_neg_numeral
% 7.75/5.70 thf(fact_4456_neg__numeral__le__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_numeral
% 7.75/5.70 thf(fact_4457_neg__numeral__le__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_numeral
% 7.75/5.70 thf(fact_4458_neg__numeral__le__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_numeral
% 7.75/5.70 thf(fact_4459_neg__numeral__le__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_numeral
% 7.75/5.70 thf(fact_4460_mult__diff__mult,axiom,
% 7.75/5.70 ! [X: rat,Y: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 7.75/5.70 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_diff_mult
% 7.75/5.70 thf(fact_4461_mult__diff__mult,axiom,
% 7.75/5.70 ! [X: real,Y: real,A: real,B: real] :
% 7.75/5.70 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 7.75/5.70 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_diff_mult
% 7.75/5.70 thf(fact_4462_mult__diff__mult,axiom,
% 7.75/5.70 ! [X: int,Y: int,A: int,B: int] :
% 7.75/5.70 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 7.75/5.70 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_diff_mult
% 7.75/5.70 thf(fact_4463_mult__diff__mult,axiom,
% 7.75/5.70 ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 7.75/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ ( minus_8373710615458151222nteger @ Y @ B ) ) @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ A ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_diff_mult
% 7.75/5.70 thf(fact_4464_mult__diff__mult,axiom,
% 7.75/5.70 ! [X: complex,Y: complex,A: complex,B: complex] :
% 7.75/5.70 ( ( minus_minus_complex @ ( times_times_complex @ X @ Y ) @ ( times_times_complex @ A @ B ) )
% 7.75/5.70 = ( plus_plus_complex @ ( times_times_complex @ X @ ( minus_minus_complex @ Y @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X @ A ) @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_diff_mult
% 7.75/5.70 thf(fact_4465_square__diff__square__factored,axiom,
% 7.75/5.70 ! [X: rat,Y: rat] :
% 7.75/5.70 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 7.75/5.70 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_square_factored
% 7.75/5.70 thf(fact_4466_square__diff__square__factored,axiom,
% 7.75/5.70 ! [X: real,Y: real] :
% 7.75/5.70 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 7.75/5.70 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_square_factored
% 7.75/5.70 thf(fact_4467_square__diff__square__factored,axiom,
% 7.75/5.70 ! [X: int,Y: int] :
% 7.75/5.70 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 7.75/5.70 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_square_factored
% 7.75/5.70 thf(fact_4468_square__diff__square__factored,axiom,
% 7.75/5.70 ! [X: code_integer,Y: code_integer] :
% 7.75/5.70 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 7.75/5.70 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( minus_8373710615458151222nteger @ X @ Y ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_square_factored
% 7.75/5.70 thf(fact_4469_square__diff__square__factored,axiom,
% 7.75/5.70 ! [X: complex,Y: complex] :
% 7.75/5.70 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ ( times_times_complex @ Y @ Y ) )
% 7.75/5.70 = ( times_times_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_complex @ X @ Y ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_square_factored
% 7.75/5.70 thf(fact_4470_eq__add__iff2,axiom,
% 7.75/5.70 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 7.75/5.70 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 7.75/5.70 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( C
% 7.75/5.70 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff2
% 7.75/5.70 thf(fact_4471_eq__add__iff2,axiom,
% 7.75/5.70 ! [A: real,E: real,C: real,B: real,D2: real] :
% 7.75/5.70 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 7.75/5.70 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( C
% 7.75/5.70 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff2
% 7.75/5.70 thf(fact_4472_eq__add__iff2,axiom,
% 7.75/5.70 ! [A: int,E: int,C: int,B: int,D2: int] :
% 7.75/5.70 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 7.75/5.70 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( C
% 7.75/5.70 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff2
% 7.75/5.70 thf(fact_4473_eq__add__iff2,axiom,
% 7.75/5.70 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 7.75/5.70 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 7.75/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( C
% 7.75/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff2
% 7.75/5.70 thf(fact_4474_eq__add__iff2,axiom,
% 7.75/5.70 ! [A: complex,E: complex,C: complex,B: complex,D2: complex] :
% 7.75/5.70 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 7.75/5.70 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( C
% 7.75/5.70 = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff2
% 7.75/5.70 thf(fact_4475_eq__add__iff1,axiom,
% 7.75/5.70 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 7.75/5.70 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 7.75/5.70 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 7.75/5.70 = D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff1
% 7.75/5.70 thf(fact_4476_eq__add__iff1,axiom,
% 7.75/5.70 ! [A: real,E: real,C: real,B: real,D2: real] :
% 7.75/5.70 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 7.75/5.70 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 7.75/5.70 = D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff1
% 7.75/5.70 thf(fact_4477_eq__add__iff1,axiom,
% 7.75/5.70 ! [A: int,E: int,C: int,B: int,D2: int] :
% 7.75/5.70 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 7.75/5.70 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 7.75/5.70 = D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff1
% 7.75/5.70 thf(fact_4478_eq__add__iff1,axiom,
% 7.75/5.70 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 7.75/5.70 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 7.75/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C )
% 7.75/5.70 = D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff1
% 7.75/5.70 thf(fact_4479_eq__add__iff1,axiom,
% 7.75/5.70 ! [A: complex,E: complex,C: complex,B: complex,D2: complex] :
% 7.75/5.70 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E ) @ C )
% 7.75/5.70 = ( plus_plus_complex @ ( times_times_complex @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E ) @ C )
% 7.75/5.70 = D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_add_iff1
% 7.75/5.70 thf(fact_4480_neg__numeral__less__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_numeral
% 7.75/5.70 thf(fact_4481_neg__numeral__less__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_numeral
% 7.75/5.70 thf(fact_4482_neg__numeral__less__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_numeral
% 7.75/5.70 thf(fact_4483_neg__numeral__less__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_numeral
% 7.75/5.70 thf(fact_4484_not__numeral__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_less_neg_numeral
% 7.75/5.70 thf(fact_4485_not__numeral__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_less_neg_numeral
% 7.75/5.70 thf(fact_4486_not__numeral__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_less_neg_numeral
% 7.75/5.70 thf(fact_4487_not__numeral__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num,N: num] :
% 7.75/5.70 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_less_neg_numeral
% 7.75/5.70 thf(fact_4488_add__eq__0__iff,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( ( plus_plus_int @ A @ B )
% 7.75/5.70 = zero_zero_int )
% 7.75/5.70 = ( B
% 7.75/5.70 = ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_eq_0_iff
% 7.75/5.70 thf(fact_4489_add__eq__0__iff,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( ( plus_plus_real @ A @ B )
% 7.75/5.70 = zero_zero_real )
% 7.75/5.70 = ( B
% 7.75/5.70 = ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_eq_0_iff
% 7.75/5.70 thf(fact_4490_add__eq__0__iff,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 7.75/5.70 = zero_z3403309356797280102nteger )
% 7.75/5.70 = ( B
% 7.75/5.70 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_eq_0_iff
% 7.75/5.70 thf(fact_4491_add__eq__0__iff,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( ( plus_plus_complex @ A @ B )
% 7.75/5.70 = zero_zero_complex )
% 7.75/5.70 = ( B
% 7.75/5.70 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_eq_0_iff
% 7.75/5.70 thf(fact_4492_add__eq__0__iff,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( ( plus_plus_rat @ A @ B )
% 7.75/5.70 = zero_zero_rat )
% 7.75/5.70 = ( B
% 7.75/5.70 = ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_eq_0_iff
% 7.75/5.70 thf(fact_4493_ab__group__add__class_Oab__left__minus,axiom,
% 7.75/5.70 ! [A: int] :
% 7.75/5.70 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 7.75/5.70 = zero_zero_int ) ).
% 7.75/5.70
% 7.75/5.70 % ab_group_add_class.ab_left_minus
% 7.75/5.70 thf(fact_4494_ab__group__add__class_Oab__left__minus,axiom,
% 7.75/5.70 ! [A: real] :
% 7.75/5.70 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 7.75/5.70 = zero_zero_real ) ).
% 7.75/5.70
% 7.75/5.70 % ab_group_add_class.ab_left_minus
% 7.75/5.70 thf(fact_4495_ab__group__add__class_Oab__left__minus,axiom,
% 7.75/5.70 ! [A: code_integer] :
% 7.75/5.70 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 7.75/5.70 = zero_z3403309356797280102nteger ) ).
% 7.75/5.70
% 7.75/5.70 % ab_group_add_class.ab_left_minus
% 7.75/5.70 thf(fact_4496_ab__group__add__class_Oab__left__minus,axiom,
% 7.75/5.70 ! [A: complex] :
% 7.75/5.70 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 7.75/5.70 = zero_zero_complex ) ).
% 7.75/5.70
% 7.75/5.70 % ab_group_add_class.ab_left_minus
% 7.75/5.70 thf(fact_4497_ab__group__add__class_Oab__left__minus,axiom,
% 7.75/5.70 ! [A: rat] :
% 7.75/5.70 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 7.75/5.70 = zero_zero_rat ) ).
% 7.75/5.70
% 7.75/5.70 % ab_group_add_class.ab_left_minus
% 7.75/5.70 thf(fact_4498_add_Oinverse__unique,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( ( plus_plus_int @ A @ B )
% 7.75/5.70 = zero_zero_int )
% 7.75/5.70 => ( ( uminus_uminus_int @ A )
% 7.75/5.70 = B ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_unique
% 7.75/5.70 thf(fact_4499_add_Oinverse__unique,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( ( plus_plus_real @ A @ B )
% 7.75/5.70 = zero_zero_real )
% 7.75/5.70 => ( ( uminus_uminus_real @ A )
% 7.75/5.70 = B ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_unique
% 7.75/5.70 thf(fact_4500_add_Oinverse__unique,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 7.75/5.70 = zero_z3403309356797280102nteger )
% 7.75/5.70 => ( ( uminus1351360451143612070nteger @ A )
% 7.75/5.70 = B ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_unique
% 7.75/5.70 thf(fact_4501_add_Oinverse__unique,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( ( plus_plus_complex @ A @ B )
% 7.75/5.70 = zero_zero_complex )
% 7.75/5.70 => ( ( uminus1482373934393186551omplex @ A )
% 7.75/5.70 = B ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_unique
% 7.75/5.70 thf(fact_4502_add_Oinverse__unique,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( ( plus_plus_rat @ A @ B )
% 7.75/5.70 = zero_zero_rat )
% 7.75/5.70 => ( ( uminus_uminus_rat @ A )
% 7.75/5.70 = B ) ) ).
% 7.75/5.70
% 7.75/5.70 % add.inverse_unique
% 7.75/5.70 thf(fact_4503_eq__neg__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( uminus_uminus_int @ B ) )
% 7.75/5.70 = ( ( plus_plus_int @ A @ B )
% 7.75/5.70 = zero_zero_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_neg_iff_add_eq_0
% 7.75/5.70 thf(fact_4504_eq__neg__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( uminus_uminus_real @ B ) )
% 7.75/5.70 = ( ( plus_plus_real @ A @ B )
% 7.75/5.70 = zero_zero_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_neg_iff_add_eq_0
% 7.75/5.70 thf(fact_4505_eq__neg__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.70 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 7.75/5.70 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_neg_iff_add_eq_0
% 7.75/5.70 thf(fact_4506_eq__neg__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.70 = ( ( plus_plus_complex @ A @ B )
% 7.75/5.70 = zero_zero_complex ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_neg_iff_add_eq_0
% 7.75/5.70 thf(fact_4507_eq__neg__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( uminus_uminus_rat @ B ) )
% 7.75/5.70 = ( ( plus_plus_rat @ A @ B )
% 7.75/5.70 = zero_zero_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_neg_iff_add_eq_0
% 7.75/5.70 thf(fact_4508_neg__eq__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( ( uminus_uminus_int @ A )
% 7.75/5.70 = B )
% 7.75/5.70 = ( ( plus_plus_int @ A @ B )
% 7.75/5.70 = zero_zero_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_eq_iff_add_eq_0
% 7.75/5.70 thf(fact_4509_neg__eq__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( ( uminus_uminus_real @ A )
% 7.75/5.70 = B )
% 7.75/5.70 = ( ( plus_plus_real @ A @ B )
% 7.75/5.70 = zero_zero_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_eq_iff_add_eq_0
% 7.75/5.70 thf(fact_4510_neg__eq__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ( uminus1351360451143612070nteger @ A )
% 7.75/5.70 = B )
% 7.75/5.70 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 7.75/5.70 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_eq_iff_add_eq_0
% 7.75/5.70 thf(fact_4511_neg__eq__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( ( uminus1482373934393186551omplex @ A )
% 7.75/5.70 = B )
% 7.75/5.70 = ( ( plus_plus_complex @ A @ B )
% 7.75/5.70 = zero_zero_complex ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_eq_iff_add_eq_0
% 7.75/5.70 thf(fact_4512_neg__eq__iff__add__eq__0,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( ( uminus_uminus_rat @ A )
% 7.75/5.70 = B )
% 7.75/5.70 = ( ( plus_plus_rat @ A @ B )
% 7.75/5.70 = zero_zero_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_eq_iff_add_eq_0
% 7.75/5.70 thf(fact_4513_zero__neq__neg__one,axiom,
% 7.75/5.70 ( zero_zero_int
% 7.75/5.70 != ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_one
% 7.75/5.70 thf(fact_4514_zero__neq__neg__one,axiom,
% 7.75/5.70 ( zero_zero_real
% 7.75/5.70 != ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_one
% 7.75/5.70 thf(fact_4515_zero__neq__neg__one,axiom,
% 7.75/5.70 ( zero_z3403309356797280102nteger
% 7.75/5.70 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_one
% 7.75/5.70 thf(fact_4516_zero__neq__neg__one,axiom,
% 7.75/5.70 ( zero_zero_complex
% 7.75/5.70 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_one
% 7.75/5.70 thf(fact_4517_zero__neq__neg__one,axiom,
% 7.75/5.70 ( zero_zero_rat
% 7.75/5.70 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % zero_neq_neg_one
% 7.75/5.70 thf(fact_4518_le__minus__one__simps_I4_J,axiom,
% 7.75/5.70 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(4)
% 7.75/5.70 thf(fact_4519_le__minus__one__simps_I4_J,axiom,
% 7.75/5.70 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(4)
% 7.75/5.70 thf(fact_4520_le__minus__one__simps_I4_J,axiom,
% 7.75/5.70 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(4)
% 7.75/5.70 thf(fact_4521_le__minus__one__simps_I4_J,axiom,
% 7.75/5.70 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(4)
% 7.75/5.70 thf(fact_4522_le__minus__one__simps_I2_J,axiom,
% 7.75/5.70 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(2)
% 7.75/5.70 thf(fact_4523_le__minus__one__simps_I2_J,axiom,
% 7.75/5.70 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(2)
% 7.75/5.70 thf(fact_4524_le__minus__one__simps_I2_J,axiom,
% 7.75/5.70 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(2)
% 7.75/5.70 thf(fact_4525_le__minus__one__simps_I2_J,axiom,
% 7.75/5.70 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(2)
% 7.75/5.70 thf(fact_4526_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 7.75/5.70 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 7.75/5.70 thf(fact_4527_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 7.75/5.70 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 7.75/5.70 thf(fact_4528_less__minus__one__simps_I2_J,axiom,
% 7.75/5.70 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(2)
% 7.75/5.70 thf(fact_4529_less__minus__one__simps_I2_J,axiom,
% 7.75/5.70 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(2)
% 7.75/5.70 thf(fact_4530_less__minus__one__simps_I2_J,axiom,
% 7.75/5.70 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(2)
% 7.75/5.70 thf(fact_4531_less__minus__one__simps_I2_J,axiom,
% 7.75/5.70 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(2)
% 7.75/5.70 thf(fact_4532_less__minus__one__simps_I4_J,axiom,
% 7.75/5.70 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(4)
% 7.75/5.70 thf(fact_4533_less__minus__one__simps_I4_J,axiom,
% 7.75/5.70 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(4)
% 7.75/5.70 thf(fact_4534_less__minus__one__simps_I4_J,axiom,
% 7.75/5.70 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(4)
% 7.75/5.70 thf(fact_4535_less__minus__one__simps_I4_J,axiom,
% 7.75/5.70 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(4)
% 7.75/5.70 thf(fact_4536_numeral__neq__neg__one,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numeral_numeral_int @ N )
% 7.75/5.70 != ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_one
% 7.75/5.70 thf(fact_4537_numeral__neq__neg__one,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numeral_numeral_real @ N )
% 7.75/5.70 != ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_one
% 7.75/5.70 thf(fact_4538_numeral__neq__neg__one,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numera6620942414471956472nteger @ N )
% 7.75/5.70 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_one
% 7.75/5.70 thf(fact_4539_numeral__neq__neg__one,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numera6690914467698888265omplex @ N )
% 7.75/5.70 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_one
% 7.75/5.70 thf(fact_4540_numeral__neq__neg__one,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numeral_numeral_rat @ N )
% 7.75/5.70 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_neq_neg_one
% 7.75/5.70 thf(fact_4541_one__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( one_one_int
% 7.75/5.70 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_numeral
% 7.75/5.70 thf(fact_4542_one__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( one_one_real
% 7.75/5.70 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_numeral
% 7.75/5.70 thf(fact_4543_one__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( one_one_Code_integer
% 7.75/5.70 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_numeral
% 7.75/5.70 thf(fact_4544_one__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( one_one_complex
% 7.75/5.70 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_numeral
% 7.75/5.70 thf(fact_4545_one__neq__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( one_one_rat
% 7.75/5.70 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % one_neq_neg_numeral
% 7.75/5.70 thf(fact_4546_numeral__times__minus__swap,axiom,
% 7.75/5.70 ! [W: num,X: int] :
% 7.75/5.70 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 7.75/5.70 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_times_minus_swap
% 7.75/5.70 thf(fact_4547_numeral__times__minus__swap,axiom,
% 7.75/5.70 ! [W: num,X: real] :
% 7.75/5.70 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 7.75/5.70 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_times_minus_swap
% 7.75/5.70 thf(fact_4548_numeral__times__minus__swap,axiom,
% 7.75/5.70 ! [W: num,X: code_integer] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 7.75/5.70 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_times_minus_swap
% 7.75/5.70 thf(fact_4549_numeral__times__minus__swap,axiom,
% 7.75/5.70 ! [W: num,X: complex] :
% 7.75/5.70 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 7.75/5.70 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_times_minus_swap
% 7.75/5.70 thf(fact_4550_numeral__times__minus__swap,axiom,
% 7.75/5.70 ! [W: num,X: rat] :
% 7.75/5.70 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 7.75/5.70 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_times_minus_swap
% 7.75/5.70 thf(fact_4551_nonzero__minus__divide__right,axiom,
% 7.75/5.70 ! [B: real,A: real] :
% 7.75/5.70 ( ( B != zero_zero_real )
% 7.75/5.70 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.70 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_minus_divide_right
% 7.75/5.70 thf(fact_4552_nonzero__minus__divide__right,axiom,
% 7.75/5.70 ! [B: complex,A: complex] :
% 7.75/5.70 ( ( B != zero_zero_complex )
% 7.75/5.70 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_minus_divide_right
% 7.75/5.70 thf(fact_4553_nonzero__minus__divide__right,axiom,
% 7.75/5.70 ! [B: rat,A: rat] :
% 7.75/5.70 ( ( B != zero_zero_rat )
% 7.75/5.70 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 7.75/5.70 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_minus_divide_right
% 7.75/5.70 thf(fact_4554_nonzero__minus__divide__divide,axiom,
% 7.75/5.70 ! [B: real,A: real] :
% 7.75/5.70 ( ( B != zero_zero_real )
% 7.75/5.70 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 7.75/5.70 = ( divide_divide_real @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_minus_divide_divide
% 7.75/5.70 thf(fact_4555_nonzero__minus__divide__divide,axiom,
% 7.75/5.70 ! [B: complex,A: complex] :
% 7.75/5.70 ( ( B != zero_zero_complex )
% 7.75/5.70 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_minus_divide_divide
% 7.75/5.70 thf(fact_4556_nonzero__minus__divide__divide,axiom,
% 7.75/5.70 ! [B: rat,A: rat] :
% 7.75/5.70 ( ( B != zero_zero_rat )
% 7.75/5.70 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 7.75/5.70 = ( divide_divide_rat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_minus_divide_divide
% 7.75/5.70 thf(fact_4557_square__eq__1__iff,axiom,
% 7.75/5.70 ! [X: int] :
% 7.75/5.70 ( ( ( times_times_int @ X @ X )
% 7.75/5.70 = one_one_int )
% 7.75/5.70 = ( ( X = one_one_int )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_1_iff
% 7.75/5.70 thf(fact_4558_square__eq__1__iff,axiom,
% 7.75/5.70 ! [X: real] :
% 7.75/5.70 ( ( ( times_times_real @ X @ X )
% 7.75/5.70 = one_one_real )
% 7.75/5.70 = ( ( X = one_one_real )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_1_iff
% 7.75/5.70 thf(fact_4559_square__eq__1__iff,axiom,
% 7.75/5.70 ! [X: code_integer] :
% 7.75/5.70 ( ( ( times_3573771949741848930nteger @ X @ X )
% 7.75/5.70 = one_one_Code_integer )
% 7.75/5.70 = ( ( X = one_one_Code_integer )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_1_iff
% 7.75/5.70 thf(fact_4560_square__eq__1__iff,axiom,
% 7.75/5.70 ! [X: complex] :
% 7.75/5.70 ( ( ( times_times_complex @ X @ X )
% 7.75/5.70 = one_one_complex )
% 7.75/5.70 = ( ( X = one_one_complex )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_1_iff
% 7.75/5.70 thf(fact_4561_square__eq__1__iff,axiom,
% 7.75/5.70 ! [X: rat] :
% 7.75/5.70 ( ( ( times_times_rat @ X @ X )
% 7.75/5.70 = one_one_rat )
% 7.75/5.70 = ( ( X = one_one_rat )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_eq_1_iff
% 7.75/5.70 thf(fact_4562_num_Oexhaust,axiom,
% 7.75/5.70 ! [Y: num] :
% 7.75/5.70 ( ( Y != one )
% 7.75/5.70 => ( ! [X23: num] :
% 7.75/5.70 ( Y
% 7.75/5.70 != ( bit0 @ X23 ) )
% 7.75/5.70 => ~ ! [X33: num] :
% 7.75/5.70 ( Y
% 7.75/5.70 != ( bit1 @ X33 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % num.exhaust
% 7.75/5.70 thf(fact_4563_of__nat__dvd__iff,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.70 = ( dvd_dvd_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_dvd_iff
% 7.75/5.70 thf(fact_4564_of__nat__dvd__iff,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 7.75/5.70 = ( dvd_dvd_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_dvd_iff
% 7.75/5.70 thf(fact_4565_nat__less__real__le,axiom,
% 7.75/5.70 ( ord_less_nat
% 7.75/5.70 = ( ^ [N3: nat,M4: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M4 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_less_real_le
% 7.75/5.70 thf(fact_4566_dvd__div__neg,axiom,
% 7.75/5.70 ! [B: int,A: int] :
% 7.75/5.70 ( ( dvd_dvd_int @ B @ A )
% 7.75/5.70 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 7.75/5.70 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_div_neg
% 7.75/5.70 thf(fact_4567_dvd__div__neg,axiom,
% 7.75/5.70 ! [B: real,A: real] :
% 7.75/5.70 ( ( dvd_dvd_real @ B @ A )
% 7.75/5.70 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 7.75/5.70 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_div_neg
% 7.75/5.70 thf(fact_4568_dvd__div__neg,axiom,
% 7.75/5.70 ! [B: code_integer,A: code_integer] :
% 7.75/5.70 ( ( dvd_dvd_Code_integer @ B @ A )
% 7.75/5.70 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 7.75/5.70 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_div_neg
% 7.75/5.70 thf(fact_4569_dvd__div__neg,axiom,
% 7.75/5.70 ! [B: complex,A: complex] :
% 7.75/5.70 ( ( dvd_dvd_complex @ B @ A )
% 7.75/5.70 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_div_neg
% 7.75/5.70 thf(fact_4570_dvd__div__neg,axiom,
% 7.75/5.70 ! [B: rat,A: rat] :
% 7.75/5.70 ( ( dvd_dvd_rat @ B @ A )
% 7.75/5.70 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 7.75/5.70 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_div_neg
% 7.75/5.70 thf(fact_4571_dvd__neg__div,axiom,
% 7.75/5.70 ! [B: int,A: int] :
% 7.75/5.70 ( ( dvd_dvd_int @ B @ A )
% 7.75/5.70 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.70 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_neg_div
% 7.75/5.70 thf(fact_4572_dvd__neg__div,axiom,
% 7.75/5.70 ! [B: real,A: real] :
% 7.75/5.70 ( ( dvd_dvd_real @ B @ A )
% 7.75/5.70 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 7.75/5.70 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_neg_div
% 7.75/5.70 thf(fact_4573_dvd__neg__div,axiom,
% 7.75/5.70 ! [B: code_integer,A: code_integer] :
% 7.75/5.70 ( ( dvd_dvd_Code_integer @ B @ A )
% 7.75/5.70 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 7.75/5.70 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_neg_div
% 7.75/5.70 thf(fact_4574_dvd__neg__div,axiom,
% 7.75/5.70 ! [B: complex,A: complex] :
% 7.75/5.70 ( ( dvd_dvd_complex @ B @ A )
% 7.75/5.70 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_neg_div
% 7.75/5.70 thf(fact_4575_dvd__neg__div,axiom,
% 7.75/5.70 ! [B: rat,A: rat] :
% 7.75/5.70 ( ( dvd_dvd_rat @ B @ A )
% 7.75/5.70 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 7.75/5.70 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_neg_div
% 7.75/5.70 thf(fact_4576_nat__le__real__less,axiom,
% 7.75/5.70 ( ord_less_eq_nat
% 7.75/5.70 = ( ^ [N3: nat,M4: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M4 ) @ one_one_real ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_le_real_less
% 7.75/5.70 thf(fact_4577_mod__eq__dvd__iff,axiom,
% 7.75/5.70 ! [A: int,C: int,B: int] :
% 7.75/5.70 ( ( ( modulo_modulo_int @ A @ C )
% 7.75/5.70 = ( modulo_modulo_int @ B @ C ) )
% 7.75/5.70 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_eq_dvd_iff
% 7.75/5.70 thf(fact_4578_mod__eq__dvd__iff,axiom,
% 7.75/5.70 ! [A: code_integer,C: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ( modulo364778990260209775nteger @ A @ C )
% 7.75/5.70 = ( modulo364778990260209775nteger @ B @ C ) )
% 7.75/5.70 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_eq_dvd_iff
% 7.75/5.70 thf(fact_4579_dvd__minus__mod,axiom,
% 7.75/5.70 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_minus_mod
% 7.75/5.70 thf(fact_4580_dvd__minus__mod,axiom,
% 7.75/5.70 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_minus_mod
% 7.75/5.70 thf(fact_4581_dvd__minus__mod,axiom,
% 7.75/5.70 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_minus_mod
% 7.75/5.70 thf(fact_4582_of__nat__mod,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_mod
% 7.75/5.70 thf(fact_4583_of__nat__mod,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 7.75/5.70 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_mod
% 7.75/5.70 thf(fact_4584_of__nat__mod,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 7.75/5.70 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_mod
% 7.75/5.70 thf(fact_4585_Suc__to__right,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ( suc @ N )
% 7.75/5.70 = M )
% 7.75/5.70 => ( N
% 7.75/5.70 = ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Suc_to_right
% 7.75/5.70 thf(fact_4586_Suc__diff__Suc,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ N @ M )
% 7.75/5.70 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 7.75/5.70 = ( minus_minus_nat @ M @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Suc_diff_Suc
% 7.75/5.70 thf(fact_4587_diff__less__Suc,axiom,
% 7.75/5.70 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_less_Suc
% 7.75/5.70 thf(fact_4588_diff__less,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.70 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_less
% 7.75/5.70 thf(fact_4589_real__of__nat__div4,axiom,
% 7.75/5.70 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % real_of_nat_div4
% 7.75/5.70 thf(fact_4590_diff__Suc__eq__diff__pred,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 7.75/5.70 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_Suc_eq_diff_pred
% 7.75/5.70 thf(fact_4591_diff__add__0,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 7.75/5.70 = zero_zero_nat ) ).
% 7.75/5.70
% 7.75/5.70 % diff_add_0
% 7.75/5.70 thf(fact_4592_add__diff__inverse__nat,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ~ ( ord_less_nat @ M @ N )
% 7.75/5.70 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 = M ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_diff_inverse_nat
% 7.75/5.70 thf(fact_4593_less__diff__conv,axiom,
% 7.75/5.70 ! [I: nat,J: nat,K: nat] :
% 7.75/5.70 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 7.75/5.70 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_diff_conv
% 7.75/5.70 thf(fact_4594_less__diff__conv2,axiom,
% 7.75/5.70 ! [K: nat,J: nat,I: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ K @ J )
% 7.75/5.70 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 7.75/5.70 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_diff_conv2
% 7.75/5.70 thf(fact_4595_int__le__induct,axiom,
% 7.75/5.70 ! [I: int,K: int,P: int > $o] :
% 7.75/5.70 ( ( ord_less_eq_int @ I @ K )
% 7.75/5.70 => ( ( P @ K )
% 7.75/5.70 => ( ! [I3: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ I3 @ K )
% 7.75/5.70 => ( ( P @ I3 )
% 7.75/5.70 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 7.75/5.70 => ( P @ I ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % int_le_induct
% 7.75/5.70 thf(fact_4596_int__less__induct,axiom,
% 7.75/5.70 ! [I: int,K: int,P: int > $o] :
% 7.75/5.70 ( ( ord_less_int @ I @ K )
% 7.75/5.70 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 7.75/5.70 => ( ! [I3: int] :
% 7.75/5.70 ( ( ord_less_int @ I3 @ K )
% 7.75/5.70 => ( ( P @ I3 )
% 7.75/5.70 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 7.75/5.70 => ( P @ I ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % int_less_induct
% 7.75/5.70 thf(fact_4597_nat__diff__add__eq2,axiom,
% 7.75/5.70 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.70 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 7.75/5.70 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_diff_add_eq2
% 7.75/5.70 thf(fact_4598_nat__diff__add__eq1,axiom,
% 7.75/5.70 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ J @ I )
% 7.75/5.70 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 7.75/5.70 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_diff_add_eq1
% 7.75/5.70 thf(fact_4599_nat__le__add__iff2,axiom,
% 7.75/5.70 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.70 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 7.75/5.70 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_le_add_iff2
% 7.75/5.70 thf(fact_4600_nat__le__add__iff1,axiom,
% 7.75/5.70 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ J @ I )
% 7.75/5.70 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 7.75/5.70 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_le_add_iff1
% 7.75/5.70 thf(fact_4601_nat__eq__add__iff2,axiom,
% 7.75/5.70 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.70 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 7.75/5.70 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 7.75/5.70 = ( M
% 7.75/5.70 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_eq_add_iff2
% 7.75/5.70 thf(fact_4602_nat__eq__add__iff1,axiom,
% 7.75/5.70 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ J @ I )
% 7.75/5.70 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 7.75/5.70 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 7.75/5.70 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 7.75/5.70 = N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_eq_add_iff1
% 7.75/5.70 thf(fact_4603_dvd__minus__self,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 7.75/5.70 = ( ( ord_less_nat @ N @ M )
% 7.75/5.70 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_minus_self
% 7.75/5.70 thf(fact_4604_nat__minus__mod,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( modulo_modulo_nat @ ( minus_minus_nat @ N @ ( modulo_modulo_nat @ N @ M ) ) @ M )
% 7.75/5.70 = zero_zero_nat ) ).
% 7.75/5.70
% 7.75/5.70 % nat_minus_mod
% 7.75/5.70 thf(fact_4605_mod__nat__sub,axiom,
% 7.75/5.70 ! [X: nat,Z: nat,Y: nat] :
% 7.75/5.70 ( ( ord_less_nat @ X @ Z )
% 7.75/5.70 => ( ( modulo_modulo_nat @ ( minus_minus_nat @ X @ Y ) @ Z )
% 7.75/5.70 = ( minus_minus_nat @ X @ Y ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_nat_sub
% 7.75/5.70 thf(fact_4606_mod__geq,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ~ ( ord_less_nat @ M @ N )
% 7.75/5.70 => ( ( modulo_modulo_nat @ M @ N )
% 7.75/5.70 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_geq
% 7.75/5.70 thf(fact_4607_mod__if,axiom,
% 7.75/5.70 ( modulo_modulo_nat
% 7.75/5.70 = ( ^ [M4: nat,N3: nat] : ( if_nat @ ( ord_less_nat @ M4 @ N3 ) @ M4 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M4 @ N3 ) @ N3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_if
% 7.75/5.70 thf(fact_4608_pos__zmult__eq__1__iff__lemma,axiom,
% 7.75/5.70 ! [M: int,N: int] :
% 7.75/5.70 ( ( ( times_times_int @ M @ N )
% 7.75/5.70 = one_one_int )
% 7.75/5.70 => ( ( M = one_one_int )
% 7.75/5.70 | ( M
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % pos_zmult_eq_1_iff_lemma
% 7.75/5.70 thf(fact_4609_zmult__eq__1__iff,axiom,
% 7.75/5.70 ! [M: int,N: int] :
% 7.75/5.70 ( ( ( times_times_int @ M @ N )
% 7.75/5.70 = one_one_int )
% 7.75/5.70 = ( ( ( M = one_one_int )
% 7.75/5.70 & ( N = one_one_int ) )
% 7.75/5.70 | ( ( M
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.70 & ( N
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zmult_eq_1_iff
% 7.75/5.70 thf(fact_4610_zmod__zminus1__not__zero,axiom,
% 7.75/5.70 ! [K: int,L: int] :
% 7.75/5.70 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 7.75/5.70 != zero_zero_int )
% 7.75/5.70 => ( ( modulo_modulo_int @ K @ L )
% 7.75/5.70 != zero_zero_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % zmod_zminus1_not_zero
% 7.75/5.70 thf(fact_4611_zmod__zminus2__not__zero,axiom,
% 7.75/5.70 ! [K: int,L: int] :
% 7.75/5.70 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 7.75/5.70 != zero_zero_int )
% 7.75/5.70 => ( ( modulo_modulo_int @ K @ L )
% 7.75/5.70 != zero_zero_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % zmod_zminus2_not_zero
% 7.75/5.70 thf(fact_4612_nat__minus__mod__plus__right,axiom,
% 7.75/5.70 ! [N: nat,X: nat,M: nat] :
% 7.75/5.70 ( ( modulo_modulo_nat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ X ) @ ( modulo_modulo_nat @ N @ M ) ) @ M )
% 7.75/5.70 = ( modulo_modulo_nat @ X @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_minus_mod_plus_right
% 7.75/5.70 thf(fact_4613_bezout1__nat,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ? [D3: nat,X3: nat,Y3: nat] :
% 7.75/5.70 ( ( dvd_dvd_nat @ D3 @ A )
% 7.75/5.70 & ( dvd_dvd_nat @ D3 @ B )
% 7.75/5.70 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 7.75/5.70 = D3 )
% 7.75/5.70 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 7.75/5.70 = D3 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % bezout1_nat
% 7.75/5.70 thf(fact_4614_mod__eq__dvd__iff__nat,axiom,
% 7.75/5.70 ! [N: nat,M: nat,Q3: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 7.75/5.70 = ( modulo_modulo_nat @ N @ Q3 ) )
% 7.75/5.70 = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_eq_dvd_iff_nat
% 7.75/5.70 thf(fact_4615_of__nat__gt__0,axiom,
% 7.75/5.70 ! [K: nat] :
% 7.75/5.70 ( ( ( semiri681578069525770553at_rat @ K )
% 7.75/5.70 != zero_zero_rat )
% 7.75/5.70 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_gt_0
% 7.75/5.70 thf(fact_4616_of__nat__gt__0,axiom,
% 7.75/5.70 ! [K: nat] :
% 7.75/5.70 ( ( ( semiri5074537144036343181t_real @ K )
% 7.75/5.70 != zero_zero_real )
% 7.75/5.70 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_gt_0
% 7.75/5.70 thf(fact_4617_of__nat__gt__0,axiom,
% 7.75/5.70 ! [K: nat] :
% 7.75/5.70 ( ( ( semiri1314217659103216013at_int @ K )
% 7.75/5.70 != zero_zero_int )
% 7.75/5.70 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_gt_0
% 7.75/5.70 thf(fact_4618_of__nat__gt__0,axiom,
% 7.75/5.70 ! [K: nat] :
% 7.75/5.70 ( ( ( semiri1316708129612266289at_nat @ K )
% 7.75/5.70 != zero_zero_nat )
% 7.75/5.70 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_gt_0
% 7.75/5.70 thf(fact_4619_of__nat__gt__0,axiom,
% 7.75/5.70 ! [K: nat] :
% 7.75/5.70 ( ( ( semiri8010041392384452111omplex @ K )
% 7.75/5.70 != zero_zero_complex )
% 7.75/5.70 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_gt_0
% 7.75/5.70 thf(fact_4620_small__powers__of__2,axiom,
% 7.75/5.70 ! [X: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ X )
% 7.75/5.70 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ X @ one_one_nat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % small_powers_of_2
% 7.75/5.70 thf(fact_4621_ordered__ring__class_Ole__add__iff2,axiom,
% 7.75/5.70 ! [A: real,E: real,C: real,B: real,D2: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_ring_class.le_add_iff2
% 7.75/5.70 thf(fact_4622_ordered__ring__class_Ole__add__iff2,axiom,
% 7.75/5.70 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 7.75/5.70 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_ring_class.le_add_iff2
% 7.75/5.70 thf(fact_4623_ordered__ring__class_Ole__add__iff2,axiom,
% 7.75/5.70 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_ring_class.le_add_iff2
% 7.75/5.70 thf(fact_4624_ordered__ring__class_Ole__add__iff2,axiom,
% 7.75/5.70 ! [A: int,E: int,C: int,B: int,D2: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_ring_class.le_add_iff2
% 7.75/5.70 thf(fact_4625_ordered__ring__class_Ole__add__iff1,axiom,
% 7.75/5.70 ! [A: real,E: real,C: real,B: real,D2: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_ring_class.le_add_iff1
% 7.75/5.70 thf(fact_4626_ordered__ring__class_Ole__add__iff1,axiom,
% 7.75/5.70 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 7.75/5.70 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_ring_class.le_add_iff1
% 7.75/5.70 thf(fact_4627_ordered__ring__class_Ole__add__iff1,axiom,
% 7.75/5.70 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_ring_class.le_add_iff1
% 7.75/5.70 thf(fact_4628_ordered__ring__class_Ole__add__iff1,axiom,
% 7.75/5.70 ! [A: int,E: int,C: int,B: int,D2: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % ordered_ring_class.le_add_iff1
% 7.75/5.70 thf(fact_4629_neg__numeral__le__zero,axiom,
% 7.75/5.70 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_zero
% 7.75/5.70 thf(fact_4630_neg__numeral__le__zero,axiom,
% 7.75/5.70 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_zero
% 7.75/5.70 thf(fact_4631_neg__numeral__le__zero,axiom,
% 7.75/5.70 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_zero
% 7.75/5.70 thf(fact_4632_neg__numeral__le__zero,axiom,
% 7.75/5.70 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_zero
% 7.75/5.70 thf(fact_4633_not__zero__le__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_zero_le_neg_numeral
% 7.75/5.70 thf(fact_4634_not__zero__le__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_zero_le_neg_numeral
% 7.75/5.70 thf(fact_4635_not__zero__le__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_zero_le_neg_numeral
% 7.75/5.70 thf(fact_4636_not__zero__le__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_zero_le_neg_numeral
% 7.75/5.70 thf(fact_4637_less__add__iff2,axiom,
% 7.75/5.70 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 7.75/5.70 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_add_iff2
% 7.75/5.70 thf(fact_4638_less__add__iff2,axiom,
% 7.75/5.70 ! [A: real,E: real,C: real,B: real,D2: real] :
% 7.75/5.70 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_add_iff2
% 7.75/5.70 thf(fact_4639_less__add__iff2,axiom,
% 7.75/5.70 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 7.75/5.70 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_add_iff2
% 7.75/5.70 thf(fact_4640_less__add__iff2,axiom,
% 7.75/5.70 ! [A: int,E: int,C: int,B: int,D2: int] :
% 7.75/5.70 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_add_iff2
% 7.75/5.70 thf(fact_4641_less__add__iff1,axiom,
% 7.75/5.70 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 7.75/5.70 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_add_iff1
% 7.75/5.70 thf(fact_4642_less__add__iff1,axiom,
% 7.75/5.70 ! [A: real,E: real,C: real,B: real,D2: real] :
% 7.75/5.70 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_add_iff1
% 7.75/5.70 thf(fact_4643_less__add__iff1,axiom,
% 7.75/5.70 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 7.75/5.70 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_add_iff1
% 7.75/5.70 thf(fact_4644_less__add__iff1,axiom,
% 7.75/5.70 ! [A: int,E: int,C: int,B: int,D2: int] :
% 7.75/5.70 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 7.75/5.70 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_add_iff1
% 7.75/5.70 thf(fact_4645_neg__numeral__less__zero,axiom,
% 7.75/5.70 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_zero
% 7.75/5.70 thf(fact_4646_neg__numeral__less__zero,axiom,
% 7.75/5.70 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_zero
% 7.75/5.70 thf(fact_4647_neg__numeral__less__zero,axiom,
% 7.75/5.70 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_zero
% 7.75/5.70 thf(fact_4648_neg__numeral__less__zero,axiom,
% 7.75/5.70 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_zero
% 7.75/5.70 thf(fact_4649_not__zero__less__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_zero_less_neg_numeral
% 7.75/5.70 thf(fact_4650_not__zero__less__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_zero_less_neg_numeral
% 7.75/5.70 thf(fact_4651_not__zero__less__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_zero_less_neg_numeral
% 7.75/5.70 thf(fact_4652_not__zero__less__neg__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_zero_less_neg_numeral
% 7.75/5.70 thf(fact_4653_le__minus__one__simps_I1_J,axiom,
% 7.75/5.70 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(1)
% 7.75/5.70 thf(fact_4654_le__minus__one__simps_I1_J,axiom,
% 7.75/5.70 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(1)
% 7.75/5.70 thf(fact_4655_le__minus__one__simps_I1_J,axiom,
% 7.75/5.70 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(1)
% 7.75/5.70 thf(fact_4656_le__minus__one__simps_I1_J,axiom,
% 7.75/5.70 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(1)
% 7.75/5.70 thf(fact_4657_le__minus__one__simps_I3_J,axiom,
% 7.75/5.70 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(3)
% 7.75/5.70 thf(fact_4658_le__minus__one__simps_I3_J,axiom,
% 7.75/5.70 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(3)
% 7.75/5.70 thf(fact_4659_le__minus__one__simps_I3_J,axiom,
% 7.75/5.70 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(3)
% 7.75/5.70 thf(fact_4660_le__minus__one__simps_I3_J,axiom,
% 7.75/5.70 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_one_simps(3)
% 7.75/5.70 thf(fact_4661_m1mod2k,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % m1mod2k
% 7.75/5.70 thf(fact_4662_square__diff__one__factored,axiom,
% 7.75/5.70 ! [X: rat] :
% 7.75/5.70 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 7.75/5.70 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_one_factored
% 7.75/5.70 thf(fact_4663_square__diff__one__factored,axiom,
% 7.75/5.70 ! [X: real] :
% 7.75/5.70 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 7.75/5.70 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_one_factored
% 7.75/5.70 thf(fact_4664_square__diff__one__factored,axiom,
% 7.75/5.70 ! [X: int] :
% 7.75/5.70 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 7.75/5.70 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_one_factored
% 7.75/5.70 thf(fact_4665_square__diff__one__factored,axiom,
% 7.75/5.70 ! [X: code_integer] :
% 7.75/5.70 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 7.75/5.70 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_one_factored
% 7.75/5.70 thf(fact_4666_square__diff__one__factored,axiom,
% 7.75/5.70 ! [X: complex] :
% 7.75/5.70 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 7.75/5.70 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_diff_one_factored
% 7.75/5.70 thf(fact_4667_divide__diff__eq__iff,axiom,
% 7.75/5.70 ! [Z: complex,X: complex,Y: complex] :
% 7.75/5.70 ( ( Z != zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_diff_eq_iff
% 7.75/5.70 thf(fact_4668_divide__diff__eq__iff,axiom,
% 7.75/5.70 ! [Z: real,X: real,Y: real] :
% 7.75/5.70 ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 7.75/5.70 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_diff_eq_iff
% 7.75/5.70 thf(fact_4669_divide__diff__eq__iff,axiom,
% 7.75/5.70 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.70 ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 7.75/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_diff_eq_iff
% 7.75/5.70 thf(fact_4670_diff__divide__eq__iff,axiom,
% 7.75/5.70 ! [Z: complex,X: complex,Y: complex] :
% 7.75/5.70 ( ( Z != zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_divide_eq_iff
% 7.75/5.70 thf(fact_4671_diff__divide__eq__iff,axiom,
% 7.75/5.70 ! [Z: real,X: real,Y: real] :
% 7.75/5.70 ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 7.75/5.70 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_divide_eq_iff
% 7.75/5.70 thf(fact_4672_diff__divide__eq__iff,axiom,
% 7.75/5.70 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.70 ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 7.75/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_divide_eq_iff
% 7.75/5.70 thf(fact_4673_diff__frac__eq,axiom,
% 7.75/5.70 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 7.75/5.70 ( ( Y != zero_zero_complex )
% 7.75/5.70 => ( ( Z != zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_frac_eq
% 7.75/5.70 thf(fact_4674_diff__frac__eq,axiom,
% 7.75/5.70 ! [Y: real,Z: real,X: real,W: real] :
% 7.75/5.70 ( ( Y != zero_zero_real )
% 7.75/5.70 => ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 7.75/5.70 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_frac_eq
% 7.75/5.70 thf(fact_4675_diff__frac__eq,axiom,
% 7.75/5.70 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 7.75/5.70 ( ( Y != zero_zero_rat )
% 7.75/5.70 => ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 7.75/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_frac_eq
% 7.75/5.70 thf(fact_4676_add__divide__eq__if__simps_I4_J,axiom,
% 7.75/5.70 ! [Z: complex,A: complex,B: complex] :
% 7.75/5.70 ( ( ( Z = zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 7.75/5.70 = A ) )
% 7.75/5.70 & ( ( Z != zero_zero_complex )
% 7.75/5.70 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(4)
% 7.75/5.70 thf(fact_4677_add__divide__eq__if__simps_I4_J,axiom,
% 7.75/5.70 ! [Z: real,A: real,B: real] :
% 7.75/5.70 ( ( ( Z = zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 7.75/5.70 = A ) )
% 7.75/5.70 & ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 7.75/5.70 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(4)
% 7.75/5.70 thf(fact_4678_add__divide__eq__if__simps_I4_J,axiom,
% 7.75/5.70 ! [Z: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( ( Z = zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 7.75/5.70 = A ) )
% 7.75/5.70 & ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 7.75/5.70 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(4)
% 7.75/5.70 thf(fact_4679_less__minus__one__simps_I1_J,axiom,
% 7.75/5.70 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(1)
% 7.75/5.70 thf(fact_4680_less__minus__one__simps_I1_J,axiom,
% 7.75/5.70 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(1)
% 7.75/5.70 thf(fact_4681_less__minus__one__simps_I1_J,axiom,
% 7.75/5.70 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(1)
% 7.75/5.70 thf(fact_4682_less__minus__one__simps_I1_J,axiom,
% 7.75/5.70 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(1)
% 7.75/5.70 thf(fact_4683_less__minus__one__simps_I3_J,axiom,
% 7.75/5.70 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(3)
% 7.75/5.70 thf(fact_4684_less__minus__one__simps_I3_J,axiom,
% 7.75/5.70 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(3)
% 7.75/5.70 thf(fact_4685_less__minus__one__simps_I3_J,axiom,
% 7.75/5.70 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(3)
% 7.75/5.70 thf(fact_4686_less__minus__one__simps_I3_J,axiom,
% 7.75/5.70 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_one_simps(3)
% 7.75/5.70 thf(fact_4687_neg__numeral__le__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_one
% 7.75/5.70 thf(fact_4688_neg__numeral__le__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_one
% 7.75/5.70 thf(fact_4689_neg__numeral__le__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_one
% 7.75/5.70 thf(fact_4690_neg__numeral__le__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_one
% 7.75/5.70 thf(fact_4691_neg__one__le__numeral,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_le_numeral
% 7.75/5.70 thf(fact_4692_neg__one__le__numeral,axiom,
% 7.75/5.70 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_le_numeral
% 7.75/5.70 thf(fact_4693_neg__one__le__numeral,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_le_numeral
% 7.75/5.70 thf(fact_4694_neg__one__le__numeral,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_le_numeral
% 7.75/5.70 thf(fact_4695_neg__numeral__le__neg__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_neg_one
% 7.75/5.70 thf(fact_4696_neg__numeral__le__neg__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_neg_one
% 7.75/5.70 thf(fact_4697_neg__numeral__le__neg__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_neg_one
% 7.75/5.70 thf(fact_4698_neg__numeral__le__neg__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_le_neg_one
% 7.75/5.70 thf(fact_4699_not__numeral__le__neg__one,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_le_neg_one
% 7.75/5.70 thf(fact_4700_not__numeral__le__neg__one,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_le_neg_one
% 7.75/5.70 thf(fact_4701_not__numeral__le__neg__one,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_le_neg_one
% 7.75/5.70 thf(fact_4702_not__numeral__le__neg__one,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_le_neg_one
% 7.75/5.70 thf(fact_4703_not__one__le__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_one_le_neg_numeral
% 7.75/5.70 thf(fact_4704_not__one__le__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_one_le_neg_numeral
% 7.75/5.70 thf(fact_4705_not__one__le__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_one_le_neg_numeral
% 7.75/5.70 thf(fact_4706_not__one__le__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_one_le_neg_numeral
% 7.75/5.70 thf(fact_4707_neg__numeral__less__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_one
% 7.75/5.70 thf(fact_4708_neg__numeral__less__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_one
% 7.75/5.70 thf(fact_4709_neg__numeral__less__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_one
% 7.75/5.70 thf(fact_4710_neg__numeral__less__one,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 7.75/5.70
% 7.75/5.70 % neg_numeral_less_one
% 7.75/5.70 thf(fact_4711_neg__one__less__numeral,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_less_numeral
% 7.75/5.70 thf(fact_4712_neg__one__less__numeral,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_less_numeral
% 7.75/5.70 thf(fact_4713_neg__one__less__numeral,axiom,
% 7.75/5.70 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_less_numeral
% 7.75/5.70 thf(fact_4714_neg__one__less__numeral,axiom,
% 7.75/5.70 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_one_less_numeral
% 7.75/5.70 thf(fact_4715_not__numeral__less__neg__one,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_less_neg_one
% 7.75/5.70 thf(fact_4716_not__numeral__less__neg__one,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_less_neg_one
% 7.75/5.70 thf(fact_4717_not__numeral__less__neg__one,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_less_neg_one
% 7.75/5.70 thf(fact_4718_not__numeral__less__neg__one,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_numeral_less_neg_one
% 7.75/5.70 thf(fact_4719_not__one__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_one_less_neg_numeral
% 7.75/5.70 thf(fact_4720_not__one__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_one_less_neg_numeral
% 7.75/5.70 thf(fact_4721_not__one__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_one_less_neg_numeral
% 7.75/5.70 thf(fact_4722_not__one__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_one_less_neg_numeral
% 7.75/5.70 thf(fact_4723_not__neg__one__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_neg_one_less_neg_numeral
% 7.75/5.70 thf(fact_4724_not__neg__one__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_neg_one_less_neg_numeral
% 7.75/5.70 thf(fact_4725_not__neg__one__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_neg_one_less_neg_numeral
% 7.75/5.70 thf(fact_4726_not__neg__one__less__neg__numeral,axiom,
% 7.75/5.70 ! [M: num] :
% 7.75/5.70 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % not_neg_one_less_neg_numeral
% 7.75/5.70 thf(fact_4727_uminus__numeral__One,axiom,
% 7.75/5.70 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_numeral_One
% 7.75/5.70 thf(fact_4728_uminus__numeral__One,axiom,
% 7.75/5.70 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 7.75/5.70 = ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_numeral_One
% 7.75/5.70 thf(fact_4729_uminus__numeral__One,axiom,
% 7.75/5.70 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 7.75/5.70 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_numeral_One
% 7.75/5.70 thf(fact_4730_uminus__numeral__One,axiom,
% 7.75/5.70 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_numeral_One
% 7.75/5.70 thf(fact_4731_uminus__numeral__One,axiom,
% 7.75/5.70 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 7.75/5.70 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_numeral_One
% 7.75/5.70 thf(fact_4732_mult__1s__ring__1_I1_J,axiom,
% 7.75/5.70 ! [B: int] :
% 7.75/5.70 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 7.75/5.70 = ( uminus_uminus_int @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(1)
% 7.75/5.70 thf(fact_4733_mult__1s__ring__1_I1_J,axiom,
% 7.75/5.70 ! [B: real] :
% 7.75/5.70 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 7.75/5.70 = ( uminus_uminus_real @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(1)
% 7.75/5.70 thf(fact_4734_mult__1s__ring__1_I1_J,axiom,
% 7.75/5.70 ! [B: code_integer] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 7.75/5.70 = ( uminus1351360451143612070nteger @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(1)
% 7.75/5.70 thf(fact_4735_mult__1s__ring__1_I1_J,axiom,
% 7.75/5.70 ! [B: complex] :
% 7.75/5.70 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(1)
% 7.75/5.70 thf(fact_4736_mult__1s__ring__1_I1_J,axiom,
% 7.75/5.70 ! [B: rat] :
% 7.75/5.70 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 7.75/5.70 = ( uminus_uminus_rat @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(1)
% 7.75/5.70 thf(fact_4737_mult__1s__ring__1_I2_J,axiom,
% 7.75/5.70 ! [B: int] :
% 7.75/5.70 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 7.75/5.70 = ( uminus_uminus_int @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(2)
% 7.75/5.70 thf(fact_4738_mult__1s__ring__1_I2_J,axiom,
% 7.75/5.70 ! [B: real] :
% 7.75/5.70 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 7.75/5.70 = ( uminus_uminus_real @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(2)
% 7.75/5.70 thf(fact_4739_mult__1s__ring__1_I2_J,axiom,
% 7.75/5.70 ! [B: code_integer] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 7.75/5.70 = ( uminus1351360451143612070nteger @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(2)
% 7.75/5.70 thf(fact_4740_mult__1s__ring__1_I2_J,axiom,
% 7.75/5.70 ! [B: complex] :
% 7.75/5.70 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(2)
% 7.75/5.70 thf(fact_4741_mult__1s__ring__1_I2_J,axiom,
% 7.75/5.70 ! [B: rat] :
% 7.75/5.70 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 7.75/5.70 = ( uminus_uminus_rat @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_1s_ring_1(2)
% 7.75/5.70 thf(fact_4742_divide__eq__minus__1__iff,axiom,
% 7.75/5.70 ! [A: real,B: real] :
% 7.75/5.70 ( ( ( divide_divide_real @ A @ B )
% 7.75/5.70 = ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.70 = ( ( B != zero_zero_real )
% 7.75/5.70 & ( A
% 7.75/5.70 = ( uminus_uminus_real @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_eq_minus_1_iff
% 7.75/5.70 thf(fact_4743_divide__eq__minus__1__iff,axiom,
% 7.75/5.70 ! [A: complex,B: complex] :
% 7.75/5.70 ( ( ( divide1717551699836669952omplex @ A @ B )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.70 = ( ( B != zero_zero_complex )
% 7.75/5.70 & ( A
% 7.75/5.70 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_eq_minus_1_iff
% 7.75/5.70 thf(fact_4744_divide__eq__minus__1__iff,axiom,
% 7.75/5.70 ! [A: rat,B: rat] :
% 7.75/5.70 ( ( ( divide_divide_rat @ A @ B )
% 7.75/5.70 = ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.70 = ( ( B != zero_zero_rat )
% 7.75/5.70 & ( A
% 7.75/5.70 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_eq_minus_1_iff
% 7.75/5.70 thf(fact_4745_nonzero__neg__divide__eq__eq2,axiom,
% 7.75/5.70 ! [B: real,C: real,A: real] :
% 7.75/5.70 ( ( B != zero_zero_real )
% 7.75/5.70 => ( ( C
% 7.75/5.70 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 7.75/5.70 = ( ( times_times_real @ C @ B )
% 7.75/5.70 = ( uminus_uminus_real @ A ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_neg_divide_eq_eq2
% 7.75/5.70 thf(fact_4746_nonzero__neg__divide__eq__eq2,axiom,
% 7.75/5.70 ! [B: complex,C: complex,A: complex] :
% 7.75/5.70 ( ( B != zero_zero_complex )
% 7.75/5.70 => ( ( C
% 7.75/5.70 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 7.75/5.70 = ( ( times_times_complex @ C @ B )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_neg_divide_eq_eq2
% 7.75/5.70 thf(fact_4747_nonzero__neg__divide__eq__eq2,axiom,
% 7.75/5.70 ! [B: rat,C: rat,A: rat] :
% 7.75/5.70 ( ( B != zero_zero_rat )
% 7.75/5.70 => ( ( C
% 7.75/5.70 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 7.75/5.70 = ( ( times_times_rat @ C @ B )
% 7.75/5.70 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_neg_divide_eq_eq2
% 7.75/5.70 thf(fact_4748_nonzero__neg__divide__eq__eq,axiom,
% 7.75/5.70 ! [B: real,A: real,C: real] :
% 7.75/5.70 ( ( B != zero_zero_real )
% 7.75/5.70 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.70 = C )
% 7.75/5.70 = ( ( uminus_uminus_real @ A )
% 7.75/5.70 = ( times_times_real @ C @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_neg_divide_eq_eq
% 7.75/5.70 thf(fact_4749_nonzero__neg__divide__eq__eq,axiom,
% 7.75/5.70 ! [B: complex,A: complex,C: complex] :
% 7.75/5.70 ( ( B != zero_zero_complex )
% 7.75/5.70 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 7.75/5.70 = C )
% 7.75/5.70 = ( ( uminus1482373934393186551omplex @ A )
% 7.75/5.70 = ( times_times_complex @ C @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_neg_divide_eq_eq
% 7.75/5.70 thf(fact_4750_nonzero__neg__divide__eq__eq,axiom,
% 7.75/5.70 ! [B: rat,A: rat,C: rat] :
% 7.75/5.70 ( ( B != zero_zero_rat )
% 7.75/5.70 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 7.75/5.70 = C )
% 7.75/5.70 = ( ( uminus_uminus_rat @ A )
% 7.75/5.70 = ( times_times_rat @ C @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nonzero_neg_divide_eq_eq
% 7.75/5.70 thf(fact_4751_minus__divide__eq__eq,axiom,
% 7.75/5.70 ! [B: real,C: real,A: real] :
% 7.75/5.70 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 7.75/5.70 = A )
% 7.75/5.70 = ( ( ( C != zero_zero_real )
% 7.75/5.70 => ( ( uminus_uminus_real @ B )
% 7.75/5.70 = ( times_times_real @ A @ C ) ) )
% 7.75/5.70 & ( ( C = zero_zero_real )
% 7.75/5.70 => ( A = zero_zero_real ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_eq_eq
% 7.75/5.70 thf(fact_4752_minus__divide__eq__eq,axiom,
% 7.75/5.70 ! [B: complex,C: complex,A: complex] :
% 7.75/5.70 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.70 = A )
% 7.75/5.70 = ( ( ( C != zero_zero_complex )
% 7.75/5.70 => ( ( uminus1482373934393186551omplex @ B )
% 7.75/5.70 = ( times_times_complex @ A @ C ) ) )
% 7.75/5.70 & ( ( C = zero_zero_complex )
% 7.75/5.70 => ( A = zero_zero_complex ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_eq_eq
% 7.75/5.70 thf(fact_4753_minus__divide__eq__eq,axiom,
% 7.75/5.70 ! [B: rat,C: rat,A: rat] :
% 7.75/5.70 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.70 = A )
% 7.75/5.70 = ( ( ( C != zero_zero_rat )
% 7.75/5.70 => ( ( uminus_uminus_rat @ B )
% 7.75/5.70 = ( times_times_rat @ A @ C ) ) )
% 7.75/5.70 & ( ( C = zero_zero_rat )
% 7.75/5.70 => ( A = zero_zero_rat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_eq_eq
% 7.75/5.70 thf(fact_4754_eq__minus__divide__eq,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 7.75/5.70 = ( ( ( C != zero_zero_real )
% 7.75/5.70 => ( ( times_times_real @ A @ C )
% 7.75/5.70 = ( uminus_uminus_real @ B ) ) )
% 7.75/5.70 & ( ( C = zero_zero_real )
% 7.75/5.70 => ( A = zero_zero_real ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_minus_divide_eq
% 7.75/5.70 thf(fact_4755_eq__minus__divide__eq,axiom,
% 7.75/5.70 ! [A: complex,B: complex,C: complex] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 7.75/5.70 = ( ( ( C != zero_zero_complex )
% 7.75/5.70 => ( ( times_times_complex @ A @ C )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ B ) ) )
% 7.75/5.70 & ( ( C = zero_zero_complex )
% 7.75/5.70 => ( A = zero_zero_complex ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_minus_divide_eq
% 7.75/5.70 thf(fact_4756_eq__minus__divide__eq,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 7.75/5.70 = ( ( ( C != zero_zero_rat )
% 7.75/5.70 => ( ( times_times_rat @ A @ C )
% 7.75/5.70 = ( uminus_uminus_rat @ B ) ) )
% 7.75/5.70 & ( ( C = zero_zero_rat )
% 7.75/5.70 => ( A = zero_zero_rat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_minus_divide_eq
% 7.75/5.70 thf(fact_4757_inf__period_I4_J,axiom,
% 7.75/5.70 ! [D2: rat,D4: rat,T: rat] :
% 7.75/5.70 ( ( dvd_dvd_rat @ D2 @ D4 )
% 7.75/5.70 => ! [X5: rat,K5: rat] :
% 7.75/5.70 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T ) ) )
% 7.75/5.70 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K5 @ D4 ) ) @ T ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(4)
% 7.75/5.70 thf(fact_4758_inf__period_I4_J,axiom,
% 7.75/5.70 ! [D2: real,D4: real,T: real] :
% 7.75/5.70 ( ( dvd_dvd_real @ D2 @ D4 )
% 7.75/5.70 => ! [X5: real,K5: real] :
% 7.75/5.70 ( ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ T ) ) )
% 7.75/5.70 = ( ~ ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K5 @ D4 ) ) @ T ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(4)
% 7.75/5.70 thf(fact_4759_inf__period_I4_J,axiom,
% 7.75/5.70 ! [D2: int,D4: int,T: int] :
% 7.75/5.70 ( ( dvd_dvd_int @ D2 @ D4 )
% 7.75/5.70 => ! [X5: int,K5: int] :
% 7.75/5.70 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) ) )
% 7.75/5.70 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K5 @ D4 ) ) @ T ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(4)
% 7.75/5.70 thf(fact_4760_inf__period_I4_J,axiom,
% 7.75/5.70 ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 7.75/5.70 ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 7.75/5.70 => ! [X5: code_integer,K5: code_integer] :
% 7.75/5.70 ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T ) ) )
% 7.75/5.70 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K5 @ D4 ) ) @ T ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(4)
% 7.75/5.70 thf(fact_4761_inf__period_I4_J,axiom,
% 7.75/5.70 ! [D2: complex,D4: complex,T: complex] :
% 7.75/5.70 ( ( dvd_dvd_complex @ D2 @ D4 )
% 7.75/5.70 => ! [X5: complex,K5: complex] :
% 7.75/5.70 ( ( ~ ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ X5 @ T ) ) )
% 7.75/5.70 = ( ~ ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K5 @ D4 ) ) @ T ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(4)
% 7.75/5.70 thf(fact_4762_inf__period_I3_J,axiom,
% 7.75/5.70 ! [D2: rat,D4: rat,T: rat] :
% 7.75/5.70 ( ( dvd_dvd_rat @ D2 @ D4 )
% 7.75/5.70 => ! [X5: rat,K5: rat] :
% 7.75/5.70 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T ) )
% 7.75/5.70 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K5 @ D4 ) ) @ T ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(3)
% 7.75/5.70 thf(fact_4763_inf__period_I3_J,axiom,
% 7.75/5.70 ! [D2: real,D4: real,T: real] :
% 7.75/5.70 ( ( dvd_dvd_real @ D2 @ D4 )
% 7.75/5.70 => ! [X5: real,K5: real] :
% 7.75/5.70 ( ( dvd_dvd_real @ D2 @ ( plus_plus_real @ X5 @ T ) )
% 7.75/5.70 = ( dvd_dvd_real @ D2 @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K5 @ D4 ) ) @ T ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(3)
% 7.75/5.70 thf(fact_4764_inf__period_I3_J,axiom,
% 7.75/5.70 ! [D2: int,D4: int,T: int] :
% 7.75/5.70 ( ( dvd_dvd_int @ D2 @ D4 )
% 7.75/5.70 => ! [X5: int,K5: int] :
% 7.75/5.70 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 7.75/5.70 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K5 @ D4 ) ) @ T ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(3)
% 7.75/5.70 thf(fact_4765_inf__period_I3_J,axiom,
% 7.75/5.70 ! [D2: code_integer,D4: code_integer,T: code_integer] :
% 7.75/5.70 ( ( dvd_dvd_Code_integer @ D2 @ D4 )
% 7.75/5.70 => ! [X5: code_integer,K5: code_integer] :
% 7.75/5.70 ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T ) )
% 7.75/5.70 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K5 @ D4 ) ) @ T ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(3)
% 7.75/5.70 thf(fact_4766_inf__period_I3_J,axiom,
% 7.75/5.70 ! [D2: complex,D4: complex,T: complex] :
% 7.75/5.70 ( ( dvd_dvd_complex @ D2 @ D4 )
% 7.75/5.70 => ! [X5: complex,K5: complex] :
% 7.75/5.70 ( ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ X5 @ T ) )
% 7.75/5.70 = ( dvd_dvd_complex @ D2 @ ( plus_plus_complex @ ( minus_minus_complex @ X5 @ ( times_times_complex @ K5 @ D4 ) ) @ T ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inf_period(3)
% 7.75/5.70 thf(fact_4767_power__minus,axiom,
% 7.75/5.70 ! [A: int,N: nat] :
% 7.75/5.70 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 7.75/5.70 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus
% 7.75/5.70 thf(fact_4768_power__minus,axiom,
% 7.75/5.70 ! [A: real,N: nat] :
% 7.75/5.70 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 7.75/5.70 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus
% 7.75/5.70 thf(fact_4769_power__minus,axiom,
% 7.75/5.70 ! [A: code_integer,N: nat] :
% 7.75/5.70 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 7.75/5.70 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus
% 7.75/5.70 thf(fact_4770_power__minus,axiom,
% 7.75/5.70 ! [A: complex,N: nat] :
% 7.75/5.70 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 7.75/5.70 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus
% 7.75/5.70 thf(fact_4771_power__minus,axiom,
% 7.75/5.70 ! [A: rat,N: nat] :
% 7.75/5.70 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 7.75/5.70 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus
% 7.75/5.70 thf(fact_4772_power__minus__Bit0,axiom,
% 7.75/5.70 ! [X: int,K: num] :
% 7.75/5.70 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 7.75/5.70 = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_Bit0
% 7.75/5.70 thf(fact_4773_power__minus__Bit0,axiom,
% 7.75/5.70 ! [X: real,K: num] :
% 7.75/5.70 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 7.75/5.70 = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_Bit0
% 7.75/5.70 thf(fact_4774_power__minus__Bit0,axiom,
% 7.75/5.70 ! [X: code_integer,K: num] :
% 7.75/5.70 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 7.75/5.70 = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_Bit0
% 7.75/5.70 thf(fact_4775_power__minus__Bit0,axiom,
% 7.75/5.70 ! [X: complex,K: num] :
% 7.75/5.70 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 7.75/5.70 = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_Bit0
% 7.75/5.70 thf(fact_4776_power__minus__Bit0,axiom,
% 7.75/5.70 ! [X: rat,K: num] :
% 7.75/5.70 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 7.75/5.70 = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_Bit0
% 7.75/5.70 thf(fact_4777_zmde,axiom,
% 7.75/5.70 ! [B: int,A: int] :
% 7.75/5.70 ( ( times_times_int @ B @ ( divide_divide_int @ A @ B ) )
% 7.75/5.70 = ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zmde
% 7.75/5.70 thf(fact_4778_zmde,axiom,
% 7.75/5.70 ! [B: code_integer,A: code_integer] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) )
% 7.75/5.70 = ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % zmde
% 7.75/5.70 thf(fact_4779_minus__mult__div__eq__mod,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 7.75/5.70 = ( modulo_modulo_nat @ A @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mult_div_eq_mod
% 7.75/5.70 thf(fact_4780_minus__mult__div__eq__mod,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 7.75/5.70 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mult_div_eq_mod
% 7.75/5.70 thf(fact_4781_minus__mult__div__eq__mod,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 7.75/5.70 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mult_div_eq_mod
% 7.75/5.70 thf(fact_4782_minus__mod__eq__mult__div,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 7.75/5.70 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mod_eq_mult_div
% 7.75/5.70 thf(fact_4783_minus__mod__eq__mult__div,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 7.75/5.70 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mod_eq_mult_div
% 7.75/5.70 thf(fact_4784_minus__mod__eq__mult__div,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 7.75/5.70 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mod_eq_mult_div
% 7.75/5.70 thf(fact_4785_minus__mod__eq__div__mult,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 7.75/5.70 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mod_eq_div_mult
% 7.75/5.70 thf(fact_4786_minus__mod__eq__div__mult,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 7.75/5.70 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mod_eq_div_mult
% 7.75/5.70 thf(fact_4787_minus__mod__eq__div__mult,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 7.75/5.70 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_mod_eq_div_mult
% 7.75/5.70 thf(fact_4788_minus__div__mult__eq__mod,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 7.75/5.70 = ( modulo_modulo_nat @ A @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_div_mult_eq_mod
% 7.75/5.70 thf(fact_4789_minus__div__mult__eq__mod,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 7.75/5.70 = ( modulo_modulo_int @ A @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_div_mult_eq_mod
% 7.75/5.70 thf(fact_4790_minus__div__mult__eq__mod,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 7.75/5.70 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_div_mult_eq_mod
% 7.75/5.70 thf(fact_4791_numeral__Bit1,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 7.75/5.70 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_Bit1
% 7.75/5.70 thf(fact_4792_numeral__Bit1,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 7.75/5.70 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_Bit1
% 7.75/5.70 thf(fact_4793_numeral__Bit1,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 7.75/5.70 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_Bit1
% 7.75/5.70 thf(fact_4794_numeral__Bit1,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 7.75/5.70 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_Bit1
% 7.75/5.70 thf(fact_4795_numeral__Bit1,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 7.75/5.70 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_Bit1
% 7.75/5.70 thf(fact_4796_eval__nat__numeral_I3_J,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 7.75/5.70 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eval_nat_numeral(3)
% 7.75/5.70 thf(fact_4797_power__diff,axiom,
% 7.75/5.70 ! [A: code_integer,N: nat,M: nat] :
% 7.75/5.70 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_diff
% 7.75/5.70 thf(fact_4798_power__diff,axiom,
% 7.75/5.70 ! [A: complex,N: nat,M: nat] :
% 7.75/5.70 ( ( A != zero_zero_complex )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_diff
% 7.75/5.70 thf(fact_4799_power__diff,axiom,
% 7.75/5.70 ! [A: real,N: nat,M: nat] :
% 7.75/5.70 ( ( A != zero_zero_real )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_diff
% 7.75/5.70 thf(fact_4800_power__diff,axiom,
% 7.75/5.70 ! [A: rat,N: nat,M: nat] :
% 7.75/5.70 ( ( A != zero_zero_rat )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_diff
% 7.75/5.70 thf(fact_4801_power__diff,axiom,
% 7.75/5.70 ! [A: nat,N: nat,M: nat] :
% 7.75/5.70 ( ( A != zero_zero_nat )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_diff
% 7.75/5.70 thf(fact_4802_power__diff,axiom,
% 7.75/5.70 ! [A: int,N: nat,M: nat] :
% 7.75/5.70 ( ( A != zero_zero_int )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_diff
% 7.75/5.70 thf(fact_4803_cong__exp__iff__simps_I10_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num,N: num] :
% 7.75/5.70 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(10)
% 7.75/5.70 thf(fact_4804_cong__exp__iff__simps_I10_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num,N: num] :
% 7.75/5.70 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(10)
% 7.75/5.70 thf(fact_4805_cong__exp__iff__simps_I10_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num,N: num] :
% 7.75/5.70 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(10)
% 7.75/5.70 thf(fact_4806_cong__exp__iff__simps_I12_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num,N: num] :
% 7.75/5.70 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(12)
% 7.75/5.70 thf(fact_4807_cong__exp__iff__simps_I12_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num,N: num] :
% 7.75/5.70 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(12)
% 7.75/5.70 thf(fact_4808_cong__exp__iff__simps_I12_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num,N: num] :
% 7.75/5.70 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(12)
% 7.75/5.70 thf(fact_4809_cong__exp__iff__simps_I13_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num,N: num] :
% 7.75/5.70 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.70 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 7.75/5.70 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(13)
% 7.75/5.70 thf(fact_4810_cong__exp__iff__simps_I13_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num,N: num] :
% 7.75/5.70 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.70 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 7.75/5.70 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(13)
% 7.75/5.70 thf(fact_4811_cong__exp__iff__simps_I13_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num,N: num] :
% 7.75/5.70 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.70 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(13)
% 7.75/5.70 thf(fact_4812_reals__Archimedean3,axiom,
% 7.75/5.70 ! [X: real] :
% 7.75/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.70 => ! [Y4: real] :
% 7.75/5.70 ? [N2: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % reals_Archimedean3
% 7.75/5.70 thf(fact_4813_diff__Suc__less,axiom,
% 7.75/5.70 ! [N: nat,I: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_Suc_less
% 7.75/5.70 thf(fact_4814_nz__le__conv__less,axiom,
% 7.75/5.70 ! [K: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.70 => ( ( ord_less_eq_nat @ K @ M )
% 7.75/5.70 => ( ord_less_nat @ ( minus_minus_nat @ K @ ( suc @ zero_zero_nat ) ) @ M ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nz_le_conv_less
% 7.75/5.70 thf(fact_4815_Suc__n__minus__m__eq,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.70 => ( ( ord_less_nat @ one_one_nat @ M )
% 7.75/5.70 => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 7.75/5.70 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Suc_n_minus_m_eq
% 7.75/5.70 thf(fact_4816_nat__diff__split,axiom,
% 7.75/5.70 ! [P: nat > $o,A: nat,B: nat] :
% 7.75/5.70 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 7.75/5.70 = ( ( ( ord_less_nat @ A @ B )
% 7.75/5.70 => ( P @ zero_zero_nat ) )
% 7.75/5.70 & ! [D: nat] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( plus_plus_nat @ B @ D ) )
% 7.75/5.70 => ( P @ D ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_diff_split
% 7.75/5.70 thf(fact_4817_nat__diff__split__asm,axiom,
% 7.75/5.70 ! [P: nat > $o,A: nat,B: nat] :
% 7.75/5.70 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 7.75/5.70 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 7.75/5.70 & ~ ( P @ zero_zero_nat ) )
% 7.75/5.70 | ? [D: nat] :
% 7.75/5.70 ( ( A
% 7.75/5.70 = ( plus_plus_nat @ B @ D ) )
% 7.75/5.70 & ~ ( P @ D ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_diff_split_asm
% 7.75/5.70 thf(fact_4818_real__of__nat__div,axiom,
% 7.75/5.70 ! [D2: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_nat @ D2 @ N )
% 7.75/5.70 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D2 ) )
% 7.75/5.70 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % real_of_nat_div
% 7.75/5.70 thf(fact_4819_nat__less__add__iff2,axiom,
% 7.75/5.70 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ I @ J )
% 7.75/5.70 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 7.75/5.70 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_less_add_iff2
% 7.75/5.70 thf(fact_4820_nat__less__add__iff1,axiom,
% 7.75/5.70 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ J @ I )
% 7.75/5.70 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 7.75/5.70 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_less_add_iff1
% 7.75/5.70 thf(fact_4821_real__of__nat__div__aux,axiom,
% 7.75/5.70 ! [X: nat,D2: nat] :
% 7.75/5.70 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D2 ) )
% 7.75/5.70 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D2 ) ) @ ( semiri5074537144036343181t_real @ D2 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % real_of_nat_div_aux
% 7.75/5.70 thf(fact_4822_minusinfinity,axiom,
% 7.75/5.70 ! [D2: int,P1: int > $o,P: int > $o] :
% 7.75/5.70 ( ( ord_less_int @ zero_zero_int @ D2 )
% 7.75/5.70 => ( ! [X3: int,K2: int] :
% 7.75/5.70 ( ( P1 @ X3 )
% 7.75/5.70 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 7.75/5.70 => ( ? [Z4: int] :
% 7.75/5.70 ! [X3: int] :
% 7.75/5.70 ( ( ord_less_int @ X3 @ Z4 )
% 7.75/5.70 => ( ( P @ X3 )
% 7.75/5.70 = ( P1 @ X3 ) ) )
% 7.75/5.70 => ( ? [X_12: int] : ( P1 @ X_12 )
% 7.75/5.70 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minusinfinity
% 7.75/5.70 thf(fact_4823_plusinfinity,axiom,
% 7.75/5.70 ! [D2: int,P3: int > $o,P: int > $o] :
% 7.75/5.70 ( ( ord_less_int @ zero_zero_int @ D2 )
% 7.75/5.70 => ( ! [X3: int,K2: int] :
% 7.75/5.70 ( ( P3 @ X3 )
% 7.75/5.70 = ( P3 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 7.75/5.70 => ( ? [Z4: int] :
% 7.75/5.70 ! [X3: int] :
% 7.75/5.70 ( ( ord_less_int @ Z4 @ X3 )
% 7.75/5.70 => ( ( P @ X3 )
% 7.75/5.70 = ( P3 @ X3 ) ) )
% 7.75/5.70 => ( ? [X_12: int] : ( P3 @ X_12 )
% 7.75/5.70 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % plusinfinity
% 7.75/5.70 thf(fact_4824_less__1__helper,axiom,
% 7.75/5.70 ! [N: int,M: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ N @ M )
% 7.75/5.70 => ( ord_less_int @ ( minus_minus_int @ N @ one_one_int ) @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_1_helper
% 7.75/5.70 thf(fact_4825_int__induct,axiom,
% 7.75/5.70 ! [P: int > $o,K: int,I: int] :
% 7.75/5.70 ( ( P @ K )
% 7.75/5.70 => ( ! [I3: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ K @ I3 )
% 7.75/5.70 => ( ( P @ I3 )
% 7.75/5.70 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 7.75/5.70 => ( ! [I3: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ I3 @ K )
% 7.75/5.70 => ( ( P @ I3 )
% 7.75/5.70 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 7.75/5.70 => ( P @ I ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % int_induct
% 7.75/5.70 thf(fact_4826_int__mod__le_H,axiom,
% 7.75/5.70 ! [B: int,N: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ B @ N ) )
% 7.75/5.70 => ( ord_less_eq_int @ ( modulo_modulo_int @ B @ N ) @ ( minus_minus_int @ B @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % int_mod_le'
% 7.75/5.70 thf(fact_4827_mod__nat__add,axiom,
% 7.75/5.70 ! [X: nat,Z: nat,Y: nat] :
% 7.75/5.70 ( ( ord_less_nat @ X @ Z )
% 7.75/5.70 => ( ( ord_less_nat @ Y @ Z )
% 7.75/5.70 => ( ( ( ord_less_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 7.75/5.70 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 7.75/5.70 = ( plus_plus_nat @ X @ Y ) ) )
% 7.75/5.70 & ( ~ ( ord_less_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 7.75/5.70 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 7.75/5.70 = ( minus_minus_nat @ ( plus_plus_nat @ X @ Y ) @ Z ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_nat_add
% 7.75/5.70 thf(fact_4828_dvd__minus__add,axiom,
% 7.75/5.70 ! [Q3: nat,N: nat,R2: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ Q3 @ N )
% 7.75/5.70 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M ) )
% 7.75/5.70 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q3 ) )
% 7.75/5.70 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q3 ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % dvd_minus_add
% 7.75/5.70 thf(fact_4829_diff__mod__le,axiom,
% 7.75/5.70 ! [A: nat,D2: nat,B: nat] :
% 7.75/5.70 ( ( ord_less_nat @ A @ D2 )
% 7.75/5.70 => ( ( dvd_dvd_nat @ B @ D2 )
% 7.75/5.70 => ( ord_less_eq_nat @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) @ ( minus_minus_nat @ D2 @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_mod_le
% 7.75/5.70 thf(fact_4830_mod__nat__eqI,axiom,
% 7.75/5.70 ! [R2: nat,N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ R2 @ N )
% 7.75/5.70 => ( ( ord_less_eq_nat @ R2 @ M )
% 7.75/5.70 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 7.75/5.70 => ( ( modulo_modulo_nat @ M @ N )
% 7.75/5.70 = R2 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_nat_eqI
% 7.75/5.70 thf(fact_4831_modulo__nat__def,axiom,
% 7.75/5.70 ( modulo_modulo_nat
% 7.75/5.70 = ( ^ [M4: nat,N3: nat] : ( minus_minus_nat @ M4 @ ( times_times_nat @ ( divide_divide_nat @ M4 @ N3 ) @ N3 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % modulo_nat_def
% 7.75/5.70 thf(fact_4832_mod__div__equality__div__eq,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ B )
% 7.75/5.70 = ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_div_equality_div_eq
% 7.75/5.70 thf(fact_4833_m1mod22k,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % m1mod22k
% 7.75/5.70 thf(fact_4834_inverse__of__nat__le,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( N != zero_zero_nat )
% 7.75/5.70 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inverse_of_nat_le
% 7.75/5.70 thf(fact_4835_inverse__of__nat__le,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( N != zero_zero_nat )
% 7.75/5.70 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % inverse_of_nat_le
% 7.75/5.70 thf(fact_4836_mod__mult2__eq_H,axiom,
% 7.75/5.70 ! [A: code_integer,M: nat,N: nat] :
% 7.75/5.70 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 7.75/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_mult2_eq'
% 7.75/5.70 thf(fact_4837_mod__mult2__eq_H,axiom,
% 7.75/5.70 ! [A: int,M: nat,N: nat] :
% 7.75/5.70 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 7.75/5.70 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_mult2_eq'
% 7.75/5.70 thf(fact_4838_mod__mult2__eq_H,axiom,
% 7.75/5.70 ! [A: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 7.75/5.70 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_mult2_eq'
% 7.75/5.70 thf(fact_4839_frac__le__eq,axiom,
% 7.75/5.70 ! [Y: real,Z: real,X: real,W: real] :
% 7.75/5.70 ( ( Y != zero_zero_real )
% 7.75/5.70 => ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 7.75/5.70 = ( 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 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % frac_le_eq
% 7.75/5.70 thf(fact_4840_frac__le__eq,axiom,
% 7.75/5.70 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 7.75/5.70 ( ( Y != zero_zero_rat )
% 7.75/5.70 => ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 7.75/5.70 = ( 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 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % frac_le_eq
% 7.75/5.70 thf(fact_4841_frac__less__eq,axiom,
% 7.75/5.70 ! [Y: real,Z: real,X: real,W: real] :
% 7.75/5.70 ( ( Y != zero_zero_real )
% 7.75/5.70 => ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 7.75/5.70 = ( 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 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % frac_less_eq
% 7.75/5.70 thf(fact_4842_frac__less__eq,axiom,
% 7.75/5.70 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 7.75/5.70 ( ( Y != zero_zero_rat )
% 7.75/5.70 => ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 7.75/5.70 = ( 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 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % frac_less_eq
% 7.75/5.70 thf(fact_4843_pos__minus__divide__less__eq,axiom,
% 7.75/5.70 ! [C: real,B: real,A: real] :
% 7.75/5.70 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 7.75/5.70 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % pos_minus_divide_less_eq
% 7.75/5.70 thf(fact_4844_pos__minus__divide__less__eq,axiom,
% 7.75/5.70 ! [C: rat,B: rat,A: rat] :
% 7.75/5.70 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 7.75/5.70 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % pos_minus_divide_less_eq
% 7.75/5.70 thf(fact_4845_pos__less__minus__divide__eq,axiom,
% 7.75/5.70 ! [C: real,A: real,B: real] :
% 7.75/5.70 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 7.75/5.70 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % pos_less_minus_divide_eq
% 7.75/5.70 thf(fact_4846_pos__less__minus__divide__eq,axiom,
% 7.75/5.70 ! [C: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 7.75/5.70 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % pos_less_minus_divide_eq
% 7.75/5.70 thf(fact_4847_neg__minus__divide__less__eq,axiom,
% 7.75/5.70 ! [C: real,B: real,A: real] :
% 7.75/5.70 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 7.75/5.70 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_minus_divide_less_eq
% 7.75/5.70 thf(fact_4848_neg__minus__divide__less__eq,axiom,
% 7.75/5.70 ! [C: rat,B: rat,A: rat] :
% 7.75/5.70 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 7.75/5.70 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_minus_divide_less_eq
% 7.75/5.70 thf(fact_4849_neg__less__minus__divide__eq,axiom,
% 7.75/5.70 ! [C: real,A: real,B: real] :
% 7.75/5.70 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 7.75/5.70 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_less_minus_divide_eq
% 7.75/5.70 thf(fact_4850_neg__less__minus__divide__eq,axiom,
% 7.75/5.70 ! [C: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 7.75/5.70 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_less_minus_divide_eq
% 7.75/5.70 thf(fact_4851_minus__divide__less__eq,axiom,
% 7.75/5.70 ! [B: real,C: real,A: real] :
% 7.75/5.70 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 7.75/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_less_eq
% 7.75/5.70 thf(fact_4852_minus__divide__less__eq,axiom,
% 7.75/5.70 ! [B: rat,C: rat,A: rat] :
% 7.75/5.70 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 7.75/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_less_eq
% 7.75/5.70 thf(fact_4853_less__minus__divide__eq,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 7.75/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_divide_eq
% 7.75/5.70 thf(fact_4854_less__minus__divide__eq,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 7.75/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_minus_divide_eq
% 7.75/5.70 thf(fact_4855_eq__divide__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [W: num,B: real,C: real] :
% 7.75/5.70 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 7.75/5.70 = ( divide_divide_real @ B @ C ) )
% 7.75/5.70 = ( ( ( C != zero_zero_real )
% 7.75/5.70 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 7.75/5.70 = B ) )
% 7.75/5.70 & ( ( C = zero_zero_real )
% 7.75/5.70 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 7.75/5.70 = zero_zero_real ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_divide_eq_numeral(2)
% 7.75/5.70 thf(fact_4856_eq__divide__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [W: num,B: complex,C: complex] :
% 7.75/5.70 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.70 = ( divide1717551699836669952omplex @ B @ C ) )
% 7.75/5.70 = ( ( ( C != zero_zero_complex )
% 7.75/5.70 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 7.75/5.70 = B ) )
% 7.75/5.70 & ( ( C = zero_zero_complex )
% 7.75/5.70 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.70 = zero_zero_complex ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_divide_eq_numeral(2)
% 7.75/5.70 thf(fact_4857_eq__divide__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [W: num,B: rat,C: rat] :
% 7.75/5.70 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 7.75/5.70 = ( divide_divide_rat @ B @ C ) )
% 7.75/5.70 = ( ( ( C != zero_zero_rat )
% 7.75/5.70 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 7.75/5.70 = B ) )
% 7.75/5.70 & ( ( C = zero_zero_rat )
% 7.75/5.70 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 7.75/5.70 = zero_zero_rat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % eq_divide_eq_numeral(2)
% 7.75/5.70 thf(fact_4858_divide__eq__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [B: real,C: real,W: num] :
% 7.75/5.70 ( ( ( divide_divide_real @ B @ C )
% 7.75/5.70 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.70 = ( ( ( C != zero_zero_real )
% 7.75/5.70 => ( B
% 7.75/5.70 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ( C = zero_zero_real )
% 7.75/5.70 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 7.75/5.70 = zero_zero_real ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_eq_eq_numeral(2)
% 7.75/5.70 thf(fact_4859_divide__eq__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [B: complex,C: complex,W: num] :
% 7.75/5.70 ( ( ( divide1717551699836669952omplex @ B @ C )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 7.75/5.70 = ( ( ( C != zero_zero_complex )
% 7.75/5.70 => ( B
% 7.75/5.70 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ( C = zero_zero_complex )
% 7.75/5.70 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.70 = zero_zero_complex ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_eq_eq_numeral(2)
% 7.75/5.70 thf(fact_4860_divide__eq__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [B: rat,C: rat,W: num] :
% 7.75/5.70 ( ( ( divide_divide_rat @ B @ C )
% 7.75/5.70 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 7.75/5.70 = ( ( ( C != zero_zero_rat )
% 7.75/5.70 => ( B
% 7.75/5.70 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ( C = zero_zero_rat )
% 7.75/5.70 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 7.75/5.70 = zero_zero_rat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_eq_eq_numeral(2)
% 7.75/5.70 thf(fact_4861_power2__commute,axiom,
% 7.75/5.70 ! [X: code_integer,Y: code_integer] :
% 7.75/5.70 ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_commute
% 7.75/5.70 thf(fact_4862_power2__commute,axiom,
% 7.75/5.70 ! [X: complex,Y: complex] :
% 7.75/5.70 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( power_power_complex @ ( minus_minus_complex @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_commute
% 7.75/5.70 thf(fact_4863_power2__commute,axiom,
% 7.75/5.70 ! [X: real,Y: real] :
% 7.75/5.70 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( power_power_real @ ( minus_minus_real @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_commute
% 7.75/5.70 thf(fact_4864_power2__commute,axiom,
% 7.75/5.70 ! [X: int,Y: int] :
% 7.75/5.70 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( power_power_int @ ( minus_minus_int @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_commute
% 7.75/5.70 thf(fact_4865_minus__divide__add__eq__iff,axiom,
% 7.75/5.70 ! [Z: real,X: real,Y: real] :
% 7.75/5.70 ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 7.75/5.70 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_add_eq_iff
% 7.75/5.70 thf(fact_4866_minus__divide__add__eq__iff,axiom,
% 7.75/5.70 ! [Z: complex,X: complex,Y: complex] :
% 7.75/5.70 ( ( Z != zero_zero_complex )
% 7.75/5.70 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_add_eq_iff
% 7.75/5.70 thf(fact_4867_minus__divide__add__eq__iff,axiom,
% 7.75/5.70 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.70 ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 7.75/5.70 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_add_eq_iff
% 7.75/5.70 thf(fact_4868_add__divide__eq__if__simps_I3_J,axiom,
% 7.75/5.70 ! [Z: real,A: real,B: real] :
% 7.75/5.70 ( ( ( Z = zero_zero_real )
% 7.75/5.70 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 7.75/5.70 = B ) )
% 7.75/5.70 & ( ( Z != zero_zero_real )
% 7.75/5.70 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 7.75/5.70 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(3)
% 7.75/5.70 thf(fact_4869_add__divide__eq__if__simps_I3_J,axiom,
% 7.75/5.70 ! [Z: complex,A: complex,B: complex] :
% 7.75/5.70 ( ( ( Z = zero_zero_complex )
% 7.75/5.70 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 7.75/5.70 = B ) )
% 7.75/5.70 & ( ( Z != zero_zero_complex )
% 7.75/5.70 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 7.75/5.70 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(3)
% 7.75/5.70 thf(fact_4870_add__divide__eq__if__simps_I3_J,axiom,
% 7.75/5.70 ! [Z: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( ( Z = zero_zero_rat )
% 7.75/5.70 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 7.75/5.70 = B ) )
% 7.75/5.70 & ( ( Z != zero_zero_rat )
% 7.75/5.70 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 7.75/5.70 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_divide_eq_if_simps(3)
% 7.75/5.70 thf(fact_4871_odd__mod__4__div__2,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.70 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % odd_mod_4_div_2
% 7.75/5.70 thf(fact_4872_even__minus,axiom,
% 7.75/5.70 ! [A: int] :
% 7.75/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 7.75/5.70 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_minus
% 7.75/5.70 thf(fact_4873_even__minus,axiom,
% 7.75/5.70 ! [A: code_integer] :
% 7.75/5.70 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.70 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_minus
% 7.75/5.70 thf(fact_4874_power2__eq__iff,axiom,
% 7.75/5.70 ! [X: int,Y: int] :
% 7.75/5.70 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = ( ( X = Y )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_iff
% 7.75/5.70 thf(fact_4875_power2__eq__iff,axiom,
% 7.75/5.70 ! [X: real,Y: real] :
% 7.75/5.70 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = ( ( X = Y )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_iff
% 7.75/5.70 thf(fact_4876_power2__eq__iff,axiom,
% 7.75/5.70 ! [X: code_integer,Y: code_integer] :
% 7.75/5.70 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = ( ( X = Y )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_iff
% 7.75/5.70 thf(fact_4877_power2__eq__iff,axiom,
% 7.75/5.70 ! [X: complex,Y: complex] :
% 7.75/5.70 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = ( ( X = Y )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_iff
% 7.75/5.70 thf(fact_4878_power2__eq__iff,axiom,
% 7.75/5.70 ! [X: rat,Y: rat] :
% 7.75/5.70 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = ( ( X = Y )
% 7.75/5.70 | ( X
% 7.75/5.70 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_iff
% 7.75/5.70 thf(fact_4879_numeral__Bit1__div__2,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( numeral_numeral_nat @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_Bit1_div_2
% 7.75/5.70 thf(fact_4880_numeral__Bit1__div__2,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( numeral_numeral_int @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_Bit1_div_2
% 7.75/5.70 thf(fact_4881_real__archimedian__rdiv__eq__0,axiom,
% 7.75/5.70 ! [X: real,C: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ! [M2: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 7.75/5.70 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ X ) @ C ) )
% 7.75/5.70 => ( X = zero_zero_real ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % real_archimedian_rdiv_eq_0
% 7.75/5.70 thf(fact_4882_cong__exp__iff__simps_I3_J,axiom,
% 7.75/5.70 ! [N: num,Q3: num] :
% 7.75/5.70 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 != zero_zero_nat ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(3)
% 7.75/5.70 thf(fact_4883_cong__exp__iff__simps_I3_J,axiom,
% 7.75/5.70 ! [N: num,Q3: num] :
% 7.75/5.70 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 != zero_zero_int ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(3)
% 7.75/5.70 thf(fact_4884_cong__exp__iff__simps_I3_J,axiom,
% 7.75/5.70 ! [N: num,Q3: num] :
% 7.75/5.70 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 != zero_z3403309356797280102nteger ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(3)
% 7.75/5.70 thf(fact_4885_odd__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % odd_numeral
% 7.75/5.70 thf(fact_4886_odd__numeral,axiom,
% 7.75/5.70 ! [N: num] :
% 7.75/5.70 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % odd_numeral
% 7.75/5.70 thf(fact_4887_power__diff__power__eq,axiom,
% 7.75/5.70 ! [A: code_integer,N: nat,M: nat] :
% 7.75/5.70 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.70 => ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.70 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 7.75/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.70 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_diff_power_eq
% 7.75/5.70 thf(fact_4888_power__diff__power__eq,axiom,
% 7.75/5.70 ! [A: nat,N: nat,M: nat] :
% 7.75/5.70 ( ( A != zero_zero_nat )
% 7.75/5.70 => ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 7.75/5.70 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 7.75/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 7.75/5.70 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_diff_power_eq
% 7.75/5.70 thf(fact_4889_power__diff__power__eq,axiom,
% 7.75/5.70 ! [A: int,N: nat,M: nat] :
% 7.75/5.70 ( ( A != zero_zero_int )
% 7.75/5.70 => ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 7.75/5.70 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 7.75/5.70 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 7.75/5.70 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_diff_power_eq
% 7.75/5.70 thf(fact_4890_power3__eq__cube,axiom,
% 7.75/5.70 ! [A: assn] :
% 7.75/5.70 ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.70 = ( times_times_assn @ ( times_times_assn @ A @ A ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % power3_eq_cube
% 7.75/5.70 thf(fact_4891_power3__eq__cube,axiom,
% 7.75/5.70 ! [A: real] :
% 7.75/5.70 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.70 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % power3_eq_cube
% 7.75/5.70 thf(fact_4892_power3__eq__cube,axiom,
% 7.75/5.70 ! [A: nat] :
% 7.75/5.70 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.70 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % power3_eq_cube
% 7.75/5.70 thf(fact_4893_power3__eq__cube,axiom,
% 7.75/5.70 ! [A: int] :
% 7.75/5.70 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.70 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % power3_eq_cube
% 7.75/5.70 thf(fact_4894_power3__eq__cube,axiom,
% 7.75/5.70 ! [A: code_integer] :
% 7.75/5.70 ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.70 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ A ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % power3_eq_cube
% 7.75/5.70 thf(fact_4895_power3__eq__cube,axiom,
% 7.75/5.70 ! [A: complex] :
% 7.75/5.70 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.70 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 7.75/5.70
% 7.75/5.70 % power3_eq_cube
% 7.75/5.70 thf(fact_4896_numeral__3__eq__3,axiom,
% 7.75/5.70 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.70 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % numeral_3_eq_3
% 7.75/5.70 thf(fact_4897_Suc3__eq__add__3,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 7.75/5.70 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % Suc3_eq_add_3
% 7.75/5.70 thf(fact_4898_diff__le__diff__pow,axiom,
% 7.75/5.70 ! [K: nat,M: nat,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 7.75/5.70 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % diff_le_diff_pow
% 7.75/5.70 thf(fact_4899_Suc__diff__eq__diff__pred,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 7.75/5.70 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Suc_diff_eq_diff_pred
% 7.75/5.70 thf(fact_4900_Suc__pred_H,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( N
% 7.75/5.70 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Suc_pred'
% 7.75/5.70 thf(fact_4901_add__eq__if,axiom,
% 7.75/5.70 ( plus_plus_nat
% 7.75/5.70 = ( ^ [M4: nat,N3: nat] : ( if_nat @ ( M4 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M4 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % add_eq_if
% 7.75/5.70 thf(fact_4902_div__if,axiom,
% 7.75/5.70 ( divide_divide_nat
% 7.75/5.70 = ( ^ [M4: nat,N3: nat] :
% 7.75/5.70 ( if_nat
% 7.75/5.70 @ ( ( ord_less_nat @ M4 @ N3 )
% 7.75/5.70 | ( N3 = zero_zero_nat ) )
% 7.75/5.70 @ zero_zero_nat
% 7.75/5.70 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M4 @ N3 ) @ N3 ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_if
% 7.75/5.70 thf(fact_4903_div__geq,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ~ ( ord_less_nat @ M @ N )
% 7.75/5.70 => ( ( divide_divide_nat @ M @ N )
% 7.75/5.70 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_geq
% 7.75/5.70 thf(fact_4904_le__div__geq,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( divide_divide_nat @ M @ N )
% 7.75/5.70 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_div_geq
% 7.75/5.70 thf(fact_4905_mult__eq__if,axiom,
% 7.75/5.70 ( times_times_nat
% 7.75/5.70 = ( ^ [M4: nat,N3: nat] : ( if_nat @ ( M4 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N3 @ ( times_times_nat @ ( minus_minus_nat @ M4 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_eq_if
% 7.75/5.70 thf(fact_4906_power__sub,axiom,
% 7.75/5.70 ! [N: nat,M: nat,A: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.70 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 7.75/5.70 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 7.75/5.70 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_sub
% 7.75/5.70 thf(fact_4907_nat__mult__power__less__eq,axiom,
% 7.75/5.70 ! [B: nat,A: nat,N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.70 => ( ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ B @ N ) ) @ ( power_power_nat @ B @ M ) )
% 7.75/5.70 = ( ord_less_nat @ A @ ( power_power_nat @ B @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_mult_power_less_eq
% 7.75/5.70 thf(fact_4908_decr__mult__lemma,axiom,
% 7.75/5.70 ! [D2: int,P: int > $o,K: int] :
% 7.75/5.70 ( ( ord_less_int @ zero_zero_int @ D2 )
% 7.75/5.70 => ( ! [X3: int] :
% 7.75/5.70 ( ( P @ X3 )
% 7.75/5.70 => ( P @ ( minus_minus_int @ X3 @ D2 ) ) )
% 7.75/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.70 => ! [X5: int] :
% 7.75/5.70 ( ( P @ X5 )
% 7.75/5.70 => ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % decr_mult_lemma
% 7.75/5.70 thf(fact_4909_mod__pos__geq,axiom,
% 7.75/5.70 ! [L: int,K: int] :
% 7.75/5.70 ( ( ord_less_int @ zero_zero_int @ L )
% 7.75/5.70 => ( ( ord_less_eq_int @ L @ K )
% 7.75/5.70 => ( ( modulo_modulo_int @ K @ L )
% 7.75/5.70 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_pos_geq
% 7.75/5.70 thf(fact_4910_verit__less__mono__div__int2,axiom,
% 7.75/5.70 ! [A2: int,B3: int,N: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ A2 @ B3 )
% 7.75/5.70 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 7.75/5.70 => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % verit_less_mono_div_int2
% 7.75/5.70 thf(fact_4911_div__eq__minus1,axiom,
% 7.75/5.70 ! [B: int] :
% 7.75/5.70 ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.70 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_eq_minus1
% 7.75/5.70 thf(fact_4912_int__div__sub__1,axiom,
% 7.75/5.70 ! [M: int,N: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ one_one_int @ M )
% 7.75/5.70 => ( ( ( dvd_dvd_int @ M @ N )
% 7.75/5.70 => ( ( divide_divide_int @ ( minus_minus_int @ N @ one_one_int ) @ M )
% 7.75/5.70 = ( minus_minus_int @ ( divide_divide_int @ N @ M ) @ one_one_int ) ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_int @ M @ N )
% 7.75/5.70 => ( ( divide_divide_int @ ( minus_minus_int @ N @ one_one_int ) @ M )
% 7.75/5.70 = ( divide_divide_int @ N @ M ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % int_div_sub_1
% 7.75/5.70 thf(fact_4913_of__nat__less__two__power,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_two_power
% 7.75/5.70 thf(fact_4914_of__nat__less__two__power,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_two_power
% 7.75/5.70 thf(fact_4915_of__nat__less__two__power,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_two_power
% 7.75/5.70 thf(fact_4916_of__nat__less__two__power,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % of_nat_less_two_power
% 7.75/5.70 thf(fact_4917_num_Osize__gen_I3_J,axiom,
% 7.75/5.70 ! [X32: num] :
% 7.75/5.70 ( ( size_num @ ( bit1 @ X32 ) )
% 7.75/5.70 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % num.size_gen(3)
% 7.75/5.70 thf(fact_4918_scaling__mono,axiom,
% 7.75/5.70 ! [U: real,V: real,R2: real,S: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ U @ V )
% 7.75/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 7.75/5.70 => ( ( ord_less_eq_real @ R2 @ S )
% 7.75/5.70 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % scaling_mono
% 7.75/5.70 thf(fact_4919_scaling__mono,axiom,
% 7.75/5.70 ! [U: rat,V: rat,R2: rat,S: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ U @ V )
% 7.75/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 7.75/5.70 => ( ( ord_less_eq_rat @ R2 @ S )
% 7.75/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % scaling_mono
% 7.75/5.70 thf(fact_4920_signed__take__bit__rec,axiom,
% 7.75/5.70 ( bit_ri6519982836138164636nteger
% 7.75/5.70 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % signed_take_bit_rec
% 7.75/5.70 thf(fact_4921_signed__take__bit__rec,axiom,
% 7.75/5.70 ( bit_ri631733984087533419it_int
% 7.75/5.70 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % signed_take_bit_rec
% 7.75/5.70 thf(fact_4922_pos__minus__divide__le__eq,axiom,
% 7.75/5.70 ! [C: real,B: real,A: real] :
% 7.75/5.70 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 7.75/5.70 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % pos_minus_divide_le_eq
% 7.75/5.70 thf(fact_4923_pos__minus__divide__le__eq,axiom,
% 7.75/5.70 ! [C: rat,B: rat,A: rat] :
% 7.75/5.70 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 7.75/5.70 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % pos_minus_divide_le_eq
% 7.75/5.70 thf(fact_4924_pos__le__minus__divide__eq,axiom,
% 7.75/5.70 ! [C: real,A: real,B: real] :
% 7.75/5.70 ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 7.75/5.70 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % pos_le_minus_divide_eq
% 7.75/5.70 thf(fact_4925_pos__le__minus__divide__eq,axiom,
% 7.75/5.70 ! [C: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 7.75/5.70 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % pos_le_minus_divide_eq
% 7.75/5.70 thf(fact_4926_neg__minus__divide__le__eq,axiom,
% 7.75/5.70 ! [C: real,B: real,A: real] :
% 7.75/5.70 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 7.75/5.70 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_minus_divide_le_eq
% 7.75/5.70 thf(fact_4927_neg__minus__divide__le__eq,axiom,
% 7.75/5.70 ! [C: rat,B: rat,A: rat] :
% 7.75/5.70 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 7.75/5.70 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_minus_divide_le_eq
% 7.75/5.70 thf(fact_4928_neg__le__minus__divide__eq,axiom,
% 7.75/5.70 ! [C: real,A: real,B: real] :
% 7.75/5.70 ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 7.75/5.70 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_le_minus_divide_eq
% 7.75/5.70 thf(fact_4929_neg__le__minus__divide__eq,axiom,
% 7.75/5.70 ! [C: rat,A: rat,B: rat] :
% 7.75/5.70 ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 7.75/5.70 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % neg_le_minus_divide_eq
% 7.75/5.70 thf(fact_4930_minus__divide__le__eq,axiom,
% 7.75/5.70 ! [B: real,C: real,A: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 7.75/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_le_eq
% 7.75/5.70 thf(fact_4931_minus__divide__le__eq,axiom,
% 7.75/5.70 ! [B: rat,C: rat,A: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 7.75/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_divide_le_eq
% 7.75/5.70 thf(fact_4932_le__minus__divide__eq,axiom,
% 7.75/5.70 ! [A: real,B: real,C: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 7.75/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_divide_eq
% 7.75/5.70 thf(fact_4933_le__minus__divide__eq,axiom,
% 7.75/5.70 ! [A: rat,B: rat,C: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 7.75/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_minus_divide_eq
% 7.75/5.70 thf(fact_4934_less__divide__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [W: num,B: real,C: real] :
% 7.75/5.70 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 7.75/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_divide_eq_numeral(2)
% 7.75/5.70 thf(fact_4935_less__divide__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [W: num,B: rat,C: rat] :
% 7.75/5.70 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_divide_eq_numeral(2)
% 7.75/5.70 thf(fact_4936_divide__less__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [B: real,C: real,W: num] :
% 7.75/5.70 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_less_eq_numeral(2)
% 7.75/5.70 thf(fact_4937_divide__less__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [B: rat,C: rat,W: num] :
% 7.75/5.70 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 7.75/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_less_eq_numeral(2)
% 7.75/5.70 thf(fact_4938_power2__eq__1__iff,axiom,
% 7.75/5.70 ! [A: int] :
% 7.75/5.70 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = one_one_int )
% 7.75/5.70 = ( ( A = one_one_int )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_1_iff
% 7.75/5.70 thf(fact_4939_power2__eq__1__iff,axiom,
% 7.75/5.70 ! [A: real] :
% 7.75/5.70 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = one_one_real )
% 7.75/5.70 = ( ( A = one_one_real )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_1_iff
% 7.75/5.70 thf(fact_4940_power2__eq__1__iff,axiom,
% 7.75/5.70 ! [A: code_integer] :
% 7.75/5.70 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = one_one_Code_integer )
% 7.75/5.70 = ( ( A = one_one_Code_integer )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_1_iff
% 7.75/5.70 thf(fact_4941_power2__eq__1__iff,axiom,
% 7.75/5.70 ! [A: complex] :
% 7.75/5.70 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = one_one_complex )
% 7.75/5.70 = ( ( A = one_one_complex )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_1_iff
% 7.75/5.70 thf(fact_4942_power2__eq__1__iff,axiom,
% 7.75/5.70 ! [A: rat] :
% 7.75/5.70 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = one_one_rat )
% 7.75/5.70 = ( ( A = one_one_rat )
% 7.75/5.70 | ( A
% 7.75/5.70 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_eq_1_iff
% 7.75/5.70 thf(fact_4943_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 != zero_z3403309356797280102nteger )
% 7.75/5.70 => ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 7.75/5.70 != zero_z3403309356797280102nteger ) ) ).
% 7.75/5.70
% 7.75/5.70 % exp_not_zero_imp_exp_diff_not_zero
% 7.75/5.70 thf(fact_4944_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 != zero_zero_nat )
% 7.75/5.70 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 7.75/5.70 != zero_zero_nat ) ) ).
% 7.75/5.70
% 7.75/5.70 % exp_not_zero_imp_exp_diff_not_zero
% 7.75/5.70 thf(fact_4945_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 != zero_zero_int )
% 7.75/5.70 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 7.75/5.70 != zero_zero_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % exp_not_zero_imp_exp_diff_not_zero
% 7.75/5.70 thf(fact_4946_cong__exp__iff__simps_I7_J,axiom,
% 7.75/5.70 ! [Q3: num,N: num] :
% 7.75/5.70 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.70 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 7.75/5.70 = zero_zero_nat ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(7)
% 7.75/5.70 thf(fact_4947_cong__exp__iff__simps_I7_J,axiom,
% 7.75/5.70 ! [Q3: num,N: num] :
% 7.75/5.70 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.70 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 7.75/5.70 = zero_zero_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(7)
% 7.75/5.70 thf(fact_4948_cong__exp__iff__simps_I7_J,axiom,
% 7.75/5.70 ! [Q3: num,N: num] :
% 7.75/5.70 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.70 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 7.75/5.70 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(7)
% 7.75/5.70 thf(fact_4949_cong__exp__iff__simps_I11_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num] :
% 7.75/5.70 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.70 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 7.75/5.70 = zero_zero_nat ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(11)
% 7.75/5.70 thf(fact_4950_cong__exp__iff__simps_I11_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num] :
% 7.75/5.70 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.70 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 7.75/5.70 = zero_zero_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(11)
% 7.75/5.70 thf(fact_4951_cong__exp__iff__simps_I11_J,axiom,
% 7.75/5.70 ! [M: num,Q3: num] :
% 7.75/5.70 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 7.75/5.70 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 7.75/5.70 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 7.75/5.70 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.70
% 7.75/5.70 % cong_exp_iff_simps(11)
% 7.75/5.70 thf(fact_4952_uminus__power__if,axiom,
% 7.75/5.70 ! [N: nat,A: int] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 7.75/5.70 = ( power_power_int @ A @ N ) ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 7.75/5.70 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_power_if
% 7.75/5.70 thf(fact_4953_uminus__power__if,axiom,
% 7.75/5.70 ! [N: nat,A: real] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 7.75/5.70 = ( power_power_real @ A @ N ) ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 7.75/5.70 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_power_if
% 7.75/5.70 thf(fact_4954_uminus__power__if,axiom,
% 7.75/5.70 ! [N: nat,A: code_integer] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 7.75/5.70 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 7.75/5.70 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_power_if
% 7.75/5.70 thf(fact_4955_uminus__power__if,axiom,
% 7.75/5.70 ! [N: nat,A: complex] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 7.75/5.70 = ( power_power_complex @ A @ N ) ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_power_if
% 7.75/5.70 thf(fact_4956_uminus__power__if,axiom,
% 7.75/5.70 ! [N: nat,A: rat] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 7.75/5.70 = ( power_power_rat @ A @ N ) ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 7.75/5.70 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % uminus_power_if
% 7.75/5.70 thf(fact_4957_power__eq__if,axiom,
% 7.75/5.70 ( power_power_rat
% 7.75/5.70 = ( ^ [P5: rat,M4: nat] : ( if_rat @ ( M4 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_eq_if
% 7.75/5.70 thf(fact_4958_power__eq__if,axiom,
% 7.75/5.70 ( power_power_assn
% 7.75/5.70 = ( ^ [P5: assn,M4: nat] : ( if_assn @ ( M4 = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P5 @ ( power_power_assn @ P5 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_eq_if
% 7.75/5.70 thf(fact_4959_power__eq__if,axiom,
% 7.75/5.70 ( power_power_real
% 7.75/5.70 = ( ^ [P5: real,M4: nat] : ( if_real @ ( M4 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_eq_if
% 7.75/5.70 thf(fact_4960_power__eq__if,axiom,
% 7.75/5.70 ( power_power_nat
% 7.75/5.70 = ( ^ [P5: nat,M4: nat] : ( if_nat @ ( M4 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_eq_if
% 7.75/5.70 thf(fact_4961_power__eq__if,axiom,
% 7.75/5.70 ( power_power_int
% 7.75/5.70 = ( ^ [P5: int,M4: nat] : ( if_int @ ( M4 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_eq_if
% 7.75/5.70 thf(fact_4962_power__eq__if,axiom,
% 7.75/5.70 ( power_8256067586552552935nteger
% 7.75/5.70 = ( ^ [P5: code_integer,M4: nat] : ( if_Code_integer @ ( M4 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P5 @ ( power_8256067586552552935nteger @ P5 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_eq_if
% 7.75/5.70 thf(fact_4963_power__eq__if,axiom,
% 7.75/5.70 ( power_power_complex
% 7.75/5.70 = ( ^ [P5: complex,M4: nat] : ( if_complex @ ( M4 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_eq_if
% 7.75/5.70 thf(fact_4964_power__minus__mult,axiom,
% 7.75/5.70 ! [N: nat,A: assn] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 7.75/5.70 = ( power_power_assn @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_mult
% 7.75/5.70 thf(fact_4965_power__minus__mult,axiom,
% 7.75/5.70 ! [N: nat,A: real] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 7.75/5.70 = ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_mult
% 7.75/5.70 thf(fact_4966_power__minus__mult,axiom,
% 7.75/5.70 ! [N: nat,A: nat] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 7.75/5.70 = ( power_power_nat @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_mult
% 7.75/5.70 thf(fact_4967_power__minus__mult,axiom,
% 7.75/5.70 ! [N: nat,A: int] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 7.75/5.70 = ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_mult
% 7.75/5.70 thf(fact_4968_power__minus__mult,axiom,
% 7.75/5.70 ! [N: nat,A: code_integer] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 7.75/5.70 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_mult
% 7.75/5.70 thf(fact_4969_power__minus__mult,axiom,
% 7.75/5.70 ! [N: nat,A: complex] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.70 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 7.75/5.70 = ( power_power_complex @ A @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_mult
% 7.75/5.70 thf(fact_4970_Suc__div__eq__add3__div,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 7.75/5.70 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % Suc_div_eq_add3_div
% 7.75/5.70 thf(fact_4971_power__minus__is__div,axiom,
% 7.75/5.70 ! [B: nat,A: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ B @ A )
% 7.75/5.70 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 7.75/5.70 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus_is_div
% 7.75/5.70 thf(fact_4972_nat__le__power__trans,axiom,
% 7.75/5.70 ! [N: nat,M: nat,K: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ K ) ) )
% 7.75/5.70 => ( ( ord_less_eq_nat @ K @ M )
% 7.75/5.70 => ( ord_less_eq_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_le_power_trans
% 7.75/5.70 thf(fact_4973_Suc__mod__eq__add3__mod,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 7.75/5.70 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % Suc_mod_eq_add3_mod
% 7.75/5.70 thf(fact_4974_even__diff__iff,axiom,
% 7.75/5.70 ! [K: int,L: int] :
% 7.75/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 7.75/5.70 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_diff_iff
% 7.75/5.70 thf(fact_4975_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 7.75/5.70 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 7.75/5.70
% 7.75/5.70 % signed_take_bit_int_greater_eq_minus_exp
% 7.75/5.70 thf(fact_4976_signed__take__bit__int__less__eq__self__iff,axiom,
% 7.75/5.70 ! [N: nat,K: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 7.75/5.70 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 7.75/5.70
% 7.75/5.70 % signed_take_bit_int_less_eq_self_iff
% 7.75/5.70 thf(fact_4977_signed__take__bit__int__greater__self__iff,axiom,
% 7.75/5.70 ! [K: int,N: nat] :
% 7.75/5.70 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 7.75/5.70 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % signed_take_bit_int_greater_self_iff
% 7.75/5.70 thf(fact_4978_mod__add__if__z,axiom,
% 7.75/5.70 ! [X: int,Z: int,Y: int] :
% 7.75/5.70 ( ( ord_less_int @ X @ Z )
% 7.75/5.70 => ( ( ord_less_int @ Y @ Z )
% 7.75/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.70 => ( ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 7.75/5.70 = ( plus_plus_int @ X @ Y ) ) )
% 7.75/5.70 & ( ~ ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 7.75/5.70 = ( minus_minus_int @ ( plus_plus_int @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_add_if_z
% 7.75/5.70 thf(fact_4979_mod__sub__if__z,axiom,
% 7.75/5.70 ! [X: int,Z: int,Y: int] :
% 7.75/5.70 ( ( ord_less_int @ X @ Z )
% 7.75/5.70 => ( ( ord_less_int @ Y @ Z )
% 7.75/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.70 => ( ( ( ord_less_eq_int @ Y @ X )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( minus_minus_int @ X @ Y ) @ Z )
% 7.75/5.70 = ( minus_minus_int @ X @ Y ) ) )
% 7.75/5.70 & ( ~ ( ord_less_eq_int @ Y @ X )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( minus_minus_int @ X @ Y ) @ Z )
% 7.75/5.70 = ( plus_plus_int @ ( minus_minus_int @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_sub_if_z
% 7.75/5.70 thf(fact_4980_le__divide__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [W: num,B: real,C: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 7.75/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_divide_eq_numeral(2)
% 7.75/5.70 thf(fact_4981_le__divide__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [W: num,B: rat,C: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 7.75/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % le_divide_eq_numeral(2)
% 7.75/5.70 thf(fact_4982_divide__le__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [B: real,C: real,W: num] :
% 7.75/5.70 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.70 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 7.75/5.70 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 7.75/5.70 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 7.75/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_le_eq_numeral(2)
% 7.75/5.70 thf(fact_4983_divide__le__eq__numeral_I2_J,axiom,
% 7.75/5.70 ! [B: rat,C: rat,W: num] :
% 7.75/5.70 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 7.75/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 7.75/5.70 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 7.75/5.70 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 7.75/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divide_le_eq_numeral(2)
% 7.75/5.70 thf(fact_4984_square__le__1,axiom,
% 7.75/5.70 ! [X: real] :
% 7.75/5.70 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.75/5.70 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.75/5.70 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_le_1
% 7.75/5.70 thf(fact_4985_square__le__1,axiom,
% 7.75/5.70 ! [X: code_integer] :
% 7.75/5.70 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 7.75/5.70 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 7.75/5.70 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_le_1
% 7.75/5.70 thf(fact_4986_square__le__1,axiom,
% 7.75/5.70 ! [X: rat] :
% 7.75/5.70 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 7.75/5.70 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 7.75/5.70 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_le_1
% 7.75/5.70 thf(fact_4987_square__le__1,axiom,
% 7.75/5.70 ! [X: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 7.75/5.70 => ( ( ord_less_eq_int @ X @ one_one_int )
% 7.75/5.70 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % square_le_1
% 7.75/5.70 thf(fact_4988_minus__power__mult__self,axiom,
% 7.75/5.70 ! [A: int,N: nat] :
% 7.75/5.70 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 7.75/5.70 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_power_mult_self
% 7.75/5.70 thf(fact_4989_minus__power__mult__self,axiom,
% 7.75/5.70 ! [A: real,N: nat] :
% 7.75/5.70 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 7.75/5.70 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_power_mult_self
% 7.75/5.70 thf(fact_4990_minus__power__mult__self,axiom,
% 7.75/5.70 ! [A: code_integer,N: nat] :
% 7.75/5.70 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 7.75/5.70 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_power_mult_self
% 7.75/5.70 thf(fact_4991_minus__power__mult__self,axiom,
% 7.75/5.70 ! [A: complex,N: nat] :
% 7.75/5.70 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 7.75/5.70 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_power_mult_self
% 7.75/5.70 thf(fact_4992_minus__power__mult__self,axiom,
% 7.75/5.70 ! [A: rat,N: nat] :
% 7.75/5.70 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 7.75/5.70 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_power_mult_self
% 7.75/5.70 thf(fact_4993_minus__one__power__iff,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 7.75/5.70 = one_one_int ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_one_power_iff
% 7.75/5.70 thf(fact_4994_minus__one__power__iff,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 7.75/5.70 = one_one_real ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 7.75/5.70 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_one_power_iff
% 7.75/5.70 thf(fact_4995_minus__one__power__iff,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 7.75/5.70 = one_one_Code_integer ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 7.75/5.70 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_one_power_iff
% 7.75/5.70 thf(fact_4996_minus__one__power__iff,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 7.75/5.70 = one_one_complex ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_one_power_iff
% 7.75/5.70 thf(fact_4997_minus__one__power__iff,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 7.75/5.70 = one_one_rat ) )
% 7.75/5.70 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 7.75/5.70 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_one_power_iff
% 7.75/5.70 thf(fact_4998_mult__exp__mod__exp__eq,axiom,
% 7.75/5.70 ! [M: nat,N: nat,A: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.70 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_exp_mod_exp_eq
% 7.75/5.70 thf(fact_4999_mult__exp__mod__exp__eq,axiom,
% 7.75/5.70 ! [M: nat,N: nat,A: int] :
% 7.75/5.70 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.70 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_exp_mod_exp_eq
% 7.75/5.70 thf(fact_5000_mult__exp__mod__exp__eq,axiom,
% 7.75/5.70 ! [M: nat,N: nat,A: code_integer] :
% 7.75/5.70 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.70 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mult_exp_mod_exp_eq
% 7.75/5.70 thf(fact_5001_signed__take__bit__int__less__eq,axiom,
% 7.75/5.70 ! [N: nat,K: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 7.75/5.70 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % signed_take_bit_int_less_eq
% 7.75/5.70 thf(fact_5002_less__two__pow__divI,axiom,
% 7.75/5.70 ! [X: nat,N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) )
% 7.75/5.70 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.70 => ( ord_less_nat @ X @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_two_pow_divI
% 7.75/5.70 thf(fact_5003_less__two__pow__divD,axiom,
% 7.75/5.70 ! [X: nat,N: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ X @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) )
% 7.75/5.70 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.70 & ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % less_two_pow_divD
% 7.75/5.70 thf(fact_5004_nat__power__less__diff,axiom,
% 7.75/5.70 ! [N: nat,Q3: nat,M: nat] :
% 7.75/5.70 ( ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Q3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.70 => ( ord_less_nat @ Q3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_power_less_diff
% 7.75/5.70 thf(fact_5005_nat__less__power__trans,axiom,
% 7.75/5.70 ! [N: nat,M: nat,K: nat] :
% 7.75/5.70 ( ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ K ) ) )
% 7.75/5.70 => ( ( ord_less_eq_nat @ K @ M )
% 7.75/5.70 => ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_less_power_trans
% 7.75/5.70 thf(fact_5006_signed__take__bit__int__eq__self__iff,axiom,
% 7.75/5.70 ! [N: nat,K: int] :
% 7.75/5.70 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 7.75/5.70 = K )
% 7.75/5.70 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 7.75/5.70 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % signed_take_bit_int_eq_self_iff
% 7.75/5.70 thf(fact_5007_signed__take__bit__int__eq__self,axiom,
% 7.75/5.70 ! [N: nat,K: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 7.75/5.70 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 7.75/5.70 = K ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % signed_take_bit_int_eq_self
% 7.75/5.70 thf(fact_5008_power__mod__div,axiom,
% 7.75/5.70 ! [X: nat,N: nat,M: nat] :
% 7.75/5.70 ( ( divide_divide_nat @ ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.70 = ( modulo_modulo_nat @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_mod_div
% 7.75/5.70 thf(fact_5009_minus__1__div__exp__eq__int,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_1_div_exp_eq_int
% 7.75/5.70 thf(fact_5010_div__pos__geq,axiom,
% 7.75/5.70 ! [L: int,K: int] :
% 7.75/5.70 ( ( ord_less_int @ zero_zero_int @ L )
% 7.75/5.70 => ( ( ord_less_eq_int @ L @ K )
% 7.75/5.70 => ( ( divide_divide_int @ K @ L )
% 7.75/5.70 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_pos_geq
% 7.75/5.70 thf(fact_5011_div__pos__neg__trivial,axiom,
% 7.75/5.70 ! [K: int,L: int] :
% 7.75/5.70 ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.70 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 7.75/5.70 => ( ( divide_divide_int @ K @ L )
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % div_pos_neg_trivial
% 7.75/5.70 thf(fact_5012_power2__diff,axiom,
% 7.75/5.70 ! [X: code_integer,Y: code_integer] :
% 7.75/5.70 ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_diff
% 7.75/5.70 thf(fact_5013_power2__diff,axiom,
% 7.75/5.70 ! [X: complex,Y: complex] :
% 7.75/5.70 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( 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 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_diff
% 7.75/5.70 thf(fact_5014_power2__diff,axiom,
% 7.75/5.70 ! [X: real,Y: real] :
% 7.75/5.70 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( 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 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_diff
% 7.75/5.70 thf(fact_5015_power2__diff,axiom,
% 7.75/5.70 ! [X: rat,Y: rat] :
% 7.75/5.70 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( 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 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_diff
% 7.75/5.70 thf(fact_5016_power2__diff,axiom,
% 7.75/5.70 ! [X: int,Y: int] :
% 7.75/5.70 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 = ( 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 ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % power2_diff
% 7.75/5.70 thf(fact_5017_even__mask__div__iff_H,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_mask_div_iff'
% 7.75/5.70 thf(fact_5018_even__mask__div__iff_H,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_mask_div_iff'
% 7.75/5.70 thf(fact_5019_even__mask__div__iff_H,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( ord_less_eq_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_mask_div_iff'
% 7.75/5.70 thf(fact_5020_power__minus1__odd,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus1_odd
% 7.75/5.70 thf(fact_5021_power__minus1__odd,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus1_odd
% 7.75/5.70 thf(fact_5022_power__minus1__odd,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus1_odd
% 7.75/5.70 thf(fact_5023_power__minus1__odd,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus1_odd
% 7.75/5.70 thf(fact_5024_power__minus1__odd,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.70
% 7.75/5.70 % power_minus1_odd
% 7.75/5.70 thf(fact_5025_Bernoulli__inequality__even,axiom,
% 7.75/5.70 ! [N: nat,X: real] :
% 7.75/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % Bernoulli_inequality_even
% 7.75/5.70 thf(fact_5026_int__bit__induct,axiom,
% 7.75/5.70 ! [P: int > $o,K: int] :
% 7.75/5.70 ( ( P @ zero_zero_int )
% 7.75/5.70 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.70 => ( ! [K2: int] :
% 7.75/5.70 ( ( P @ K2 )
% 7.75/5.70 => ( ( K2 != zero_zero_int )
% 7.75/5.70 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.70 => ( ! [K2: int] :
% 7.75/5.70 ( ( P @ K2 )
% 7.75/5.70 => ( ( K2
% 7.75/5.70 != ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.70 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.70 => ( P @ K ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % int_bit_induct
% 7.75/5.70 thf(fact_5027_int__power__div__base,axiom,
% 7.75/5.70 ! [M: nat,K: int] :
% 7.75/5.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.70 => ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.70 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 7.75/5.70 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % int_power_div_base
% 7.75/5.70 thf(fact_5028_divmod__digit__1_I2_J,axiom,
% 7.75/5.70 ! [A: code_integer,B: code_integer] :
% 7.75/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.70 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.70 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 7.75/5.70 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 7.75/5.70 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divmod_digit_1(2)
% 7.75/5.70 thf(fact_5029_divmod__digit__1_I2_J,axiom,
% 7.75/5.70 ! [A: nat,B: nat] :
% 7.75/5.70 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 7.75/5.70 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 7.75/5.70 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 7.75/5.70 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 7.75/5.70 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divmod_digit_1(2)
% 7.75/5.70 thf(fact_5030_divmod__digit__1_I2_J,axiom,
% 7.75/5.70 ! [A: int,B: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.70 => ( ( ord_less_int @ zero_zero_int @ B )
% 7.75/5.70 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 7.75/5.70 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 7.75/5.70 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % divmod_digit_1(2)
% 7.75/5.70 thf(fact_5031_even__mask__div__iff,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 = zero_z3403309356797280102nteger )
% 7.75/5.70 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_mask_div_iff
% 7.75/5.70 thf(fact_5032_even__mask__div__iff,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 = zero_zero_nat )
% 7.75/5.70 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_mask_div_iff
% 7.75/5.70 thf(fact_5033_even__mask__div__iff,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 7.75/5.70 = zero_zero_int )
% 7.75/5.70 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_mask_div_iff
% 7.75/5.70 thf(fact_5034_exp__div__exp__eq,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 = ( times_times_nat
% 7.75/5.70 @ ( zero_n2687167440665602831ol_nat
% 7.75/5.70 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 7.75/5.70 != zero_zero_nat )
% 7.75/5.70 & ( ord_less_eq_nat @ N @ M ) ) )
% 7.75/5.70 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % exp_div_exp_eq
% 7.75/5.70 thf(fact_5035_exp__div__exp__eq,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 = ( times_times_int
% 7.75/5.70 @ ( zero_n2684676970156552555ol_int
% 7.75/5.70 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 7.75/5.70 != zero_zero_int )
% 7.75/5.70 & ( ord_less_eq_nat @ N @ M ) ) )
% 7.75/5.70 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % exp_div_exp_eq
% 7.75/5.70 thf(fact_5036_exp__div__exp__eq,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 = ( times_3573771949741848930nteger
% 7.75/5.70 @ ( zero_n356916108424825756nteger
% 7.75/5.70 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 7.75/5.70 != zero_z3403309356797280102nteger )
% 7.75/5.70 & ( ord_less_eq_nat @ N @ M ) ) )
% 7.75/5.70 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % exp_div_exp_eq
% 7.75/5.70 thf(fact_5037_even__mod__4__div__2,axiom,
% 7.75/5.70 ! [N: nat] :
% 7.75/5.70 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = ( suc @ zero_zero_nat ) )
% 7.75/5.70 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % even_mod_4_div_2
% 7.75/5.70 thf(fact_5038_signed__take__bit__int__greater__eq,axiom,
% 7.75/5.70 ! [K: int,N: nat] :
% 7.75/5.70 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 7.75/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % signed_take_bit_int_greater_eq
% 7.75/5.70 thf(fact_5039_sb__dec__lem_H,axiom,
% 7.75/5.70 ! [K: nat,A: int] :
% 7.75/5.70 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) @ A )
% 7.75/5.70 => ( ord_less_eq_int @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % sb_dec_lem'
% 7.75/5.70 thf(fact_5040_space__cnt,axiom,
% 7.75/5.70 ! [T: vEBT_VEBT] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_space2 @ T ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_cnt @ T ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % space_cnt
% 7.75/5.70 thf(fact_5041_t__build__cnt,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8646137997579335489_i_l_d @ N ) ) @ ( times_times_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % t_build_cnt
% 7.75/5.70 thf(fact_5042_t__buildup__cnt,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8346862874174094_d_u_p @ N ) ) @ ( times_times_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % t_buildup_cnt
% 7.75/5.70 thf(fact_5043_vebt__buildup__bound,axiom,
% 7.75/5.70 ! [U: nat,N: nat] :
% 7.75/5.70 ( ( U
% 7.75/5.70 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.70 => ( ord_less_eq_nat @ ( vEBT_V8346862874174094_d_u_p @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ U ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % vebt_buildup_bound
% 7.75/5.70 thf(fact_5044_linear__plus__1__le__power,axiom,
% 7.75/5.70 ! [X: real,N: nat] :
% 7.75/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.70 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % linear_plus_1_le_power
% 7.75/5.70 thf(fact_5045_mod__exhaust__less__4,axiom,
% 7.75/5.70 ! [M: nat] :
% 7.75/5.70 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = zero_zero_nat )
% 7.75/5.70 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = one_one_nat )
% 7.75/5.70 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.70 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.75/5.70 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % mod_exhaust_less_4
% 7.75/5.70 thf(fact_5046_nat__approx__posE,axiom,
% 7.75/5.70 ! [E: rat] :
% 7.75/5.70 ( ( ord_less_rat @ zero_zero_rat @ E )
% 7.75/5.70 => ~ ! [N2: nat] :
% 7.75/5.70 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ E ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_approx_posE
% 7.75/5.70 thf(fact_5047_nat__approx__posE,axiom,
% 7.75/5.70 ! [E: real] :
% 7.75/5.70 ( ( ord_less_real @ zero_zero_real @ E )
% 7.75/5.70 => ~ ! [N2: nat] :
% 7.75/5.70 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ E ) ) ).
% 7.75/5.70
% 7.75/5.70 % nat_approx_posE
% 7.75/5.70 thf(fact_5048_buildup__build__time,axiom,
% 7.75/5.70 ! [N: nat] : ( ord_less_nat @ ( vEBT_V8346862874174094_d_u_p @ N ) @ ( vEBT_V8646137997579335489_i_l_d @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % buildup_build_time
% 7.75/5.70 thf(fact_5049_idiff__0,axiom,
% 7.75/5.70 ! [N: extended_enat] :
% 7.75/5.70 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 7.75/5.70 = zero_z5237406670263579293d_enat ) ).
% 7.75/5.70
% 7.75/5.70 % idiff_0
% 7.75/5.70 thf(fact_5050_idiff__0__right,axiom,
% 7.75/5.70 ! [N: extended_enat] :
% 7.75/5.70 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 7.75/5.70 = N ) ).
% 7.75/5.70
% 7.75/5.70 % idiff_0_right
% 7.75/5.70 thf(fact_5051_int__eq__iff__numeral,axiom,
% 7.75/5.70 ! [M: nat,V: num] :
% 7.75/5.70 ( ( ( semiri1314217659103216013at_int @ M )
% 7.75/5.70 = ( numeral_numeral_int @ V ) )
% 7.75/5.70 = ( M
% 7.75/5.70 = ( numeral_numeral_nat @ V ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % int_eq_iff_numeral
% 7.75/5.70 thf(fact_5052_negative__eq__positive,axiom,
% 7.75/5.70 ! [N: nat,M: nat] :
% 7.75/5.70 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.70 = ( semiri1314217659103216013at_int @ M ) )
% 7.75/5.70 = ( ( N = zero_zero_nat )
% 7.75/5.70 & ( M = zero_zero_nat ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % negative_eq_positive
% 7.75/5.70 thf(fact_5053_real__add__minus__iff,axiom,
% 7.75/5.70 ! [X: real,A: real] :
% 7.75/5.70 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 7.75/5.70 = zero_zero_real )
% 7.75/5.70 = ( X = A ) ) ).
% 7.75/5.70
% 7.75/5.70 % real_add_minus_iff
% 7.75/5.70 thf(fact_5054_int__dvd__int__iff,axiom,
% 7.75/5.70 ! [M: nat,N: nat] :
% 7.75/5.70 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.70 = ( dvd_dvd_nat @ M @ N ) ) ).
% 7.75/5.70
% 7.75/5.70 % int_dvd_int_iff
% 7.75/5.70 thf(fact_5055_negative__zless,axiom,
% 7.75/5.70 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 7.75/5.70
% 7.75/5.70 % negative_zless
% 7.75/5.70 thf(fact_5056_minus__real__def,axiom,
% 7.75/5.70 ( minus_minus_real
% 7.75/5.70 = ( ^ [X2: real,Y6: real] : ( plus_plus_real @ X2 @ ( uminus_uminus_real @ Y6 ) ) ) ) ).
% 7.75/5.70
% 7.75/5.70 % minus_real_def
% 7.75/5.70 thf(fact_5057_Bolzano,axiom,
% 7.75/5.70 ! [A: real,B: real,P: real > real > $o] :
% 7.75/5.70 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.70 => ( ! [A5: real,B2: real,C3: real] :
% 7.75/5.71 ( ( P @ A5 @ B2 )
% 7.75/5.71 => ( ( P @ B2 @ C3 )
% 7.75/5.71 => ( ( ord_less_eq_real @ A5 @ B2 )
% 7.75/5.71 => ( ( ord_less_eq_real @ B2 @ C3 )
% 7.75/5.71 => ( P @ A5 @ C3 ) ) ) ) )
% 7.75/5.71 => ( ! [X3: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ A @ X3 )
% 7.75/5.71 => ( ( ord_less_eq_real @ X3 @ B )
% 7.75/5.71 => ? [D5: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ D5 )
% 7.75/5.71 & ! [A5: real,B2: real] :
% 7.75/5.71 ( ( ( ord_less_eq_real @ A5 @ X3 )
% 7.75/5.71 & ( ord_less_eq_real @ X3 @ B2 )
% 7.75/5.71 & ( ord_less_real @ ( minus_minus_real @ B2 @ A5 ) @ D5 ) )
% 7.75/5.71 => ( P @ A5 @ B2 ) ) ) ) )
% 7.75/5.71 => ( P @ A @ B ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % Bolzano
% 7.75/5.71 thf(fact_5058_int__ops_I3_J,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 7.75/5.71 = ( numeral_numeral_int @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_ops(3)
% 7.75/5.71 thf(fact_5059_int__ops_I1_J,axiom,
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 7.75/5.71 = zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % int_ops(1)
% 7.75/5.71 thf(fact_5060_int__cases,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ! [N2: nat] :
% 7.75/5.71 ( Z
% 7.75/5.71 != ( semiri1314217659103216013at_int @ N2 ) )
% 7.75/5.71 => ~ ! [N2: nat] :
% 7.75/5.71 ( Z
% 7.75/5.71 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_cases
% 7.75/5.71 thf(fact_5061_int__of__nat__induct,axiom,
% 7.75/5.71 ! [P: int > $o,Z: int] :
% 7.75/5.71 ( ! [N2: nat] : ( P @ ( semiri1314217659103216013at_int @ N2 ) )
% 7.75/5.71 => ( ! [N2: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
% 7.75/5.71 => ( P @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_of_nat_induct
% 7.75/5.71 thf(fact_5062_nat__int__comparison_I2_J,axiom,
% 7.75/5.71 ( ord_less_nat
% 7.75/5.71 = ( ^ [A3: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % nat_int_comparison(2)
% 7.75/5.71 thf(fact_5063_nat__int__comparison_I3_J,axiom,
% 7.75/5.71 ( ord_less_eq_nat
% 7.75/5.71 = ( ^ [A3: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % nat_int_comparison(3)
% 7.75/5.71 thf(fact_5064_int__ops_I2_J,axiom,
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % int_ops(2)
% 7.75/5.71 thf(fact_5065_zero__le__imp__eq__int,axiom,
% 7.75/5.71 ! [K: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.71 => ? [N2: nat] :
% 7.75/5.71 ( K
% 7.75/5.71 = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_le_imp_eq_int
% 7.75/5.71 thf(fact_5066_nonneg__int__cases,axiom,
% 7.75/5.71 ! [K: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.71 => ~ ! [N2: nat] :
% 7.75/5.71 ( K
% 7.75/5.71 != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % nonneg_int_cases
% 7.75/5.71 thf(fact_5067_zadd__int__left,axiom,
% 7.75/5.71 ! [M: nat,N: nat,Z: int] :
% 7.75/5.71 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 7.75/5.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % zadd_int_left
% 7.75/5.71 thf(fact_5068_int__ops_I5_J,axiom,
% 7.75/5.71 ! [A: nat,B: nat] :
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 7.75/5.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_ops(5)
% 7.75/5.71 thf(fact_5069_int__plus,axiom,
% 7.75/5.71 ! [N: nat,M: nat] :
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 7.75/5.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_plus
% 7.75/5.71 thf(fact_5070_not__int__zless__negative,axiom,
% 7.75/5.71 ! [N: nat,M: nat] :
% 7.75/5.71 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % not_int_zless_negative
% 7.75/5.71 thf(fact_5071_int__ops_I7_J,axiom,
% 7.75/5.71 ! [A: nat,B: nat] :
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 7.75/5.71 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_ops(7)
% 7.75/5.71 thf(fact_5072_real__minus__mult__self__le,axiom,
% 7.75/5.71 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_minus_mult_self_le
% 7.75/5.71 thf(fact_5073_zdiv__int,axiom,
% 7.75/5.71 ! [A: nat,B: nat] :
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 7.75/5.71 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zdiv_int
% 7.75/5.71 thf(fact_5074_zmod__int,axiom,
% 7.75/5.71 ! [A: nat,B: nat] :
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 7.75/5.71 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zmod_int
% 7.75/5.71 thf(fact_5075_int__cases4,axiom,
% 7.75/5.71 ! [M: int] :
% 7.75/5.71 ( ! [N2: nat] :
% 7.75/5.71 ( M
% 7.75/5.71 != ( semiri1314217659103216013at_int @ N2 ) )
% 7.75/5.71 => ~ ! [N2: nat] :
% 7.75/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 7.75/5.71 => ( M
% 7.75/5.71 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_cases4
% 7.75/5.71 thf(fact_5076_int__Suc,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 7.75/5.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_Suc
% 7.75/5.71 thf(fact_5077_int__ops_I4_J,axiom,
% 7.75/5.71 ! [A: nat] :
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 7.75/5.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_ops(4)
% 7.75/5.71 thf(fact_5078_zless__iff__Suc__zadd,axiom,
% 7.75/5.71 ( ord_less_int
% 7.75/5.71 = ( ^ [W2: int,Z6: int] :
% 7.75/5.71 ? [N3: nat] :
% 7.75/5.71 ( Z6
% 7.75/5.71 = ( plus_plus_int @ W2 @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zless_iff_Suc_zadd
% 7.75/5.71 thf(fact_5079_int__zle__neg,axiom,
% 7.75/5.71 ! [N: nat,M: nat] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 7.75/5.71 = ( ( N = zero_zero_nat )
% 7.75/5.71 & ( M = zero_zero_nat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_zle_neg
% 7.75/5.71 thf(fact_5080_nonpos__int__cases,axiom,
% 7.75/5.71 ! [K: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 7.75/5.71 => ~ ! [N2: nat] :
% 7.75/5.71 ( K
% 7.75/5.71 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % nonpos_int_cases
% 7.75/5.71 thf(fact_5081_negative__zle__0,axiom,
% 7.75/5.71 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % negative_zle_0
% 7.75/5.71 thf(fact_5082_real__add__less__0__iff,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_add_less_0_iff
% 7.75/5.71 thf(fact_5083_real__0__less__add__iff,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 7.75/5.71 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_0_less_add_iff
% 7.75/5.71 thf(fact_5084_real__add__le__0__iff,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_add_le_0_iff
% 7.75/5.71 thf(fact_5085_real__0__le__add__iff,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 7.75/5.71 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_0_le_add_iff
% 7.75/5.71 thf(fact_5086_zero__less__imp__eq__int,axiom,
% 7.75/5.71 ! [K: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.71 => ? [N2: nat] :
% 7.75/5.71 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 7.75/5.71 & ( K
% 7.75/5.71 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_imp_eq_int
% 7.75/5.71 thf(fact_5087_pos__int__cases,axiom,
% 7.75/5.71 ! [K: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.71 => ~ ! [N2: nat] :
% 7.75/5.71 ( ( K
% 7.75/5.71 = ( semiri1314217659103216013at_int @ N2 ) )
% 7.75/5.71 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pos_int_cases
% 7.75/5.71 thf(fact_5088_int__cases3,axiom,
% 7.75/5.71 ! [K: int] :
% 7.75/5.71 ( ( K != zero_zero_int )
% 7.75/5.71 => ( ! [N2: nat] :
% 7.75/5.71 ( ( K
% 7.75/5.71 = ( semiri1314217659103216013at_int @ N2 ) )
% 7.75/5.71 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 7.75/5.71 => ~ ! [N2: nat] :
% 7.75/5.71 ( ( K
% 7.75/5.71 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 7.75/5.71 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_cases3
% 7.75/5.71 thf(fact_5089_zmult__zless__mono2__lemma,axiom,
% 7.75/5.71 ! [I: int,J: int,K: nat] :
% 7.75/5.71 ( ( ord_less_int @ I @ J )
% 7.75/5.71 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.71 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zmult_zless_mono2_lemma
% 7.75/5.71 thf(fact_5090_not__zle__0__negative,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % not_zle_0_negative
% 7.75/5.71 thf(fact_5091_negative__zless__0,axiom,
% 7.75/5.71 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % negative_zless_0
% 7.75/5.71 thf(fact_5092_negD,axiom,
% 7.75/5.71 ! [X: int] :
% 7.75/5.71 ( ( ord_less_int @ X @ zero_zero_int )
% 7.75/5.71 => ? [N2: nat] :
% 7.75/5.71 ( X
% 7.75/5.71 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % negD
% 7.75/5.71 thf(fact_5093_int__ops_I6_J,axiom,
% 7.75/5.71 ! [A: nat,B: nat] :
% 7.75/5.71 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 7.75/5.71 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 7.75/5.71 = zero_zero_int ) )
% 7.75/5.71 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 7.75/5.71 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 7.75/5.71 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_ops(6)
% 7.75/5.71 thf(fact_5094_neg__int__cases,axiom,
% 7.75/5.71 ! [K: int] :
% 7.75/5.71 ( ( ord_less_int @ K @ zero_zero_int )
% 7.75/5.71 => ~ ! [N2: nat] :
% 7.75/5.71 ( ( K
% 7.75/5.71 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 7.75/5.71 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_int_cases
% 7.75/5.71 thf(fact_5095_realpow__square__minus__le,axiom,
% 7.75/5.71 ! [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 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % realpow_square_minus_le
% 7.75/5.71 thf(fact_5096_zdiff__int__split,axiom,
% 7.75/5.71 ! [P: int > $o,X: nat,Y: nat] :
% 7.75/5.71 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 7.75/5.71 = ( ( ( ord_less_eq_nat @ Y @ X )
% 7.75/5.71 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 7.75/5.71 & ( ( ord_less_nat @ X @ Y )
% 7.75/5.71 => ( P @ zero_zero_int ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zdiff_int_split
% 7.75/5.71 thf(fact_5097_real__of__nat__div2,axiom,
% 7.75/5.71 ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_of_nat_div2
% 7.75/5.71 thf(fact_5098_real__of__nat__div3,axiom,
% 7.75/5.71 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % real_of_nat_div3
% 7.75/5.71 thf(fact_5099_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I1_J,axiom,
% 7.75/5.71 ( ( vEBT_V8346862874174094_d_u_p @ zero_zero_nat )
% 7.75/5.71 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(1)
% 7.75/5.71 thf(fact_5100_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I1_J,axiom,
% 7.75/5.71 ( ( vEBT_V8646137997579335489_i_l_d @ zero_zero_nat )
% 7.75/5.71 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(1)
% 7.75/5.71 thf(fact_5101_Bernoulli__inequality,axiom,
% 7.75/5.71 ! [X: real,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.75/5.71 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % Bernoulli_inequality
% 7.75/5.71 thf(fact_5102_exists__least__lemma,axiom,
% 7.75/5.71 ! [P: nat > $o] :
% 7.75/5.71 ( ~ ( P @ zero_zero_nat )
% 7.75/5.71 => ( ? [X_12: nat] : ( P @ X_12 )
% 7.75/5.71 => ? [N2: nat] :
% 7.75/5.71 ( ~ ( P @ N2 )
% 7.75/5.71 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % exists_least_lemma
% 7.75/5.71 thf(fact_5103_reals__Archimedean2,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ? [N2: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 7.75/5.71
% 7.75/5.71 % reals_Archimedean2
% 7.75/5.71 thf(fact_5104_reals__Archimedean2,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ? [N2: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 7.75/5.71
% 7.75/5.71 % reals_Archimedean2
% 7.75/5.71 thf(fact_5105_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I2_J,axiom,
% 7.75/5.71 ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ zero_zero_nat ) )
% 7.75/5.71 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(2)
% 7.75/5.71 thf(fact_5106_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I2_J,axiom,
% 7.75/5.71 ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ zero_zero_nat ) )
% 7.75/5.71 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(2)
% 7.75/5.71 thf(fact_5107_ex__less__of__nat__mult,axiom,
% 7.75/5.71 ! [X: rat,Y: rat] :
% 7.75/5.71 ( ( ord_less_rat @ zero_zero_rat @ X )
% 7.75/5.71 => ? [N2: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ex_less_of_nat_mult
% 7.75/5.71 thf(fact_5108_ex__less__of__nat__mult,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ? [N2: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ex_less_of_nat_mult
% 7.75/5.71 thf(fact_5109_space__space_H,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT] : ( ord_less_nat @ ( vEBT_VEBT_space @ T ) @ ( vEBT_VEBT_space2 @ T ) ) ).
% 7.75/5.71
% 7.75/5.71 % space_space'
% 7.75/5.71 thf(fact_5110_real__average__minus__second,axiom,
% 7.75/5.71 ! [B: real,A: real] :
% 7.75/5.71 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 7.75/5.71 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_average_minus_second
% 7.75/5.71 thf(fact_5111_real__average__minus__first,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 7.75/5.71 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_average_minus_first
% 7.75/5.71 thf(fact_5112_space__2__pow__bound,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_space2 @ T ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ one_one_real ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % space_2_pow_bound
% 7.75/5.71 thf(fact_5113_cnt__bound,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ T ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % cnt_bound
% 7.75/5.71 thf(fact_5114_cnt__bound_H,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ T ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ one_one_real ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % cnt_bound'
% 7.75/5.71 thf(fact_5115_space_H__bound,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ord_less_eq_nat @ ( vEBT_VEBT_space2 @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % space'_bound
% 7.75/5.71 thf(fact_5116_valid__0__not,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT] :
% 7.75/5.71 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 7.75/5.71
% 7.75/5.71 % valid_0_not
% 7.75/5.71 thf(fact_5117_valid__tree__deg__neq__0,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT] :
% 7.75/5.71 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 7.75/5.71
% 7.75/5.71 % valid_tree_deg_neq_0
% 7.75/5.71 thf(fact_5118_deg__not__0,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % deg_not_0
% 7.75/5.71 thf(fact_5119_buildup__gives__valid,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.71 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % buildup_gives_valid
% 7.75/5.71 thf(fact_5120_space__bound,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ord_less_eq_nat @ ( vEBT_VEBT_space @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % space_bound
% 7.75/5.71 thf(fact_5121_int__if,axiom,
% 7.75/5.71 ! [P: $o,A: nat,B: nat] :
% 7.75/5.71 ( ( P
% 7.75/5.71 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 7.75/5.71 = ( semiri1314217659103216013at_int @ A ) ) )
% 7.75/5.71 & ( ~ P
% 7.75/5.71 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 7.75/5.71 = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_if
% 7.75/5.71 thf(fact_5122_nat__int__comparison_I1_J,axiom,
% 7.75/5.71 ( ( ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 ) )
% 7.75/5.71 = ( ^ [A3: nat,B4: nat] :
% 7.75/5.71 ( ( semiri1314217659103216013at_int @ A3 )
% 7.75/5.71 = ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % nat_int_comparison(1)
% 7.75/5.71 thf(fact_5123_two__powr__height__bound__deg,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % two_powr_height_bound_deg
% 7.75/5.71 thf(fact_5124_member__bound,axiom,
% 7.75/5.71 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 7.75/5.71 ( ( vEBT_vebt_member @ Tree @ X )
% 7.75/5.71 => ( ( vEBT_invar_vebt @ Tree @ N )
% 7.75/5.71 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % member_bound
% 7.75/5.71 thf(fact_5125_dbl__dec__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(4)
% 7.75/5.71 thf(fact_5126_dbl__dec__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(4)
% 7.75/5.71 thf(fact_5127_dbl__dec__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(4)
% 7.75/5.71 thf(fact_5128_dbl__dec__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(4)
% 7.75/5.71 thf(fact_5129_dbl__dec__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(4)
% 7.75/5.71 thf(fact_5130_signed__take__bit__numeral__minus__bit1,axiom,
% 7.75/5.71 ! [L: num,K: num] :
% 7.75/5.71 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 7.75/5.71 = ( 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 ) ) ).
% 7.75/5.71
% 7.75/5.71 % signed_take_bit_numeral_minus_bit1
% 7.75/5.71 thf(fact_5131_member__valid__both__member__options,axiom,
% 7.75/5.71 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ Tree @ N )
% 7.75/5.71 => ( ( vEBT_vebt_member @ Tree @ X )
% 7.75/5.71 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 7.75/5.71 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % member_valid_both_member_options
% 7.75/5.71 thf(fact_5132_dbl__dec__simps_I3_J,axiom,
% 7.75/5.71 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 7.75/5.71 = one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(3)
% 7.75/5.71 thf(fact_5133_dbl__dec__simps_I3_J,axiom,
% 7.75/5.71 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 7.75/5.71 = one_one_rat ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(3)
% 7.75/5.71 thf(fact_5134_dbl__dec__simps_I3_J,axiom,
% 7.75/5.71 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(3)
% 7.75/5.71 thf(fact_5135_member__correct,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( vEBT_vebt_member @ T @ X )
% 7.75/5.71 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % member_correct
% 7.75/5.71 thf(fact_5136_pred__numeral__simps_I1_J,axiom,
% 7.75/5.71 ( ( pred_numeral @ one )
% 7.75/5.71 = zero_zero_nat ) ).
% 7.75/5.71
% 7.75/5.71 % pred_numeral_simps(1)
% 7.75/5.71 thf(fact_5137_Suc__eq__numeral,axiom,
% 7.75/5.71 ! [N: nat,K: num] :
% 7.75/5.71 ( ( ( suc @ N )
% 7.75/5.71 = ( numeral_numeral_nat @ K ) )
% 7.75/5.71 = ( N
% 7.75/5.71 = ( pred_numeral @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % Suc_eq_numeral
% 7.75/5.71 thf(fact_5138_eq__numeral__Suc,axiom,
% 7.75/5.71 ! [K: num,N: nat] :
% 7.75/5.71 ( ( ( numeral_numeral_nat @ K )
% 7.75/5.71 = ( suc @ N ) )
% 7.75/5.71 = ( ( pred_numeral @ K )
% 7.75/5.71 = N ) ) ).
% 7.75/5.71
% 7.75/5.71 % eq_numeral_Suc
% 7.75/5.71 thf(fact_5139_pred__numeral__simps_I3_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( pred_numeral @ ( bit1 @ K ) )
% 7.75/5.71 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pred_numeral_simps(3)
% 7.75/5.71 thf(fact_5140_less__Suc__numeral,axiom,
% 7.75/5.71 ! [N: nat,K: num] :
% 7.75/5.71 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 7.75/5.71 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % less_Suc_numeral
% 7.75/5.71 thf(fact_5141_less__numeral__Suc,axiom,
% 7.75/5.71 ! [K: num,N: nat] :
% 7.75/5.71 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 7.75/5.71 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % less_numeral_Suc
% 7.75/5.71 thf(fact_5142_le__Suc__numeral,axiom,
% 7.75/5.71 ! [N: nat,K: num] :
% 7.75/5.71 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 7.75/5.71 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % le_Suc_numeral
% 7.75/5.71 thf(fact_5143_le__numeral__Suc,axiom,
% 7.75/5.71 ! [K: num,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 7.75/5.71 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % le_numeral_Suc
% 7.75/5.71 thf(fact_5144_diff__Suc__numeral,axiom,
% 7.75/5.71 ! [N: nat,K: num] :
% 7.75/5.71 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 7.75/5.71 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % diff_Suc_numeral
% 7.75/5.71 thf(fact_5145_diff__numeral__Suc,axiom,
% 7.75/5.71 ! [K: num,N: nat] :
% 7.75/5.71 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 7.75/5.71 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % diff_numeral_Suc
% 7.75/5.71 thf(fact_5146_dbl__dec__simps_I2_J,axiom,
% 7.75/5.71 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 7.75/5.71 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(2)
% 7.75/5.71 thf(fact_5147_dbl__dec__simps_I2_J,axiom,
% 7.75/5.71 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 7.75/5.71 = ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(2)
% 7.75/5.71 thf(fact_5148_dbl__dec__simps_I2_J,axiom,
% 7.75/5.71 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 7.75/5.71 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(2)
% 7.75/5.71 thf(fact_5149_dbl__dec__simps_I2_J,axiom,
% 7.75/5.71 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 7.75/5.71 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(2)
% 7.75/5.71 thf(fact_5150_dbl__dec__simps_I2_J,axiom,
% 7.75/5.71 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 7.75/5.71 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(2)
% 7.75/5.71 thf(fact_5151_signed__take__bit__numeral__bit0,axiom,
% 7.75/5.71 ! [L: num,K: num] :
% 7.75/5.71 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 7.75/5.71 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % signed_take_bit_numeral_bit0
% 7.75/5.71 thf(fact_5152_signed__take__bit__numeral__minus__bit0,axiom,
% 7.75/5.71 ! [L: num,K: num] :
% 7.75/5.71 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 7.75/5.71 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % signed_take_bit_numeral_minus_bit0
% 7.75/5.71 thf(fact_5153_signed__take__bit__numeral__bit1,axiom,
% 7.75/5.71 ! [L: num,K: num] :
% 7.75/5.71 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 7.75/5.71 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % signed_take_bit_numeral_bit1
% 7.75/5.71 thf(fact_5154_numeral__eq__Suc,axiom,
% 7.75/5.71 ( numeral_numeral_nat
% 7.75/5.71 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_eq_Suc
% 7.75/5.71 thf(fact_5155_pred__numeral__def,axiom,
% 7.75/5.71 ( pred_numeral
% 7.75/5.71 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pred_numeral_def
% 7.75/5.71 thf(fact_5156_dbl__dec__def,axiom,
% 7.75/5.71 ( neg_nu3179335615603231917ec_rat
% 7.75/5.71 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_def
% 7.75/5.71 thf(fact_5157_dbl__dec__def,axiom,
% 7.75/5.71 ( neg_nu6511756317524482435omplex
% 7.75/5.71 = ( ^ [X2: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X2 @ X2 ) @ one_one_complex ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_def
% 7.75/5.71 thf(fact_5158_dbl__dec__def,axiom,
% 7.75/5.71 ( neg_nu6075765906172075777c_real
% 7.75/5.71 = ( ^ [X2: real] : ( minus_minus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_def
% 7.75/5.71 thf(fact_5159_dbl__dec__def,axiom,
% 7.75/5.71 ( neg_nu3811975205180677377ec_int
% 7.75/5.71 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_def
% 7.75/5.71 thf(fact_5160_delete__bound__height,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % delete_bound_height
% 7.75/5.71 thf(fact_5161_delete__bound__height_H,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % delete_bound_height'
% 7.75/5.71 thf(fact_5162_post__member__pre__member,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 7.75/5.71 => ( ( vEBT_vebt_member @ T @ Y )
% 7.75/5.71 | ( X = Y ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % post_member_pre_member
% 7.75/5.71 thf(fact_5163_height__double__log__univ__size,axiom,
% 7.75/5.71 ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 7.75/5.71 ( ( U
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 7.75/5.71 => ( ( vEBT_invar_vebt @ T @ Deg )
% 7.75/5.71 => ( 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 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % height_double_log_univ_size
% 7.75/5.71 thf(fact_5164_lemma__termdiff3,axiom,
% 7.75/5.71 ! [H2: real,Z: real,K6: real,N: nat] :
% 7.75/5.71 ( ( H2 != zero_zero_real )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K6 )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K6 )
% 7.75/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K6 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % lemma_termdiff3
% 7.75/5.71 thf(fact_5165_lemma__termdiff3,axiom,
% 7.75/5.71 ! [H2: complex,Z: complex,K6: real,N: nat] :
% 7.75/5.71 ( ( H2 != zero_zero_complex )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K6 )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K6 )
% 7.75/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K6 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % lemma_termdiff3
% 7.75/5.71 thf(fact_5166_dbl__inc__simps_I3_J,axiom,
% 7.75/5.71 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 7.75/5.71 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(3)
% 7.75/5.71 thf(fact_5167_dbl__inc__simps_I3_J,axiom,
% 7.75/5.71 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 7.75/5.71 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(3)
% 7.75/5.71 thf(fact_5168_dbl__inc__simps_I3_J,axiom,
% 7.75/5.71 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 7.75/5.71 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(3)
% 7.75/5.71 thf(fact_5169_dbl__inc__simps_I3_J,axiom,
% 7.75/5.71 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 7.75/5.71 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(3)
% 7.75/5.71 thf(fact_5170_pochhammer__double,axiom,
% 7.75/5.71 ! [Z: rat,N: nat] :
% 7.75/5.71 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_double
% 7.75/5.71 thf(fact_5171_pochhammer__double,axiom,
% 7.75/5.71 ! [Z: real,N: nat] :
% 7.75/5.71 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_double
% 7.75/5.71 thf(fact_5172_pochhammer__double,axiom,
% 7.75/5.71 ! [Z: complex,N: nat] :
% 7.75/5.71 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_double
% 7.75/5.71 thf(fact_5173_delete__bound__size__univ_H,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V1232361888498592333_e_t_e @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % delete_bound_size_univ'
% 7.75/5.71 thf(fact_5174_pochhammer__0,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 7.75/5.71 = one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_0
% 7.75/5.71 thf(fact_5175_pochhammer__0,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 7.75/5.71 = one_one_rat ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_0
% 7.75/5.71 thf(fact_5176_pochhammer__0,axiom,
% 7.75/5.71 ! [A: nat] :
% 7.75/5.71 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 7.75/5.71 = one_one_nat ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_0
% 7.75/5.71 thf(fact_5177_pochhammer__0,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_0
% 7.75/5.71 thf(fact_5178_log__one,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( log @ A @ one_one_real )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % log_one
% 7.75/5.71 thf(fact_5179_delete__bound__size__univ,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % delete_bound_size_univ
% 7.75/5.71 thf(fact_5180_dbl__inc__simps_I2_J,axiom,
% 7.75/5.71 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 7.75/5.71 = one_one_complex ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(2)
% 7.75/5.71 thf(fact_5181_dbl__inc__simps_I2_J,axiom,
% 7.75/5.71 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 7.75/5.71 = one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(2)
% 7.75/5.71 thf(fact_5182_dbl__inc__simps_I2_J,axiom,
% 7.75/5.71 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 7.75/5.71 = one_one_rat ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(2)
% 7.75/5.71 thf(fact_5183_dbl__inc__simps_I2_J,axiom,
% 7.75/5.71 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(2)
% 7.75/5.71 thf(fact_5184_dbl__inc__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.71 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(4)
% 7.75/5.71 thf(fact_5185_dbl__inc__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.71 = ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(4)
% 7.75/5.71 thf(fact_5186_dbl__inc__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.71 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(4)
% 7.75/5.71 thf(fact_5187_dbl__inc__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.71 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(4)
% 7.75/5.71 thf(fact_5188_dbl__inc__simps_I4_J,axiom,
% 7.75/5.71 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.71 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(4)
% 7.75/5.71 thf(fact_5189_dbl__inc__simps_I5_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 7.75/5.71 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(5)
% 7.75/5.71 thf(fact_5190_dbl__inc__simps_I5_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 7.75/5.71 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(5)
% 7.75/5.71 thf(fact_5191_dbl__inc__simps_I5_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 7.75/5.71 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(5)
% 7.75/5.71 thf(fact_5192_dbl__inc__simps_I5_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 7.75/5.71 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(5)
% 7.75/5.71 thf(fact_5193_log__eq__one,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.71 => ( ( A != one_one_real )
% 7.75/5.71 => ( ( log @ A @ A )
% 7.75/5.71 = one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_eq_one
% 7.75/5.71 thf(fact_5194_log__less__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 7.75/5.71 = ( ord_less_real @ X @ Y ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_less_cancel_iff
% 7.75/5.71 thf(fact_5195_log__less__one__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 7.75/5.71 = ( ord_less_real @ X @ A ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_less_one_cancel_iff
% 7.75/5.71 thf(fact_5196_one__less__log__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 7.75/5.71 = ( ord_less_real @ A @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % one_less_log_cancel_iff
% 7.75/5.71 thf(fact_5197_log__less__zero__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_less_zero_cancel_iff
% 7.75/5.71 thf(fact_5198_zero__less__log__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 7.75/5.71 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_log_cancel_iff
% 7.75/5.71 thf(fact_5199_dbl__inc__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(1)
% 7.75/5.71 thf(fact_5200_dbl__inc__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 7.75/5.71 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(1)
% 7.75/5.71 thf(fact_5201_dbl__inc__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 7.75/5.71 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(1)
% 7.75/5.71 thf(fact_5202_dbl__inc__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 7.75/5.71 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(1)
% 7.75/5.71 thf(fact_5203_dbl__inc__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 7.75/5.71 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_simps(1)
% 7.75/5.71 thf(fact_5204_dbl__dec__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(1)
% 7.75/5.71 thf(fact_5205_dbl__dec__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 7.75/5.71 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(1)
% 7.75/5.71 thf(fact_5206_dbl__dec__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 7.75/5.71 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(1)
% 7.75/5.71 thf(fact_5207_dbl__dec__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 7.75/5.71 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(1)
% 7.75/5.71 thf(fact_5208_dbl__dec__simps_I1_J,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 7.75/5.71 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_dec_simps(1)
% 7.75/5.71 thf(fact_5209_log__le__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 7.75/5.71 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_le_cancel_iff
% 7.75/5.71 thf(fact_5210_log__le__one__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 7.75/5.71 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_le_one_cancel_iff
% 7.75/5.71 thf(fact_5211_one__le__log__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 7.75/5.71 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % one_le_log_cancel_iff
% 7.75/5.71 thf(fact_5212_log__le__zero__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_le_zero_cancel_iff
% 7.75/5.71 thf(fact_5213_zero__le__log__cancel__iff,axiom,
% 7.75/5.71 ! [A: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 7.75/5.71 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_le_log_cancel_iff
% 7.75/5.71 thf(fact_5214_log__pow__cancel,axiom,
% 7.75/5.71 ! [A: real,B: nat] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.71 => ( ( A != one_one_real )
% 7.75/5.71 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 7.75/5.71 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_pow_cancel
% 7.75/5.71 thf(fact_5215_pochhammer__pos,axiom,
% 7.75/5.71 ! [X: real,N: nat] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_pos
% 7.75/5.71 thf(fact_5216_pochhammer__pos,axiom,
% 7.75/5.71 ! [X: rat,N: nat] :
% 7.75/5.71 ( ( ord_less_rat @ zero_zero_rat @ X )
% 7.75/5.71 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_pos
% 7.75/5.71 thf(fact_5217_pochhammer__pos,axiom,
% 7.75/5.71 ! [X: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_nat @ zero_zero_nat @ X )
% 7.75/5.71 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_pos
% 7.75/5.71 thf(fact_5218_pochhammer__pos,axiom,
% 7.75/5.71 ! [X: int,N: nat] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ X )
% 7.75/5.71 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_pos
% 7.75/5.71 thf(fact_5219_pochhammer__eq__0__mono,axiom,
% 7.75/5.71 ! [A: complex,N: nat,M: nat] :
% 7.75/5.71 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 7.75/5.71 = zero_zero_complex )
% 7.75/5.71 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.71 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 7.75/5.71 = zero_zero_complex ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_eq_0_mono
% 7.75/5.71 thf(fact_5220_pochhammer__eq__0__mono,axiom,
% 7.75/5.71 ! [A: real,N: nat,M: nat] :
% 7.75/5.71 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.71 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 7.75/5.71 = zero_zero_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_eq_0_mono
% 7.75/5.71 thf(fact_5221_pochhammer__eq__0__mono,axiom,
% 7.75/5.71 ! [A: rat,N: nat,M: nat] :
% 7.75/5.71 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 7.75/5.71 = zero_zero_rat )
% 7.75/5.71 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.71 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 7.75/5.71 = zero_zero_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_eq_0_mono
% 7.75/5.71 thf(fact_5222_pochhammer__neq__0__mono,axiom,
% 7.75/5.71 ! [A: complex,M: nat,N: nat] :
% 7.75/5.71 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 7.75/5.71 != zero_zero_complex )
% 7.75/5.71 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.71 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 7.75/5.71 != zero_zero_complex ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_neq_0_mono
% 7.75/5.71 thf(fact_5223_pochhammer__neq__0__mono,axiom,
% 7.75/5.71 ! [A: real,M: nat,N: nat] :
% 7.75/5.71 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 7.75/5.71 != zero_zero_real )
% 7.75/5.71 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.71 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 7.75/5.71 != zero_zero_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_neq_0_mono
% 7.75/5.71 thf(fact_5224_pochhammer__neq__0__mono,axiom,
% 7.75/5.71 ! [A: rat,M: nat,N: nat] :
% 7.75/5.71 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 7.75/5.71 != zero_zero_rat )
% 7.75/5.71 => ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.71 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 7.75/5.71 != zero_zero_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_neq_0_mono
% 7.75/5.71 thf(fact_5225_log__base__change,axiom,
% 7.75/5.71 ! [A: real,B: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.71 => ( ( A != one_one_real )
% 7.75/5.71 => ( ( log @ B @ X )
% 7.75/5.71 = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_base_change
% 7.75/5.71 thf(fact_5226_log__of__power__eq,axiom,
% 7.75/5.71 ! [M: nat,B: real,N: nat] :
% 7.75/5.71 ( ( ( semiri5074537144036343181t_real @ M )
% 7.75/5.71 = ( power_power_real @ B @ N ) )
% 7.75/5.71 => ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.71 => ( ( semiri5074537144036343181t_real @ N )
% 7.75/5.71 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_of_power_eq
% 7.75/5.71 thf(fact_5227_less__log__of__power,axiom,
% 7.75/5.71 ! [B: real,N: nat,M: real] :
% 7.75/5.71 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 7.75/5.71 => ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.71 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % less_log_of_power
% 7.75/5.71 thf(fact_5228_pochhammer__nonneg,axiom,
% 7.75/5.71 ! [X: real,N: nat] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_nonneg
% 7.75/5.71 thf(fact_5229_pochhammer__nonneg,axiom,
% 7.75/5.71 ! [X: rat,N: nat] :
% 7.75/5.71 ( ( ord_less_rat @ zero_zero_rat @ X )
% 7.75/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_nonneg
% 7.75/5.71 thf(fact_5230_pochhammer__nonneg,axiom,
% 7.75/5.71 ! [X: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_nat @ zero_zero_nat @ X )
% 7.75/5.71 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_nonneg
% 7.75/5.71 thf(fact_5231_pochhammer__nonneg,axiom,
% 7.75/5.71 ! [X: int,N: nat] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ X )
% 7.75/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_nonneg
% 7.75/5.71 thf(fact_5232_pochhammer__0__left,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( ( N = zero_zero_nat )
% 7.75/5.71 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 7.75/5.71 = one_one_complex ) )
% 7.75/5.71 & ( ( N != zero_zero_nat )
% 7.75/5.71 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 7.75/5.71 = zero_zero_complex ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_0_left
% 7.75/5.71 thf(fact_5233_pochhammer__0__left,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( ( N = zero_zero_nat )
% 7.75/5.71 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 7.75/5.71 = one_one_real ) )
% 7.75/5.71 & ( ( N != zero_zero_nat )
% 7.75/5.71 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 7.75/5.71 = zero_zero_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_0_left
% 7.75/5.71 thf(fact_5234_pochhammer__0__left,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( ( N = zero_zero_nat )
% 7.75/5.71 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 7.75/5.71 = one_one_rat ) )
% 7.75/5.71 & ( ( N != zero_zero_nat )
% 7.75/5.71 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 7.75/5.71 = zero_zero_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_0_left
% 7.75/5.71 thf(fact_5235_pochhammer__0__left,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( ( N = zero_zero_nat )
% 7.75/5.71 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 7.75/5.71 = one_one_nat ) )
% 7.75/5.71 & ( ( N != zero_zero_nat )
% 7.75/5.71 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 7.75/5.71 = zero_zero_nat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_0_left
% 7.75/5.71 thf(fact_5236_pochhammer__0__left,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( ( N = zero_zero_nat )
% 7.75/5.71 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 7.75/5.71 = one_one_int ) )
% 7.75/5.71 & ( ( N != zero_zero_nat )
% 7.75/5.71 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 7.75/5.71 = zero_zero_int ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_0_left
% 7.75/5.71 thf(fact_5237_log__mult,axiom,
% 7.75/5.71 ! [A: real,X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.71 => ( ( A != one_one_real )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ( log @ A @ ( times_times_real @ X @ Y ) )
% 7.75/5.71 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_mult
% 7.75/5.71 thf(fact_5238_le__log__of__power,axiom,
% 7.75/5.71 ! [B: real,N: nat,M: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 7.75/5.71 => ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % le_log_of_power
% 7.75/5.71 thf(fact_5239_log__divide,axiom,
% 7.75/5.71 ! [A: real,X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.71 => ( ( A != one_one_real )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ( log @ A @ ( divide_divide_real @ X @ Y ) )
% 7.75/5.71 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_divide
% 7.75/5.71 thf(fact_5240_log__base__pow,axiom,
% 7.75/5.71 ! [A: real,N: nat,X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.71 => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 7.75/5.71 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_base_pow
% 7.75/5.71 thf(fact_5241_log__nat__power,axiom,
% 7.75/5.71 ! [X: real,B: real,N: nat] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 7.75/5.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_nat_power
% 7.75/5.71 thf(fact_5242_pochhammer__rec,axiom,
% 7.75/5.71 ! [A: rat,N: nat] :
% 7.75/5.71 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec
% 7.75/5.71 thf(fact_5243_pochhammer__rec,axiom,
% 7.75/5.71 ! [A: real,N: nat] :
% 7.75/5.71 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec
% 7.75/5.71 thf(fact_5244_pochhammer__rec,axiom,
% 7.75/5.71 ! [A: nat,N: nat] :
% 7.75/5.71 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec
% 7.75/5.71 thf(fact_5245_pochhammer__rec,axiom,
% 7.75/5.71 ! [A: int,N: nat] :
% 7.75/5.71 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec
% 7.75/5.71 thf(fact_5246_pochhammer__rec,axiom,
% 7.75/5.71 ! [A: code_integer,N: nat] :
% 7.75/5.71 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec
% 7.75/5.71 thf(fact_5247_pochhammer__rec,axiom,
% 7.75/5.71 ! [A: complex,N: nat] :
% 7.75/5.71 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec
% 7.75/5.71 thf(fact_5248_dbl__inc__def,axiom,
% 7.75/5.71 ( neg_nu8295874005876285629c_real
% 7.75/5.71 = ( ^ [X2: real] : ( plus_plus_real @ ( plus_plus_real @ X2 @ X2 ) @ one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_def
% 7.75/5.71 thf(fact_5249_dbl__inc__def,axiom,
% 7.75/5.71 ( neg_nu5219082963157363817nc_rat
% 7.75/5.71 = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_def
% 7.75/5.71 thf(fact_5250_dbl__inc__def,axiom,
% 7.75/5.71 ( neg_nu5851722552734809277nc_int
% 7.75/5.71 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % dbl_inc_def
% 7.75/5.71 thf(fact_5251_log2__of__power__eq,axiom,
% 7.75/5.71 ! [M: nat,N: nat] :
% 7.75/5.71 ( ( M
% 7.75/5.71 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ( semiri5074537144036343181t_real @ N )
% 7.75/5.71 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log2_of_power_eq
% 7.75/5.71 thf(fact_5252_pochhammer__rec_H,axiom,
% 7.75/5.71 ! [Z: rat,N: nat] :
% 7.75/5.71 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec'
% 7.75/5.71 thf(fact_5253_pochhammer__rec_H,axiom,
% 7.75/5.71 ! [Z: code_integer,N: nat] :
% 7.75/5.71 ( ( comm_s8582702949713902594nteger @ Z @ ( suc @ N ) )
% 7.75/5.71 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N ) ) @ ( comm_s8582702949713902594nteger @ Z @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec'
% 7.75/5.71 thf(fact_5254_pochhammer__rec_H,axiom,
% 7.75/5.71 ! [Z: real,N: nat] :
% 7.75/5.71 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec'
% 7.75/5.71 thf(fact_5255_pochhammer__rec_H,axiom,
% 7.75/5.71 ! [Z: int,N: nat] :
% 7.75/5.71 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec'
% 7.75/5.71 thf(fact_5256_pochhammer__rec_H,axiom,
% 7.75/5.71 ! [Z: nat,N: nat] :
% 7.75/5.71 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec'
% 7.75/5.71 thf(fact_5257_pochhammer__rec_H,axiom,
% 7.75/5.71 ! [Z: complex,N: nat] :
% 7.75/5.71 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_rec'
% 7.75/5.71 thf(fact_5258_pochhammer__Suc,axiom,
% 7.75/5.71 ! [A: rat,N: nat] :
% 7.75/5.71 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_Suc
% 7.75/5.71 thf(fact_5259_pochhammer__Suc,axiom,
% 7.75/5.71 ! [A: code_integer,N: nat] :
% 7.75/5.71 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_Suc
% 7.75/5.71 thf(fact_5260_pochhammer__Suc,axiom,
% 7.75/5.71 ! [A: real,N: nat] :
% 7.75/5.71 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_Suc
% 7.75/5.71 thf(fact_5261_pochhammer__Suc,axiom,
% 7.75/5.71 ! [A: int,N: nat] :
% 7.75/5.71 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_Suc
% 7.75/5.71 thf(fact_5262_pochhammer__Suc,axiom,
% 7.75/5.71 ! [A: nat,N: nat] :
% 7.75/5.71 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_Suc
% 7.75/5.71 thf(fact_5263_pochhammer__Suc,axiom,
% 7.75/5.71 ! [A: complex,N: nat] :
% 7.75/5.71 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 7.75/5.71 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_Suc
% 7.75/5.71 thf(fact_5264_pochhammer__of__nat__eq__0__lemma,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ord_less_nat @ N @ K )
% 7.75/5.71 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 7.75/5.71 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma
% 7.75/5.71 thf(fact_5265_pochhammer__of__nat__eq__0__lemma,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ord_less_nat @ N @ K )
% 7.75/5.71 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 7.75/5.71 = zero_zero_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma
% 7.75/5.71 thf(fact_5266_pochhammer__of__nat__eq__0__lemma,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ord_less_nat @ N @ K )
% 7.75/5.71 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 7.75/5.71 = zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma
% 7.75/5.71 thf(fact_5267_pochhammer__of__nat__eq__0__lemma,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ord_less_nat @ N @ K )
% 7.75/5.71 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 7.75/5.71 = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma
% 7.75/5.71 thf(fact_5268_pochhammer__of__nat__eq__0__lemma,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ord_less_nat @ N @ K )
% 7.75/5.71 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 7.75/5.71 = zero_zero_complex ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma
% 7.75/5.71 thf(fact_5269_pochhammer__of__nat__eq__0__iff,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 7.75/5.71 = zero_z3403309356797280102nteger )
% 7.75/5.71 = ( ord_less_nat @ N @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_iff
% 7.75/5.71 thf(fact_5270_pochhammer__of__nat__eq__0__iff,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 7.75/5.71 = zero_zero_rat )
% 7.75/5.71 = ( ord_less_nat @ N @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_iff
% 7.75/5.71 thf(fact_5271_pochhammer__of__nat__eq__0__iff,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 = ( ord_less_nat @ N @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_iff
% 7.75/5.71 thf(fact_5272_pochhammer__of__nat__eq__0__iff,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 7.75/5.71 = zero_zero_int )
% 7.75/5.71 = ( ord_less_nat @ N @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_iff
% 7.75/5.71 thf(fact_5273_pochhammer__of__nat__eq__0__iff,axiom,
% 7.75/5.71 ! [N: nat,K: nat] :
% 7.75/5.71 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 7.75/5.71 = zero_zero_complex )
% 7.75/5.71 = ( ord_less_nat @ N @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_iff
% 7.75/5.71 thf(fact_5274_pochhammer__eq__0__iff,axiom,
% 7.75/5.71 ! [A: rat,N: nat] :
% 7.75/5.71 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 7.75/5.71 = zero_zero_rat )
% 7.75/5.71 = ( ? [K3: nat] :
% 7.75/5.71 ( ( ord_less_nat @ K3 @ N )
% 7.75/5.71 & ( A
% 7.75/5.71 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_eq_0_iff
% 7.75/5.71 thf(fact_5275_pochhammer__eq__0__iff,axiom,
% 7.75/5.71 ! [A: real,N: nat] :
% 7.75/5.71 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 = ( ? [K3: nat] :
% 7.75/5.71 ( ( ord_less_nat @ K3 @ N )
% 7.75/5.71 & ( A
% 7.75/5.71 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_eq_0_iff
% 7.75/5.71 thf(fact_5276_pochhammer__eq__0__iff,axiom,
% 7.75/5.71 ! [A: complex,N: nat] :
% 7.75/5.71 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 7.75/5.71 = zero_zero_complex )
% 7.75/5.71 = ( ? [K3: nat] :
% 7.75/5.71 ( ( ord_less_nat @ K3 @ N )
% 7.75/5.71 & ( A
% 7.75/5.71 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_eq_0_iff
% 7.75/5.71 thf(fact_5277_log__of__power__less,axiom,
% 7.75/5.71 ! [M: nat,B: real,N: nat] :
% 7.75/5.71 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 7.75/5.71 => ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.71 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.71 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_of_power_less
% 7.75/5.71 thf(fact_5278_pochhammer__product_H,axiom,
% 7.75/5.71 ! [Z: rat,N: nat,M: nat] :
% 7.75/5.71 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 7.75/5.71 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product'
% 7.75/5.71 thf(fact_5279_pochhammer__product_H,axiom,
% 7.75/5.71 ! [Z: code_integer,N: nat,M: nat] :
% 7.75/5.71 ( ( comm_s8582702949713902594nteger @ Z @ ( plus_plus_nat @ N @ M ) )
% 7.75/5.71 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ N ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N ) ) @ M ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product'
% 7.75/5.71 thf(fact_5280_pochhammer__product_H,axiom,
% 7.75/5.71 ! [Z: real,N: nat,M: nat] :
% 7.75/5.71 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 7.75/5.71 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product'
% 7.75/5.71 thf(fact_5281_pochhammer__product_H,axiom,
% 7.75/5.71 ! [Z: int,N: nat,M: nat] :
% 7.75/5.71 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 7.75/5.71 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product'
% 7.75/5.71 thf(fact_5282_pochhammer__product_H,axiom,
% 7.75/5.71 ! [Z: nat,N: nat,M: nat] :
% 7.75/5.71 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 7.75/5.71 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product'
% 7.75/5.71 thf(fact_5283_pochhammer__product_H,axiom,
% 7.75/5.71 ! [Z: complex,N: nat,M: nat] :
% 7.75/5.71 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 7.75/5.71 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product'
% 7.75/5.71 thf(fact_5284_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 7.75/5.71 ! [K: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.71 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 7.75/5.71 != zero_z3403309356797280102nteger ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma'
% 7.75/5.71 thf(fact_5285_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 7.75/5.71 ! [K: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.71 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 7.75/5.71 != zero_zero_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma'
% 7.75/5.71 thf(fact_5286_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 7.75/5.71 ! [K: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.71 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 7.75/5.71 != zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma'
% 7.75/5.71 thf(fact_5287_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 7.75/5.71 ! [K: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.71 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 7.75/5.71 != zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma'
% 7.75/5.71 thf(fact_5288_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 7.75/5.71 ! [K: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.71 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 7.75/5.71 != zero_zero_complex ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_of_nat_eq_0_lemma'
% 7.75/5.71 thf(fact_5289_log__of__power__le,axiom,
% 7.75/5.71 ! [M: nat,B: real,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 7.75/5.71 => ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.71 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.71 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_of_power_le
% 7.75/5.71 thf(fact_5290_pochhammer__product,axiom,
% 7.75/5.71 ! [M: nat,N: nat,Z: rat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.71 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 7.75/5.71 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product
% 7.75/5.71 thf(fact_5291_pochhammer__product,axiom,
% 7.75/5.71 ! [M: nat,N: nat,Z: code_integer] :
% 7.75/5.71 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.71 => ( ( comm_s8582702949713902594nteger @ Z @ N )
% 7.75/5.71 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product
% 7.75/5.71 thf(fact_5292_pochhammer__product,axiom,
% 7.75/5.71 ! [M: nat,N: nat,Z: real] :
% 7.75/5.71 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.71 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 7.75/5.71 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product
% 7.75/5.71 thf(fact_5293_pochhammer__product,axiom,
% 7.75/5.71 ! [M: nat,N: nat,Z: int] :
% 7.75/5.71 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.71 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 7.75/5.71 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product
% 7.75/5.71 thf(fact_5294_pochhammer__product,axiom,
% 7.75/5.71 ! [M: nat,N: nat,Z: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.71 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 7.75/5.71 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product
% 7.75/5.71 thf(fact_5295_pochhammer__product,axiom,
% 7.75/5.71 ! [M: nat,N: nat,Z: complex] :
% 7.75/5.71 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.71 => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 7.75/5.71 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_product
% 7.75/5.71 thf(fact_5296_less__log2__of__power,axiom,
% 7.75/5.71 ! [N: nat,M: nat] :
% 7.75/5.71 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 7.75/5.71 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % less_log2_of_power
% 7.75/5.71 thf(fact_5297_le__log2__of__power,axiom,
% 7.75/5.71 ! [N: nat,M: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % le_log2_of_power
% 7.75/5.71 thf(fact_5298_pochhammer__absorb__comp,axiom,
% 7.75/5.71 ! [R2: code_integer,K: nat] :
% 7.75/5.71 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 7.75/5.71 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_absorb_comp
% 7.75/5.71 thf(fact_5299_pochhammer__absorb__comp,axiom,
% 7.75/5.71 ! [R2: rat,K: nat] :
% 7.75/5.71 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 7.75/5.71 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_absorb_comp
% 7.75/5.71 thf(fact_5300_pochhammer__absorb__comp,axiom,
% 7.75/5.71 ! [R2: real,K: nat] :
% 7.75/5.71 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 7.75/5.71 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_absorb_comp
% 7.75/5.71 thf(fact_5301_pochhammer__absorb__comp,axiom,
% 7.75/5.71 ! [R2: int,K: nat] :
% 7.75/5.71 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 7.75/5.71 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_absorb_comp
% 7.75/5.71 thf(fact_5302_pochhammer__absorb__comp,axiom,
% 7.75/5.71 ! [R2: complex,K: nat] :
% 7.75/5.71 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 7.75/5.71 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_absorb_comp
% 7.75/5.71 thf(fact_5303_log2__of__power__less,axiom,
% 7.75/5.71 ! [M: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.71 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log2_of_power_less
% 7.75/5.71 thf(fact_5304_log2__of__power__le,axiom,
% 7.75/5.71 ! [M: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.71 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log2_of_power_le
% 7.75/5.71 thf(fact_5305_pochhammer__minus_H,axiom,
% 7.75/5.71 ! [B: code_integer,K: nat] :
% 7.75/5.71 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 7.75/5.71 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus'
% 7.75/5.71 thf(fact_5306_pochhammer__minus_H,axiom,
% 7.75/5.71 ! [B: rat,K: nat] :
% 7.75/5.71 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 7.75/5.71 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus'
% 7.75/5.71 thf(fact_5307_pochhammer__minus_H,axiom,
% 7.75/5.71 ! [B: real,K: nat] :
% 7.75/5.71 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 7.75/5.71 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus'
% 7.75/5.71 thf(fact_5308_pochhammer__minus_H,axiom,
% 7.75/5.71 ! [B: int,K: nat] :
% 7.75/5.71 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 7.75/5.71 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus'
% 7.75/5.71 thf(fact_5309_pochhammer__minus_H,axiom,
% 7.75/5.71 ! [B: complex,K: nat] :
% 7.75/5.71 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 7.75/5.71 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus'
% 7.75/5.71 thf(fact_5310_pochhammer__minus,axiom,
% 7.75/5.71 ! [B: code_integer,K: nat] :
% 7.75/5.71 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 7.75/5.71 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus
% 7.75/5.71 thf(fact_5311_pochhammer__minus,axiom,
% 7.75/5.71 ! [B: rat,K: nat] :
% 7.75/5.71 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 7.75/5.71 = ( 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 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus
% 7.75/5.71 thf(fact_5312_pochhammer__minus,axiom,
% 7.75/5.71 ! [B: real,K: nat] :
% 7.75/5.71 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 7.75/5.71 = ( 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 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus
% 7.75/5.71 thf(fact_5313_pochhammer__minus,axiom,
% 7.75/5.71 ! [B: int,K: nat] :
% 7.75/5.71 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 7.75/5.71 = ( 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 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus
% 7.75/5.71 thf(fact_5314_pochhammer__minus,axiom,
% 7.75/5.71 ! [B: complex,K: nat] :
% 7.75/5.71 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 7.75/5.71 = ( 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 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pochhammer_minus
% 7.75/5.71 thf(fact_5315_norm__divide__numeral,axiom,
% 7.75/5.71 ! [A: real,W: num] :
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.71 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_divide_numeral
% 7.75/5.71 thf(fact_5316_norm__divide__numeral,axiom,
% 7.75/5.71 ! [A: complex,W: num] :
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 7.75/5.71 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_divide_numeral
% 7.75/5.71 thf(fact_5317_norm__mult__numeral2,axiom,
% 7.75/5.71 ! [A: real,W: num] :
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.71 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult_numeral2
% 7.75/5.71 thf(fact_5318_norm__mult__numeral2,axiom,
% 7.75/5.71 ! [A: complex,W: num] :
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 7.75/5.71 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult_numeral2
% 7.75/5.71 thf(fact_5319_norm__mult__numeral1,axiom,
% 7.75/5.71 ! [W: num,A: real] :
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 7.75/5.71 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult_numeral1
% 7.75/5.71 thf(fact_5320_norm__mult__numeral1,axiom,
% 7.75/5.71 ! [W: num,A: complex] :
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 7.75/5.71 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult_numeral1
% 7.75/5.71 thf(fact_5321_norm__neg__numeral,axiom,
% 7.75/5.71 ! [W: num] :
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.71 = ( numeral_numeral_real @ W ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_neg_numeral
% 7.75/5.71 thf(fact_5322_norm__neg__numeral,axiom,
% 7.75/5.71 ! [W: num] :
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 7.75/5.71 = ( numeral_numeral_real @ W ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_neg_numeral
% 7.75/5.71 thf(fact_5323_norm__le__zero__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 7.75/5.71 = ( X = zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_le_zero_iff
% 7.75/5.71 thf(fact_5324_norm__le__zero__iff,axiom,
% 7.75/5.71 ! [X: complex] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 7.75/5.71 = ( X = zero_zero_complex ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_le_zero_iff
% 7.75/5.71 thf(fact_5325_zero__less__norm__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 7.75/5.71 = ( X != zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_norm_iff
% 7.75/5.71 thf(fact_5326_zero__less__norm__iff,axiom,
% 7.75/5.71 ! [X: complex] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 7.75/5.71 = ( X != zero_zero_complex ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_norm_iff
% 7.75/5.71 thf(fact_5327_set__vebt__set__vebt_H__valid,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( vEBT_set_vebt @ T )
% 7.75/5.71 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % set_vebt_set_vebt'_valid
% 7.75/5.71 thf(fact_5328_norm__eq__zero,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ( real_V7735802525324610683m_real @ X )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 = ( X = zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_eq_zero
% 7.75/5.71 thf(fact_5329_norm__eq__zero,axiom,
% 7.75/5.71 ! [X: complex] :
% 7.75/5.71 ( ( ( real_V1022390504157884413omplex @ X )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 = ( X = zero_zero_complex ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_eq_zero
% 7.75/5.71 thf(fact_5330_norm__zero,axiom,
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % norm_zero
% 7.75/5.71 thf(fact_5331_norm__zero,axiom,
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % norm_zero
% 7.75/5.71 thf(fact_5332_norm__one,axiom,
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ one_one_real )
% 7.75/5.71 = one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % norm_one
% 7.75/5.71 thf(fact_5333_norm__one,axiom,
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 7.75/5.71 = one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % norm_one
% 7.75/5.71 thf(fact_5334_norm__numeral,axiom,
% 7.75/5.71 ! [W: num] :
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 7.75/5.71 = ( numeral_numeral_real @ W ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_numeral
% 7.75/5.71 thf(fact_5335_norm__numeral,axiom,
% 7.75/5.71 ! [W: num] :
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 7.75/5.71 = ( numeral_numeral_real @ W ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_numeral
% 7.75/5.71 thf(fact_5336_pred__member,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 7.75/5.71 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 7.75/5.71 = ( ( vEBT_vebt_member @ T @ Y )
% 7.75/5.71 & ( ord_less_nat @ Y @ X )
% 7.75/5.71 & ! [Z6: nat] :
% 7.75/5.71 ( ( ( vEBT_vebt_member @ T @ Z6 )
% 7.75/5.71 & ( ord_less_nat @ Z6 @ X ) )
% 7.75/5.71 => ( ord_less_eq_nat @ Z6 @ Y ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pred_member
% 7.75/5.71 thf(fact_5337_succ__member,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 7.75/5.71 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 7.75/5.71 = ( ( vEBT_vebt_member @ T @ Y )
% 7.75/5.71 & ( ord_less_nat @ X @ Y )
% 7.75/5.71 & ! [Z6: nat] :
% 7.75/5.71 ( ( ( vEBT_vebt_member @ T @ Z6 )
% 7.75/5.71 & ( ord_less_nat @ X @ Z6 ) )
% 7.75/5.71 => ( ord_less_eq_nat @ Y @ Z6 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % succ_member
% 7.75/5.71 thf(fact_5338_norm__not__less__zero,axiom,
% 7.75/5.71 ! [X: complex] :
% 7.75/5.71 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % norm_not_less_zero
% 7.75/5.71 thf(fact_5339_norm__mult,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 7.75/5.71 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult
% 7.75/5.71 thf(fact_5340_norm__mult,axiom,
% 7.75/5.71 ! [X: complex,Y: complex] :
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 7.75/5.71 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult
% 7.75/5.71 thf(fact_5341_norm__ge__zero,axiom,
% 7.75/5.71 ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_ge_zero
% 7.75/5.71 thf(fact_5342_norm__divide,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.71 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_divide
% 7.75/5.71 thf(fact_5343_norm__divide,axiom,
% 7.75/5.71 ! [A: complex,B: complex] :
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 7.75/5.71 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_divide
% 7.75/5.71 thf(fact_5344_norm__power,axiom,
% 7.75/5.71 ! [X: real,N: nat] :
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) )
% 7.75/5.71 = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_power
% 7.75/5.71 thf(fact_5345_norm__power,axiom,
% 7.75/5.71 ! [X: complex,N: nat] :
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) )
% 7.75/5.71 = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_power
% 7.75/5.71 thf(fact_5346_norm__uminus__minus,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y ) )
% 7.75/5.71 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_uminus_minus
% 7.75/5.71 thf(fact_5347_norm__uminus__minus,axiom,
% 7.75/5.71 ! [X: complex,Y: complex] :
% 7.75/5.71 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y ) )
% 7.75/5.71 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_uminus_minus
% 7.75/5.71 thf(fact_5348_power__eq__imp__eq__norm,axiom,
% 7.75/5.71 ! [W: real,N: nat,Z: real] :
% 7.75/5.71 ( ( ( power_power_real @ W @ N )
% 7.75/5.71 = ( power_power_real @ Z @ N ) )
% 7.75/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.71 => ( ( real_V7735802525324610683m_real @ W )
% 7.75/5.71 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_eq_imp_eq_norm
% 7.75/5.71 thf(fact_5349_power__eq__imp__eq__norm,axiom,
% 7.75/5.71 ! [W: complex,N: nat,Z: complex] :
% 7.75/5.71 ( ( ( power_power_complex @ W @ N )
% 7.75/5.71 = ( power_power_complex @ Z @ N ) )
% 7.75/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.71 => ( ( real_V1022390504157884413omplex @ W )
% 7.75/5.71 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_eq_imp_eq_norm
% 7.75/5.71 thf(fact_5350_nonzero__norm__divide,axiom,
% 7.75/5.71 ! [B: real,A: real] :
% 7.75/5.71 ( ( B != zero_zero_real )
% 7.75/5.71 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.71 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % nonzero_norm_divide
% 7.75/5.71 thf(fact_5351_nonzero__norm__divide,axiom,
% 7.75/5.71 ! [B: complex,A: complex] :
% 7.75/5.71 ( ( B != zero_zero_complex )
% 7.75/5.71 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 7.75/5.71 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % nonzero_norm_divide
% 7.75/5.71 thf(fact_5352_norm__mult__less,axiom,
% 7.75/5.71 ! [X: real,R2: real,Y: real,S: real] :
% 7.75/5.71 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 7.75/5.71 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 7.75/5.71 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult_less
% 7.75/5.71 thf(fact_5353_norm__mult__less,axiom,
% 7.75/5.71 ! [X: complex,R2: real,Y: complex,S: real] :
% 7.75/5.71 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 7.75/5.71 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 7.75/5.71 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R2 @ S ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult_less
% 7.75/5.71 thf(fact_5354_norm__mult__ineq,axiom,
% 7.75/5.71 ! [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 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult_ineq
% 7.75/5.71 thf(fact_5355_norm__mult__ineq,axiom,
% 7.75/5.71 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_mult_ineq
% 7.75/5.71 thf(fact_5356_norm__add__less,axiom,
% 7.75/5.71 ! [X: real,R2: real,Y: real,S: real] :
% 7.75/5.71 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 7.75/5.71 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 7.75/5.71 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_add_less
% 7.75/5.71 thf(fact_5357_norm__add__less,axiom,
% 7.75/5.71 ! [X: complex,R2: real,Y: complex,S: real] :
% 7.75/5.71 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 7.75/5.71 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 7.75/5.71 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_add_less
% 7.75/5.71 thf(fact_5358_norm__triangle__lt,axiom,
% 7.75/5.71 ! [X: real,Y: real,E: real] :
% 7.75/5.71 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 7.75/5.71 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_triangle_lt
% 7.75/5.71 thf(fact_5359_norm__triangle__lt,axiom,
% 7.75/5.71 ! [X: complex,Y: complex,E: real] :
% 7.75/5.71 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 7.75/5.71 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_triangle_lt
% 7.75/5.71 thf(fact_5360_norm__triangle__mono,axiom,
% 7.75/5.71 ! [A: real,R2: real,B: real,S: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 7.75/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_triangle_mono
% 7.75/5.71 thf(fact_5361_norm__triangle__mono,axiom,
% 7.75/5.71 ! [A: complex,R2: real,B: complex,S: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 7.75/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_triangle_mono
% 7.75/5.71 thf(fact_5362_norm__triangle__ineq,axiom,
% 7.75/5.71 ! [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 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_triangle_ineq
% 7.75/5.71 thf(fact_5363_norm__triangle__ineq,axiom,
% 7.75/5.71 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_triangle_ineq
% 7.75/5.71 thf(fact_5364_norm__triangle__le,axiom,
% 7.75/5.71 ! [X: real,Y: real,E: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 7.75/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_triangle_le
% 7.75/5.71 thf(fact_5365_norm__triangle__le,axiom,
% 7.75/5.71 ! [X: complex,Y: complex,E: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 7.75/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_triangle_le
% 7.75/5.71 thf(fact_5366_norm__add__leD,axiom,
% 7.75/5.71 ! [A: real,B: real,C: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 7.75/5.71 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_add_leD
% 7.75/5.71 thf(fact_5367_norm__add__leD,axiom,
% 7.75/5.71 ! [A: complex,B: complex,C: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 7.75/5.71 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_add_leD
% 7.75/5.71 thf(fact_5368_norm__diff__triangle__less,axiom,
% 7.75/5.71 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 7.75/5.71 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 7.75/5.71 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 7.75/5.71 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_diff_triangle_less
% 7.75/5.71 thf(fact_5369_norm__diff__triangle__less,axiom,
% 7.75/5.71 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 7.75/5.71 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 7.75/5.71 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 7.75/5.71 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_diff_triangle_less
% 7.75/5.71 thf(fact_5370_norm__power__ineq,axiom,
% 7.75/5.71 ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_power_ineq
% 7.75/5.71 thf(fact_5371_norm__power__ineq,axiom,
% 7.75/5.71 ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_power_ineq
% 7.75/5.71 thf(fact_5372_norm__diff__ineq,axiom,
% 7.75/5.71 ! [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 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_diff_ineq
% 7.75/5.71 thf(fact_5373_norm__diff__ineq,axiom,
% 7.75/5.71 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_diff_ineq
% 7.75/5.71 thf(fact_5374_power__eq__1__iff,axiom,
% 7.75/5.71 ! [W: real,N: nat] :
% 7.75/5.71 ( ( ( power_power_real @ W @ N )
% 7.75/5.71 = one_one_real )
% 7.75/5.71 => ( ( ( real_V7735802525324610683m_real @ W )
% 7.75/5.71 = one_one_real )
% 7.75/5.71 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_eq_1_iff
% 7.75/5.71 thf(fact_5375_power__eq__1__iff,axiom,
% 7.75/5.71 ! [W: complex,N: nat] :
% 7.75/5.71 ( ( ( power_power_complex @ W @ N )
% 7.75/5.71 = one_one_complex )
% 7.75/5.71 => ( ( ( real_V1022390504157884413omplex @ W )
% 7.75/5.71 = one_one_real )
% 7.75/5.71 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_eq_1_iff
% 7.75/5.71 thf(fact_5376_norm__diff__triangle__ineq,axiom,
% 7.75/5.71 ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_diff_triangle_ineq
% 7.75/5.71 thf(fact_5377_norm__diff__triangle__ineq,axiom,
% 7.75/5.71 ! [A: complex,B: complex,C: complex,D2: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D2 ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_diff_triangle_ineq
% 7.75/5.71 thf(fact_5378_square__norm__one,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.71 = one_one_real )
% 7.75/5.71 => ( ( real_V7735802525324610683m_real @ X )
% 7.75/5.71 = one_one_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % square_norm_one
% 7.75/5.71 thf(fact_5379_square__norm__one,axiom,
% 7.75/5.71 ! [X: complex] :
% 7.75/5.71 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.71 = one_one_complex )
% 7.75/5.71 => ( ( real_V1022390504157884413omplex @ X )
% 7.75/5.71 = one_one_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % square_norm_one
% 7.75/5.71 thf(fact_5380_norm__power__diff,axiom,
% 7.75/5.71 ! [Z: real,W: real,M: nat] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 7.75/5.71 => ( 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 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_power_diff
% 7.75/5.71 thf(fact_5381_norm__power__diff,axiom,
% 7.75/5.71 ! [Z: complex,W: complex,M: nat] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 7.75/5.71 => ( 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 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % norm_power_diff
% 7.75/5.71 thf(fact_5382_inrange,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % inrange
% 7.75/5.71 thf(fact_5383_arcosh__1,axiom,
% 7.75/5.71 ( ( arcosh_real @ one_one_real )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % arcosh_1
% 7.75/5.71 thf(fact_5384_heigt__uplog__rel,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 7.75/5.71 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % heigt_uplog_rel
% 7.75/5.71 thf(fact_5385_valid__insert__both__member__options__add,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % valid_insert_both_member_options_add
% 7.75/5.71 thf(fact_5386_valid__insert__both__member__options__pres,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 7.75/5.71 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % valid_insert_both_member_options_pres
% 7.75/5.71 thf(fact_5387_artanh__0,axiom,
% 7.75/5.71 ( ( artanh_real @ zero_zero_real )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % artanh_0
% 7.75/5.71 thf(fact_5388_valid__member__both__member__options,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 7.75/5.71 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % valid_member_both_member_options
% 7.75/5.71 thf(fact_5389_both__member__options__equiv__member,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 7.75/5.71 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % both_member_options_equiv_member
% 7.75/5.71 thf(fact_5390_both__member__options__def,axiom,
% 7.75/5.71 ( vEBT_V8194947554948674370ptions
% 7.75/5.71 = ( ^ [T2: vEBT_VEBT,X2: nat] :
% 7.75/5.71 ( ( vEBT_V5719532721284313246member @ T2 @ X2 )
% 7.75/5.71 | ( vEBT_VEBT_membermima @ T2 @ X2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % both_member_options_def
% 7.75/5.71 thf(fact_5391_ceiling__zero,axiom,
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 7.75/5.71 = zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_zero
% 7.75/5.71 thf(fact_5392_ceiling__zero,axiom,
% 7.75/5.71 ( ( archim7802044766580827645g_real @ zero_zero_real )
% 7.75/5.71 = zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_zero
% 7.75/5.71 thf(fact_5393_ceiling__numeral,axiom,
% 7.75/5.71 ! [V: num] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 7.75/5.71 = ( numeral_numeral_int @ V ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_numeral
% 7.75/5.71 thf(fact_5394_ceiling__numeral,axiom,
% 7.75/5.71 ! [V: num] :
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 7.75/5.71 = ( numeral_numeral_int @ V ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_numeral
% 7.75/5.71 thf(fact_5395_ceiling__one,axiom,
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_one
% 7.75/5.71 thf(fact_5396_ceiling__one,axiom,
% 7.75/5.71 ( ( archim7802044766580827645g_real @ one_one_real )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_one
% 7.75/5.71 thf(fact_5397_ceiling__le__zero,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 7.75/5.71 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le_zero
% 7.75/5.71 thf(fact_5398_ceiling__le__zero,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 7.75/5.71 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le_zero
% 7.75/5.71 thf(fact_5399_ceiling__le__numeral,axiom,
% 7.75/5.71 ! [X: real,V: num] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.71 = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le_numeral
% 7.75/5.71 thf(fact_5400_ceiling__le__numeral,axiom,
% 7.75/5.71 ! [X: rat,V: num] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.71 = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le_numeral
% 7.75/5.71 thf(fact_5401_zero__less__ceiling,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_ceiling
% 7.75/5.71 thf(fact_5402_zero__less__ceiling,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_ceiling
% 7.75/5.71 thf(fact_5403_numeral__less__ceiling,axiom,
% 7.75/5.71 ! [V: num,X: real] :
% 7.75/5.71 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_less_ceiling
% 7.75/5.71 thf(fact_5404_numeral__less__ceiling,axiom,
% 7.75/5.71 ! [V: num,X: rat] :
% 7.75/5.71 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_less_ceiling
% 7.75/5.71 thf(fact_5405_ceiling__less__one,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 7.75/5.71 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_one
% 7.75/5.71 thf(fact_5406_ceiling__less__one,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 7.75/5.71 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_one
% 7.75/5.71 thf(fact_5407_one__le__ceiling,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % one_le_ceiling
% 7.75/5.71 thf(fact_5408_one__le__ceiling,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % one_le_ceiling
% 7.75/5.71 thf(fact_5409_ceiling__add__numeral,axiom,
% 7.75/5.71 ! [X: real,V: num] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.71 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_add_numeral
% 7.75/5.71 thf(fact_5410_ceiling__add__numeral,axiom,
% 7.75/5.71 ! [X: rat,V: num] :
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.71 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_add_numeral
% 7.75/5.71 thf(fact_5411_ceiling__le__one,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 7.75/5.71 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le_one
% 7.75/5.71 thf(fact_5412_ceiling__le__one,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 7.75/5.71 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le_one
% 7.75/5.71 thf(fact_5413_one__less__ceiling,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % one_less_ceiling
% 7.75/5.71 thf(fact_5414_one__less__ceiling,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ one_one_real @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % one_less_ceiling
% 7.75/5.71 thf(fact_5415_ceiling__neg__numeral,axiom,
% 7.75/5.71 ! [V: num] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_neg_numeral
% 7.75/5.71 thf(fact_5416_ceiling__neg__numeral,axiom,
% 7.75/5.71 ! [V: num] :
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_neg_numeral
% 7.75/5.71 thf(fact_5417_ceiling__diff__numeral,axiom,
% 7.75/5.71 ! [X: real,V: num] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.71 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_diff_numeral
% 7.75/5.71 thf(fact_5418_ceiling__diff__numeral,axiom,
% 7.75/5.71 ! [X: rat,V: num] :
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.71 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_diff_numeral
% 7.75/5.71 thf(fact_5419_ceiling__add__one,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 7.75/5.71 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_add_one
% 7.75/5.71 thf(fact_5420_ceiling__add__one,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ one_one_real ) )
% 7.75/5.71 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_add_one
% 7.75/5.71 thf(fact_5421_ceiling__numeral__power,axiom,
% 7.75/5.71 ! [X: num,N: nat] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 7.75/5.71 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_numeral_power
% 7.75/5.71 thf(fact_5422_ceiling__numeral__power,axiom,
% 7.75/5.71 ! [X: num,N: nat] :
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 7.75/5.71 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_numeral_power
% 7.75/5.71 thf(fact_5423_ceiling__diff__one,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 7.75/5.71 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_diff_one
% 7.75/5.71 thf(fact_5424_ceiling__diff__one,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ one_one_real ) )
% 7.75/5.71 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_diff_one
% 7.75/5.71 thf(fact_5425_ceiling__less__zero,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 7.75/5.71 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_zero
% 7.75/5.71 thf(fact_5426_ceiling__less__zero,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 7.75/5.71 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_zero
% 7.75/5.71 thf(fact_5427_zero__le__ceiling,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_le_ceiling
% 7.75/5.71 thf(fact_5428_zero__le__ceiling,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_le_ceiling
% 7.75/5.71 thf(fact_5429_ceiling__divide__eq__div__numeral,axiom,
% 7.75/5.71 ! [A: num,B: num] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_divide_eq_div_numeral
% 7.75/5.71 thf(fact_5430_ceiling__less__numeral,axiom,
% 7.75/5.71 ! [X: real,V: num] :
% 7.75/5.71 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.71 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_numeral
% 7.75/5.71 thf(fact_5431_ceiling__less__numeral,axiom,
% 7.75/5.71 ! [X: rat,V: num] :
% 7.75/5.71 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.71 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_numeral
% 7.75/5.71 thf(fact_5432_numeral__le__ceiling,axiom,
% 7.75/5.71 ! [V: num,X: real] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_le_ceiling
% 7.75/5.71 thf(fact_5433_numeral__le__ceiling,axiom,
% 7.75/5.71 ! [V: num,X: rat] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_le_ceiling
% 7.75/5.71 thf(fact_5434_ceiling__le__neg__numeral,axiom,
% 7.75/5.71 ! [X: real,V: num] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.71 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le_neg_numeral
% 7.75/5.71 thf(fact_5435_ceiling__le__neg__numeral,axiom,
% 7.75/5.71 ! [X: rat,V: num] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.71 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le_neg_numeral
% 7.75/5.71 thf(fact_5436_neg__numeral__less__ceiling,axiom,
% 7.75/5.71 ! [V: num,X: real] :
% 7.75/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_less_ceiling
% 7.75/5.71 thf(fact_5437_neg__numeral__less__ceiling,axiom,
% 7.75/5.71 ! [V: num,X: rat] :
% 7.75/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_less_ceiling
% 7.75/5.71 thf(fact_5438_ceiling__minus__divide__eq__div__numeral,axiom,
% 7.75/5.71 ! [A: num,B: num] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_minus_divide_eq_div_numeral
% 7.75/5.71 thf(fact_5439_ceiling__less__neg__numeral,axiom,
% 7.75/5.71 ! [X: real,V: num] :
% 7.75/5.71 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.71 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_neg_numeral
% 7.75/5.71 thf(fact_5440_ceiling__less__neg__numeral,axiom,
% 7.75/5.71 ! [X: rat,V: num] :
% 7.75/5.71 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.71 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_neg_numeral
% 7.75/5.71 thf(fact_5441_neg__numeral__le__ceiling,axiom,
% 7.75/5.71 ! [V: num,X: real] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_le_ceiling
% 7.75/5.71 thf(fact_5442_neg__numeral__le__ceiling,axiom,
% 7.75/5.71 ! [V: num,X: rat] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_le_ceiling
% 7.75/5.71 thf(fact_5443_atLeastatMost__psubset__iff,axiom,
% 7.75/5.71 ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 7.75/5.71 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D2 ) )
% 7.75/5.71 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 7.75/5.71 | ( ( ord_less_eq_set_nat @ C @ A )
% 7.75/5.71 & ( ord_less_eq_set_nat @ B @ D2 )
% 7.75/5.71 & ( ( ord_less_set_nat @ C @ A )
% 7.75/5.71 | ( ord_less_set_nat @ B @ D2 ) ) ) )
% 7.75/5.71 & ( ord_less_eq_set_nat @ C @ D2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % atLeastatMost_psubset_iff
% 7.75/5.71 thf(fact_5444_atLeastatMost__psubset__iff,axiom,
% 7.75/5.71 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.75/5.71 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 7.75/5.71 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 7.75/5.71 | ( ( ord_less_eq_rat @ C @ A )
% 7.75/5.71 & ( ord_less_eq_rat @ B @ D2 )
% 7.75/5.71 & ( ( ord_less_rat @ C @ A )
% 7.75/5.71 | ( ord_less_rat @ B @ D2 ) ) ) )
% 7.75/5.71 & ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % atLeastatMost_psubset_iff
% 7.75/5.71 thf(fact_5445_atLeastatMost__psubset__iff,axiom,
% 7.75/5.71 ! [A: num,B: num,C: num,D2: num] :
% 7.75/5.71 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 7.75/5.71 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 7.75/5.71 | ( ( ord_less_eq_num @ C @ A )
% 7.75/5.71 & ( ord_less_eq_num @ B @ D2 )
% 7.75/5.71 & ( ( ord_less_num @ C @ A )
% 7.75/5.71 | ( ord_less_num @ B @ D2 ) ) ) )
% 7.75/5.71 & ( ord_less_eq_num @ C @ D2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % atLeastatMost_psubset_iff
% 7.75/5.71 thf(fact_5446_atLeastatMost__psubset__iff,axiom,
% 7.75/5.71 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.75/5.71 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 7.75/5.71 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 7.75/5.71 | ( ( ord_less_eq_nat @ C @ A )
% 7.75/5.71 & ( ord_less_eq_nat @ B @ D2 )
% 7.75/5.71 & ( ( ord_less_nat @ C @ A )
% 7.75/5.71 | ( ord_less_nat @ B @ D2 ) ) ) )
% 7.75/5.71 & ( ord_less_eq_nat @ C @ D2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % atLeastatMost_psubset_iff
% 7.75/5.71 thf(fact_5447_atLeastatMost__psubset__iff,axiom,
% 7.75/5.71 ! [A: int,B: int,C: int,D2: int] :
% 7.75/5.71 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 7.75/5.71 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 7.75/5.71 | ( ( ord_less_eq_int @ C @ A )
% 7.75/5.71 & ( ord_less_eq_int @ B @ D2 )
% 7.75/5.71 & ( ( ord_less_int @ C @ A )
% 7.75/5.71 | ( ord_less_int @ B @ D2 ) ) ) )
% 7.75/5.71 & ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % atLeastatMost_psubset_iff
% 7.75/5.71 thf(fact_5448_atLeastatMost__psubset__iff,axiom,
% 7.75/5.71 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.75/5.71 ( ( ord_le1307284697595431911nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or189985376899183464nteger @ C @ D2 ) )
% 7.75/5.71 = ( ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.71 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 7.75/5.71 & ( ord_le3102999989581377725nteger @ B @ D2 )
% 7.75/5.71 & ( ( ord_le6747313008572928689nteger @ C @ A )
% 7.75/5.71 | ( ord_le6747313008572928689nteger @ B @ D2 ) ) ) )
% 7.75/5.71 & ( ord_le3102999989581377725nteger @ C @ D2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % atLeastatMost_psubset_iff
% 7.75/5.71 thf(fact_5449_atLeastatMost__psubset__iff,axiom,
% 7.75/5.71 ! [A: real,B: real,C: real,D2: real] :
% 7.75/5.71 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D2 ) )
% 7.75/5.71 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 7.75/5.71 | ( ( ord_less_eq_real @ C @ A )
% 7.75/5.71 & ( ord_less_eq_real @ B @ D2 )
% 7.75/5.71 & ( ( ord_less_real @ C @ A )
% 7.75/5.71 | ( ord_less_real @ B @ D2 ) ) ) )
% 7.75/5.71 & ( ord_less_eq_real @ C @ D2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % atLeastatMost_psubset_iff
% 7.75/5.71 thf(fact_5450_ceiling__less__cancel,axiom,
% 7.75/5.71 ! [X: rat,Y: rat] :
% 7.75/5.71 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 7.75/5.71 => ( ord_less_rat @ X @ Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_cancel
% 7.75/5.71 thf(fact_5451_ceiling__less__cancel,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) )
% 7.75/5.71 => ( ord_less_real @ X @ Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_cancel
% 7.75/5.71 thf(fact_5452_ex__nat__less,axiom,
% 7.75/5.71 ! [N: nat,P: nat > $o] :
% 7.75/5.71 ( ( ? [M4: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ M4 @ N )
% 7.75/5.71 & ( P @ M4 ) ) )
% 7.75/5.71 = ( ? [X2: nat] :
% 7.75/5.71 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 7.75/5.71 & ( P @ X2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ex_nat_less
% 7.75/5.71 thf(fact_5453_all__nat__less,axiom,
% 7.75/5.71 ! [N: nat,P: nat > $o] :
% 7.75/5.71 ( ( ! [M4: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ M4 @ N )
% 7.75/5.71 => ( P @ M4 ) ) )
% 7.75/5.71 = ( ! [X2: nat] :
% 7.75/5.71 ( ( member_nat @ X2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 7.75/5.71 => ( P @ X2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % all_nat_less
% 7.75/5.71 thf(fact_5454_ceiling__add__le,axiom,
% 7.75/5.71 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_add_le
% 7.75/5.71 thf(fact_5455_ceiling__add__le,axiom,
% 7.75/5.71 ! [X: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_add_le
% 7.75/5.71 thf(fact_5456_mult__ceiling__le,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.71 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % mult_ceiling_le
% 7.75/5.71 thf(fact_5457_mult__ceiling__le,axiom,
% 7.75/5.71 ! [A: rat,B: rat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.71 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % mult_ceiling_le
% 7.75/5.71 thf(fact_5458_ceiling__log__nat__eq__if,axiom,
% 7.75/5.71 ! [B: nat,N: nat,K: nat] :
% 7.75/5.71 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 7.75/5.71 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 7.75/5.71 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 7.75/5.71 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 7.75/5.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_log_nat_eq_if
% 7.75/5.71 thf(fact_5459_ceiling__log2__div2,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.71 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 7.75/5.71 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_log2_div2
% 7.75/5.71 thf(fact_5460_ceiling__log__nat__eq__powr__iff,axiom,
% 7.75/5.71 ! [B: nat,K: nat,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 7.75/5.71 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.71 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 7.75/5.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 7.75/5.71 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 7.75/5.71 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_log_nat_eq_powr_iff
% 7.75/5.71 thf(fact_5461_artanh__def,axiom,
% 7.75/5.71 ( artanh_real
% 7.75/5.71 = ( ^ [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 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % artanh_def
% 7.75/5.71 thf(fact_5462_log__ceil__idem,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ one_one_real @ X )
% 7.75/5.71 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 7.75/5.71 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_ceil_idem
% 7.75/5.71 thf(fact_5463_arsinh__0,axiom,
% 7.75/5.71 ( ( arsinh_real @ zero_zero_real )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % arsinh_0
% 7.75/5.71 thf(fact_5464_is__succ__in__set__def,axiom,
% 7.75/5.71 ( vEBT_is_succ_in_set
% 7.75/5.71 = ( ^ [Xs: set_nat,X2: nat,Y6: nat] :
% 7.75/5.71 ( ( member_nat @ Y6 @ Xs )
% 7.75/5.71 & ( ord_less_nat @ X2 @ Y6 )
% 7.75/5.71 & ! [Z6: nat] :
% 7.75/5.71 ( ( member_nat @ Z6 @ Xs )
% 7.75/5.71 => ( ( ord_less_nat @ X2 @ Z6 )
% 7.75/5.71 => ( ord_less_eq_nat @ Y6 @ Z6 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % is_succ_in_set_def
% 7.75/5.71 thf(fact_5465_is__pred__in__set__def,axiom,
% 7.75/5.71 ( vEBT_is_pred_in_set
% 7.75/5.71 = ( ^ [Xs: set_nat,X2: nat,Y6: nat] :
% 7.75/5.71 ( ( member_nat @ Y6 @ Xs )
% 7.75/5.71 & ( ord_less_nat @ Y6 @ X2 )
% 7.75/5.71 & ! [Z6: nat] :
% 7.75/5.71 ( ( member_nat @ Z6 @ Xs )
% 7.75/5.71 => ( ( ord_less_nat @ Z6 @ X2 )
% 7.75/5.71 => ( ord_less_eq_nat @ Z6 @ Y6 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % is_pred_in_set_def
% 7.75/5.71 thf(fact_5466_member__bound__size__univ,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( 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 ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % member_bound_size_univ
% 7.75/5.71 thf(fact_5467_ln__less__cancel__iff,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 7.75/5.71 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_less_cancel_iff
% 7.75/5.71 thf(fact_5468_ln__inj__iff,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ( ( ln_ln_real @ X )
% 7.75/5.71 = ( ln_ln_real @ Y ) )
% 7.75/5.71 = ( X = Y ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_inj_iff
% 7.75/5.71 thf(fact_5469_of__int__ceiling__cancel,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = X )
% 7.75/5.71 = ( ? [N3: int] :
% 7.75/5.71 ( X
% 7.75/5.71 = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_ceiling_cancel
% 7.75/5.71 thf(fact_5470_of__int__eq__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ( ring_1_of_int_rat @ Z )
% 7.75/5.71 = zero_zero_rat )
% 7.75/5.71 = ( Z = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_0_iff
% 7.75/5.71 thf(fact_5471_of__int__eq__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ( ring_1_of_int_int @ Z )
% 7.75/5.71 = zero_zero_int )
% 7.75/5.71 = ( Z = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_0_iff
% 7.75/5.71 thf(fact_5472_of__int__eq__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ( ring_1_of_int_real @ Z )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 = ( Z = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_0_iff
% 7.75/5.71 thf(fact_5473_of__int__eq__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ( ring_17405671764205052669omplex @ Z )
% 7.75/5.71 = zero_zero_complex )
% 7.75/5.71 = ( Z = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_0_iff
% 7.75/5.71 thf(fact_5474_of__int__0__eq__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( zero_zero_rat
% 7.75/5.71 = ( ring_1_of_int_rat @ Z ) )
% 7.75/5.71 = ( Z = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_eq_iff
% 7.75/5.71 thf(fact_5475_of__int__0__eq__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( zero_zero_int
% 7.75/5.71 = ( ring_1_of_int_int @ Z ) )
% 7.75/5.71 = ( Z = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_eq_iff
% 7.75/5.71 thf(fact_5476_of__int__0__eq__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( zero_zero_real
% 7.75/5.71 = ( ring_1_of_int_real @ Z ) )
% 7.75/5.71 = ( Z = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_eq_iff
% 7.75/5.71 thf(fact_5477_of__int__0__eq__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( zero_zero_complex
% 7.75/5.71 = ( ring_17405671764205052669omplex @ Z ) )
% 7.75/5.71 = ( Z = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_eq_iff
% 7.75/5.71 thf(fact_5478_of__int__0,axiom,
% 7.75/5.71 ( ( ring_1_of_int_rat @ zero_zero_int )
% 7.75/5.71 = zero_zero_rat ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0
% 7.75/5.71 thf(fact_5479_of__int__0,axiom,
% 7.75/5.71 ( ( ring_1_of_int_int @ zero_zero_int )
% 7.75/5.71 = zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0
% 7.75/5.71 thf(fact_5480_of__int__0,axiom,
% 7.75/5.71 ( ( ring_1_of_int_real @ zero_zero_int )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0
% 7.75/5.71 thf(fact_5481_of__int__0,axiom,
% 7.75/5.71 ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 7.75/5.71 = zero_zero_complex ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0
% 7.75/5.71 thf(fact_5482_of__int__numeral,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 7.75/5.71 = ( numera6690914467698888265omplex @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral
% 7.75/5.71 thf(fact_5483_of__int__numeral,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 7.75/5.71 = ( numeral_numeral_real @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral
% 7.75/5.71 thf(fact_5484_of__int__numeral,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 7.75/5.71 = ( numeral_numeral_rat @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral
% 7.75/5.71 thf(fact_5485_of__int__numeral,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 7.75/5.71 = ( numeral_numeral_int @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral
% 7.75/5.71 thf(fact_5486_of__int__eq__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ( ring_17405671764205052669omplex @ Z )
% 7.75/5.71 = ( numera6690914467698888265omplex @ N ) )
% 7.75/5.71 = ( Z
% 7.75/5.71 = ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_numeral_iff
% 7.75/5.71 thf(fact_5487_of__int__eq__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ( ring_1_of_int_real @ Z )
% 7.75/5.71 = ( numeral_numeral_real @ N ) )
% 7.75/5.71 = ( Z
% 7.75/5.71 = ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_numeral_iff
% 7.75/5.71 thf(fact_5488_of__int__eq__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ( ring_1_of_int_rat @ Z )
% 7.75/5.71 = ( numeral_numeral_rat @ N ) )
% 7.75/5.71 = ( Z
% 7.75/5.71 = ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_numeral_iff
% 7.75/5.71 thf(fact_5489_of__int__eq__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ( ring_1_of_int_int @ Z )
% 7.75/5.71 = ( numeral_numeral_int @ N ) )
% 7.75/5.71 = ( Z
% 7.75/5.71 = ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_numeral_iff
% 7.75/5.71 thf(fact_5490_of__int__less__iff,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 7.75/5.71 = ( ord_less_int @ W @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_iff
% 7.75/5.71 thf(fact_5491_of__int__less__iff,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 7.75/5.71 = ( ord_less_int @ W @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_iff
% 7.75/5.71 thf(fact_5492_of__int__less__iff,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 7.75/5.71 = ( ord_less_int @ W @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_iff
% 7.75/5.71 thf(fact_5493_ln__le__cancel__iff,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 7.75/5.71 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_le_cancel_iff
% 7.75/5.71 thf(fact_5494_of__int__eq__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ( ring_1_of_int_rat @ Z )
% 7.75/5.71 = one_one_rat )
% 7.75/5.71 = ( Z = one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_1_iff
% 7.75/5.71 thf(fact_5495_of__int__eq__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ( ring_1_of_int_int @ Z )
% 7.75/5.71 = one_one_int )
% 7.75/5.71 = ( Z = one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_1_iff
% 7.75/5.71 thf(fact_5496_of__int__eq__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ( ring_1_of_int_real @ Z )
% 7.75/5.71 = one_one_real )
% 7.75/5.71 = ( Z = one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_1_iff
% 7.75/5.71 thf(fact_5497_of__int__eq__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ( ring_17405671764205052669omplex @ Z )
% 7.75/5.71 = one_one_complex )
% 7.75/5.71 = ( Z = one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_1_iff
% 7.75/5.71 thf(fact_5498_of__int__1,axiom,
% 7.75/5.71 ( ( ring_1_of_int_rat @ one_one_int )
% 7.75/5.71 = one_one_rat ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1
% 7.75/5.71 thf(fact_5499_of__int__1,axiom,
% 7.75/5.71 ( ( ring_1_of_int_int @ one_one_int )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1
% 7.75/5.71 thf(fact_5500_of__int__1,axiom,
% 7.75/5.71 ( ( ring_1_of_int_real @ one_one_int )
% 7.75/5.71 = one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1
% 7.75/5.71 thf(fact_5501_of__int__1,axiom,
% 7.75/5.71 ( ( ring_17405671764205052669omplex @ one_one_int )
% 7.75/5.71 = one_one_complex ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1
% 7.75/5.71 thf(fact_5502_of__int__add,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 7.75/5.71 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_add
% 7.75/5.71 thf(fact_5503_of__int__add,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 7.75/5.71 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_add
% 7.75/5.71 thf(fact_5504_of__int__add,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 7.75/5.71 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_add
% 7.75/5.71 thf(fact_5505_of__int__add,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 7.75/5.71 = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_add
% 7.75/5.71 thf(fact_5506_ln__less__zero__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_less_zero_iff
% 7.75/5.71 thf(fact_5507_ln__gt__zero__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_gt_zero_iff
% 7.75/5.71 thf(fact_5508_ln__eq__zero__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ( ln_ln_real @ X )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 = ( X = one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_eq_zero_iff
% 7.75/5.71 thf(fact_5509_of__int__mult,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 7.75/5.71 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_mult
% 7.75/5.71 thf(fact_5510_of__int__mult,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 7.75/5.71 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_mult
% 7.75/5.71 thf(fact_5511_of__int__mult,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ring_18347121197199848620nteger @ ( times_times_int @ W @ Z ) )
% 7.75/5.71 = ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ W ) @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_mult
% 7.75/5.71 thf(fact_5512_of__int__mult,axiom,
% 7.75/5.71 ! [W: int,Z: int] :
% 7.75/5.71 ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 7.75/5.71 = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_mult
% 7.75/5.71 thf(fact_5513_ln__one,axiom,
% 7.75/5.71 ( ( ln_ln_real @ one_one_real )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % ln_one
% 7.75/5.71 thf(fact_5514_of__int__power,axiom,
% 7.75/5.71 ! [Z: int,N: nat] :
% 7.75/5.71 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 7.75/5.71 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power
% 7.75/5.71 thf(fact_5515_of__int__power,axiom,
% 7.75/5.71 ! [Z: int,N: nat] :
% 7.75/5.71 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 7.75/5.71 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power
% 7.75/5.71 thf(fact_5516_of__int__power,axiom,
% 7.75/5.71 ! [Z: int,N: nat] :
% 7.75/5.71 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 7.75/5.71 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power
% 7.75/5.71 thf(fact_5517_of__int__power,axiom,
% 7.75/5.71 ! [Z: int,N: nat] :
% 7.75/5.71 ( ( ring_18347121197199848620nteger @ ( power_power_int @ Z @ N ) )
% 7.75/5.71 = ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ Z ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power
% 7.75/5.71 thf(fact_5518_of__int__eq__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 7.75/5.71 = ( ring_1_of_int_real @ X ) )
% 7.75/5.71 = ( ( power_power_int @ B @ W )
% 7.75/5.71 = X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5519_of__int__eq__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 7.75/5.71 = ( ring_1_of_int_int @ X ) )
% 7.75/5.71 = ( ( power_power_int @ B @ W )
% 7.75/5.71 = X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5520_of__int__eq__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 7.75/5.71 = ( ring_17405671764205052669omplex @ X ) )
% 7.75/5.71 = ( ( power_power_int @ B @ W )
% 7.75/5.71 = X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5521_of__int__eq__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W )
% 7.75/5.71 = ( ring_18347121197199848620nteger @ X ) )
% 7.75/5.71 = ( ( power_power_int @ B @ W )
% 7.75/5.71 = X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5522_of__int__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ( ring_1_of_int_real @ X )
% 7.75/5.71 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 7.75/5.71 = ( X
% 7.75/5.71 = ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5523_of__int__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ( ring_1_of_int_int @ X )
% 7.75/5.71 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 7.75/5.71 = ( X
% 7.75/5.71 = ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5524_of__int__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ( ring_17405671764205052669omplex @ X )
% 7.75/5.71 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 7.75/5.71 = ( X
% 7.75/5.71 = ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5525_of__int__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ( ring_18347121197199848620nteger @ X )
% 7.75/5.71 = ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W ) )
% 7.75/5.71 = ( X
% 7.75/5.71 = ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5526_ln__le__zero__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_le_zero_iff
% 7.75/5.71 thf(fact_5527_ln__ge__zero__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 7.75/5.71 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_ge_zero_iff
% 7.75/5.71 thf(fact_5528_ceiling__add__of__int,axiom,
% 7.75/5.71 ! [X: rat,Z: int] :
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 7.75/5.71 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_add_of_int
% 7.75/5.71 thf(fact_5529_ceiling__add__of__int,axiom,
% 7.75/5.71 ! [X: real,Z: int] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 7.75/5.71 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_add_of_int
% 7.75/5.71 thf(fact_5530_of__int__le__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_0_iff
% 7.75/5.71 thf(fact_5531_of__int__le__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 7.75/5.71 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_0_iff
% 7.75/5.71 thf(fact_5532_of__int__le__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 7.75/5.71 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_0_iff
% 7.75/5.71 thf(fact_5533_of__int__0__le__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 7.75/5.71 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_le_iff
% 7.75/5.71 thf(fact_5534_of__int__0__le__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 7.75/5.71 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_le_iff
% 7.75/5.71 thf(fact_5535_of__int__0__le__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 7.75/5.71 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_le_iff
% 7.75/5.71 thf(fact_5536_of__int__le__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_numeral_iff
% 7.75/5.71 thf(fact_5537_of__int__le__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_numeral_iff
% 7.75/5.71 thf(fact_5538_of__int__le__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_numeral_iff
% 7.75/5.71 thf(fact_5539_of__int__numeral__le__iff,axiom,
% 7.75/5.71 ! [N: num,Z: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral_le_iff
% 7.75/5.71 thf(fact_5540_of__int__numeral__le__iff,axiom,
% 7.75/5.71 ! [N: num,Z: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral_le_iff
% 7.75/5.71 thf(fact_5541_of__int__numeral__le__iff,axiom,
% 7.75/5.71 ! [N: num,Z: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral_le_iff
% 7.75/5.71 thf(fact_5542_of__int__less__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_0_iff
% 7.75/5.71 thf(fact_5543_of__int__less__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 7.75/5.71 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_0_iff
% 7.75/5.71 thf(fact_5544_of__int__less__0__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 7.75/5.71 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_0_iff
% 7.75/5.71 thf(fact_5545_of__int__0__less__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 7.75/5.71 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_less_iff
% 7.75/5.71 thf(fact_5546_of__int__0__less__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 7.75/5.71 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_less_iff
% 7.75/5.71 thf(fact_5547_of__int__0__less__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 7.75/5.71 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_0_less_iff
% 7.75/5.71 thf(fact_5548_of__int__numeral__less__iff,axiom,
% 7.75/5.71 ! [N: num,Z: int] :
% 7.75/5.71 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 7.75/5.71 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral_less_iff
% 7.75/5.71 thf(fact_5549_of__int__numeral__less__iff,axiom,
% 7.75/5.71 ! [N: num,Z: int] :
% 7.75/5.71 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 7.75/5.71 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral_less_iff
% 7.75/5.71 thf(fact_5550_of__int__numeral__less__iff,axiom,
% 7.75/5.71 ! [N: num,Z: int] :
% 7.75/5.71 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 7.75/5.71 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_numeral_less_iff
% 7.75/5.71 thf(fact_5551_of__int__less__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.71 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_numeral_iff
% 7.75/5.71 thf(fact_5552_of__int__less__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 7.75/5.71 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_numeral_iff
% 7.75/5.71 thf(fact_5553_of__int__less__numeral__iff,axiom,
% 7.75/5.71 ! [Z: int,N: num] :
% 7.75/5.71 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 7.75/5.71 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_numeral_iff
% 7.75/5.71 thf(fact_5554_of__int__le__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 7.75/5.71 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_1_iff
% 7.75/5.71 thf(fact_5555_of__int__le__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 7.75/5.71 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_1_iff
% 7.75/5.71 thf(fact_5556_of__int__le__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 7.75/5.71 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_1_iff
% 7.75/5.71 thf(fact_5557_of__int__1__le__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 7.75/5.71 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1_le_iff
% 7.75/5.71 thf(fact_5558_of__int__1__le__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 7.75/5.71 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1_le_iff
% 7.75/5.71 thf(fact_5559_of__int__1__le__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 7.75/5.71 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1_le_iff
% 7.75/5.71 thf(fact_5560_of__int__less__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 7.75/5.71 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_1_iff
% 7.75/5.71 thf(fact_5561_of__int__less__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 7.75/5.71 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_1_iff
% 7.75/5.71 thf(fact_5562_of__int__less__1__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 7.75/5.71 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_1_iff
% 7.75/5.71 thf(fact_5563_of__int__1__less__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 7.75/5.71 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1_less_iff
% 7.75/5.71 thf(fact_5564_of__int__1__less__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 7.75/5.71 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1_less_iff
% 7.75/5.71 thf(fact_5565_of__int__1__less__iff,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 7.75/5.71 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_1_less_iff
% 7.75/5.71 thf(fact_5566_numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N )
% 7.75/5.71 = ( ring_18347121197199848620nteger @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5567_numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 7.75/5.71 = ( ring_17405671764205052669omplex @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5568_numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 7.75/5.71 = ( ring_1_of_int_real @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5569_numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 7.75/5.71 = ( ring_1_of_int_rat @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5570_numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 7.75/5.71 = ( ring_1_of_int_int @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5571_of__int__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_18347121197199848620nteger @ Y )
% 7.75/5.71 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5572_of__int__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_17405671764205052669omplex @ Y )
% 7.75/5.71 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5573_of__int__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_1_of_int_real @ Y )
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5574_of__int__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_1_of_int_rat @ Y )
% 7.75/5.71 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5575_of__int__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_1_of_int_int @ Y )
% 7.75/5.71 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5576_of__int__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 7.75/5.71 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5577_of__int__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ X ) @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W ) )
% 7.75/5.71 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5578_of__int__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 7.75/5.71 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5579_of__int__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 7.75/5.71 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5580_of__int__le__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5581_of__int__le__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W ) @ ( ring_18347121197199848620nteger @ X ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5582_of__int__le__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5583_of__int__le__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5584_of__int__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ X ) @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W ) )
% 7.75/5.71 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5585_of__int__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 7.75/5.71 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5586_of__int__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 7.75/5.71 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5587_of__int__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: int,B: int,W: nat] :
% 7.75/5.71 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 7.75/5.71 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5588_of__int__less__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( ring_18347121197199848620nteger @ B ) @ W ) @ ( ring_18347121197199848620nteger @ X ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5589_of__int__less__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5590_of__int__less__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5591_of__int__less__of__int__power__cancel__iff,axiom,
% 7.75/5.71 ! [B: int,W: nat,X: int] :
% 7.75/5.71 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_of_int_power_cancel_iff
% 7.75/5.71 thf(fact_5592_numeral__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5593_numeral__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5594_numeral__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5595_numeral__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5596_of__int__le__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5597_of__int__le__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5598_of__int__le__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5599_of__int__le__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5600_numeral__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5601_numeral__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5602_numeral__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5603_numeral__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % numeral_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5604_of__int__less__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N ) )
% 7.75/5.71 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5605_of__int__less__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 7.75/5.71 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5606_of__int__less__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 7.75/5.71 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5607_of__int__less__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 7.75/5.71 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5608_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 7.75/5.71 = ( ring_1_of_int_int @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5609_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 7.75/5.71 = ( ring_1_of_int_real @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5610_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 7.75/5.71 = ( ring_18347121197199848620nteger @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5611_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 7.75/5.71 = ( ring_17405671764205052669omplex @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5612_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,Y: int] :
% 7.75/5.71 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 7.75/5.71 = ( ring_1_of_int_rat @ Y ) )
% 7.75/5.71 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 7.75/5.71 = Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_eq_of_int_cancel_iff
% 7.75/5.71 thf(fact_5613_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_1_of_int_int @ Y )
% 7.75/5.71 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5614_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_1_of_int_real @ Y )
% 7.75/5.71 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5615_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_18347121197199848620nteger @ Y )
% 7.75/5.71 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5616_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_17405671764205052669omplex @ Y )
% 7.75/5.71 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5617_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [Y: int,X: num,N: nat] :
% 7.75/5.71 ( ( ( ring_1_of_int_rat @ Y )
% 7.75/5.71 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 7.75/5.71 = ( Y
% 7.75/5.71 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_eq_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5618_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5619_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5620_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5621_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 7.75/5.71 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_le_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5622_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5623_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5624_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5625_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 7.75/5.71 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_le_of_int_cancel_iff
% 7.75/5.71 thf(fact_5626_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5627_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5628_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5629_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 7.75/5.71 ! [X: num,N: nat,A: int] :
% 7.75/5.71 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 7.75/5.71 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % neg_numeral_power_less_of_int_cancel_iff
% 7.75/5.71 thf(fact_5630_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 7.75/5.71 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5631_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 7.75/5.71 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5632_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 7.75/5.71 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5633_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 7.75/5.71 ! [A: int,X: num,N: nat] :
% 7.75/5.71 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 7.75/5.71 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_less_neg_numeral_power_cancel_iff
% 7.75/5.71 thf(fact_5634_ex__less__of__int,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ? [Z3: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z3 ) ) ).
% 7.75/5.71
% 7.75/5.71 % ex_less_of_int
% 7.75/5.71 thf(fact_5635_ex__less__of__int,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ? [Z3: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 7.75/5.71
% 7.75/5.71 % ex_less_of_int
% 7.75/5.71 thf(fact_5636_ex__of__int__less,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X ) ).
% 7.75/5.71
% 7.75/5.71 % ex_of_int_less
% 7.75/5.71 thf(fact_5637_ex__of__int__less,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X ) ).
% 7.75/5.71
% 7.75/5.71 % ex_of_int_less
% 7.75/5.71 thf(fact_5638_mult__of__int__commute,axiom,
% 7.75/5.71 ! [X: int,Y: real] :
% 7.75/5.71 ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y )
% 7.75/5.71 = ( times_times_real @ Y @ ( ring_1_of_int_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % mult_of_int_commute
% 7.75/5.71 thf(fact_5639_mult__of__int__commute,axiom,
% 7.75/5.71 ! [X: int,Y: int] :
% 7.75/5.71 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 7.75/5.71 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % mult_of_int_commute
% 7.75/5.71 thf(fact_5640_mult__of__int__commute,axiom,
% 7.75/5.71 ! [X: int,Y: code_integer] :
% 7.75/5.71 ( ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ X ) @ Y )
% 7.75/5.71 = ( times_3573771949741848930nteger @ Y @ ( ring_18347121197199848620nteger @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % mult_of_int_commute
% 7.75/5.71 thf(fact_5641_mult__of__int__commute,axiom,
% 7.75/5.71 ! [X: int,Y: complex] :
% 7.75/5.71 ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X ) @ Y )
% 7.75/5.71 = ( times_times_complex @ Y @ ( ring_17405671764205052669omplex @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % mult_of_int_commute
% 7.75/5.71 thf(fact_5642_ln__less__self,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_less_self
% 7.75/5.71 thf(fact_5643_log__def,axiom,
% 7.75/5.71 ( log
% 7.75/5.71 = ( ^ [A3: real,X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ A3 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_def
% 7.75/5.71 thf(fact_5644_ln__bound,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_bound
% 7.75/5.71 thf(fact_5645_ln__gt__zero__imp__gt__one,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_gt_zero_imp_gt_one
% 7.75/5.71 thf(fact_5646_ln__less__zero,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ X @ one_one_real )
% 7.75/5.71 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_less_zero
% 7.75/5.71 thf(fact_5647_ln__gt__zero,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ one_one_real @ X )
% 7.75/5.71 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_gt_zero
% 7.75/5.71 thf(fact_5648_ln__ge__zero,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ one_one_real @ X )
% 7.75/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_ge_zero
% 7.75/5.71 thf(fact_5649_bset_I1_J,axiom,
% 7.75/5.71 ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 7.75/5.71 ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ B3 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( P @ X3 )
% 7.75/5.71 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ B3 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( Q @ X3 )
% 7.75/5.71 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ( P @ X5 )
% 7.75/5.71 & ( Q @ X5 ) )
% 7.75/5.71 => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 7.75/5.71 & ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(1)
% 7.75/5.71 thf(fact_5650_bset_I2_J,axiom,
% 7.75/5.71 ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 7.75/5.71 ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ B3 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( P @ X3 )
% 7.75/5.71 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ B3 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( Q @ X3 )
% 7.75/5.71 => ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ( P @ X5 )
% 7.75/5.71 | ( Q @ X5 ) )
% 7.75/5.71 => ( ( P @ ( minus_minus_int @ X5 @ D4 ) )
% 7.75/5.71 | ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(2)
% 7.75/5.71 thf(fact_5651_aset_I1_J,axiom,
% 7.75/5.71 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 7.75/5.71 ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ A2 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( P @ X3 )
% 7.75/5.71 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ A2 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( Q @ X3 )
% 7.75/5.71 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ( P @ X5 )
% 7.75/5.71 & ( Q @ X5 ) )
% 7.75/5.71 => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 7.75/5.71 & ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(1)
% 7.75/5.71 thf(fact_5652_aset_I2_J,axiom,
% 7.75/5.71 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 7.75/5.71 ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ A2 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( P @ X3 )
% 7.75/5.71 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ A2 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( Q @ X3 )
% 7.75/5.71 => ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ( P @ X5 )
% 7.75/5.71 | ( Q @ X5 ) )
% 7.75/5.71 => ( ( P @ ( plus_plus_int @ X5 @ D4 ) )
% 7.75/5.71 | ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(2)
% 7.75/5.71 thf(fact_5653_ceiling__le,axiom,
% 7.75/5.71 ! [X: real,A: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) )
% 7.75/5.71 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le
% 7.75/5.71 thf(fact_5654_ceiling__le,axiom,
% 7.75/5.71 ! [X: rat,A: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) )
% 7.75/5.71 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_le
% 7.75/5.71 thf(fact_5655_less__ceiling__iff,axiom,
% 7.75/5.71 ! [Z: int,X: rat] :
% 7.75/5.71 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % less_ceiling_iff
% 7.75/5.71 thf(fact_5656_less__ceiling__iff,axiom,
% 7.75/5.71 ! [Z: int,X: real] :
% 7.75/5.71 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % less_ceiling_iff
% 7.75/5.71 thf(fact_5657_real__of__int__div4,axiom,
% 7.75/5.71 ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_of_int_div4
% 7.75/5.71 thf(fact_5658_real__of__int__div,axiom,
% 7.75/5.71 ! [D2: int,N: int] :
% 7.75/5.71 ( ( dvd_dvd_int @ D2 @ N )
% 7.75/5.71 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D2 ) )
% 7.75/5.71 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_of_int_div
% 7.75/5.71 thf(fact_5659_ln__ge__zero__imp__ge__one,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_ge_zero_imp_ge_one
% 7.75/5.71 thf(fact_5660_ln__add__one__self__le__self,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_add_one_self_le_self
% 7.75/5.71 thf(fact_5661_ln__mult,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 7.75/5.71 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_mult
% 7.75/5.71 thf(fact_5662_ln__eq__minus__one,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ( ln_ln_real @ X )
% 7.75/5.71 = ( minus_minus_real @ X @ one_one_real ) )
% 7.75/5.71 => ( X = one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_eq_minus_one
% 7.75/5.71 thf(fact_5663_ln__div,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 7.75/5.71 = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_div
% 7.75/5.71 thf(fact_5664_of__int__nonneg,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.71 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_nonneg
% 7.75/5.71 thf(fact_5665_of__int__nonneg,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_nonneg
% 7.75/5.71 thf(fact_5666_of__int__nonneg,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_nonneg
% 7.75/5.71 thf(fact_5667_of__int__pos,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ Z )
% 7.75/5.71 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_pos
% 7.75/5.71 thf(fact_5668_of__int__pos,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ Z )
% 7.75/5.71 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_pos
% 7.75/5.71 thf(fact_5669_of__int__pos,axiom,
% 7.75/5.71 ! [Z: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ Z )
% 7.75/5.71 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_pos
% 7.75/5.71 thf(fact_5670_floor__exists1,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ? [X3: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X3 ) @ X )
% 7.75/5.71 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 7.75/5.71 & ! [Y4: int] :
% 7.75/5.71 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X )
% 7.75/5.71 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 7.75/5.71 => ( Y4 = X3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % floor_exists1
% 7.75/5.71 thf(fact_5671_floor__exists1,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ? [X3: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X )
% 7.75/5.71 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 7.75/5.71 & ! [Y4: int] :
% 7.75/5.71 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X )
% 7.75/5.71 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 7.75/5.71 => ( Y4 = X3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % floor_exists1
% 7.75/5.71 thf(fact_5672_floor__exists,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ? [Z3: int] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X )
% 7.75/5.71 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % floor_exists
% 7.75/5.71 thf(fact_5673_floor__exists,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ? [Z3: int] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X )
% 7.75/5.71 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % floor_exists
% 7.75/5.71 thf(fact_5674_of__int__neg__numeral,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_neg_numeral
% 7.75/5.71 thf(fact_5675_of__int__neg__numeral,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 7.75/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_neg_numeral
% 7.75/5.71 thf(fact_5676_of__int__neg__numeral,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 7.75/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_neg_numeral
% 7.75/5.71 thf(fact_5677_of__int__neg__numeral,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 7.75/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_neg_numeral
% 7.75/5.71 thf(fact_5678_of__int__neg__numeral,axiom,
% 7.75/5.71 ! [K: num] :
% 7.75/5.71 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 7.75/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_neg_numeral
% 7.75/5.71 thf(fact_5679_of__int__ceiling__le__add__one,axiom,
% 7.75/5.71 ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_ceiling_le_add_one
% 7.75/5.71 thf(fact_5680_of__int__ceiling__le__add__one,axiom,
% 7.75/5.71 ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_ceiling_le_add_one
% 7.75/5.71 thf(fact_5681_of__int__ceiling__diff__one__le,axiom,
% 7.75/5.71 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_ceiling_diff_one_le
% 7.75/5.71 thf(fact_5682_of__int__ceiling__diff__one__le,axiom,
% 7.75/5.71 ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 7.75/5.71
% 7.75/5.71 % of_int_ceiling_diff_one_le
% 7.75/5.71 thf(fact_5683_of__nat__less__of__int__iff,axiom,
% 7.75/5.71 ! [N: nat,X: int] :
% 7.75/5.71 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 7.75/5.71 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_nat_less_of_int_iff
% 7.75/5.71 thf(fact_5684_of__nat__less__of__int__iff,axiom,
% 7.75/5.71 ! [N: nat,X: int] :
% 7.75/5.71 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 7.75/5.71 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_nat_less_of_int_iff
% 7.75/5.71 thf(fact_5685_of__nat__less__of__int__iff,axiom,
% 7.75/5.71 ! [N: nat,X: int] :
% 7.75/5.71 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 7.75/5.71 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % of_nat_less_of_int_iff
% 7.75/5.71 thf(fact_5686_aset_I10_J,axiom,
% 7.75/5.71 ! [D2: int,D4: int,A2: set_int,T: int] :
% 7.75/5.71 ( ( dvd_dvd_int @ D2 @ D4 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 7.75/5.71 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(10)
% 7.75/5.71 thf(fact_5687_aset_I9_J,axiom,
% 7.75/5.71 ! [D2: int,D4: int,A2: set_int,T: int] :
% 7.75/5.71 ( ( dvd_dvd_int @ D2 @ D4 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 7.75/5.71 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(9)
% 7.75/5.71 thf(fact_5688_bset_I10_J,axiom,
% 7.75/5.71 ! [D2: int,D4: int,B3: set_int,T: int] :
% 7.75/5.71 ( ( dvd_dvd_int @ D2 @ D4 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 7.75/5.71 => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(10)
% 7.75/5.71 thf(fact_5689_bset_I9_J,axiom,
% 7.75/5.71 ! [D2: int,D4: int,B3: set_int,T: int] :
% 7.75/5.71 ( ( dvd_dvd_int @ D2 @ D4 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T ) )
% 7.75/5.71 => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(9)
% 7.75/5.71 thf(fact_5690_int__le__real__less,axiom,
% 7.75/5.71 ( ord_less_eq_int
% 7.75/5.71 = ( ^ [N3: int,M4: int] : ( ord_less_real @ ( ring_1_of_int_real @ N3 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M4 ) @ one_one_real ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_le_real_less
% 7.75/5.71 thf(fact_5691_int__less__real__le,axiom,
% 7.75/5.71 ( ord_less_int
% 7.75/5.71 = ( ^ [N3: int,M4: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N3 ) @ one_one_real ) @ ( ring_1_of_int_real @ M4 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % int_less_real_le
% 7.75/5.71 thf(fact_5692_ceiling__divide__eq__div,axiom,
% 7.75/5.71 ! [A: int,B: int] :
% 7.75/5.71 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_divide_eq_div
% 7.75/5.71 thf(fact_5693_ceiling__divide__eq__div,axiom,
% 7.75/5.71 ! [A: int,B: int] :
% 7.75/5.71 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_divide_eq_div
% 7.75/5.71 thf(fact_5694_real__of__int__div__aux,axiom,
% 7.75/5.71 ! [X: int,D2: int] :
% 7.75/5.71 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D2 ) )
% 7.75/5.71 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D2 ) ) @ ( ring_1_of_int_real @ D2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_of_int_div_aux
% 7.75/5.71 thf(fact_5695_ln__2__less__1,axiom,
% 7.75/5.71 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 7.75/5.71
% 7.75/5.71 % ln_2_less_1
% 7.75/5.71 thf(fact_5696_ln__le__minus__one,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_le_minus_one
% 7.75/5.71 thf(fact_5697_ln__diff__le,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.71 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_diff_le
% 7.75/5.71 thf(fact_5698_ln__add__one__self__le__self2,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.75/5.71 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_add_one_self_le_self2
% 7.75/5.71 thf(fact_5699_ln__realpow,axiom,
% 7.75/5.71 ! [X: real,N: nat] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 7.75/5.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_realpow
% 7.75/5.71 thf(fact_5700_ceiling__correct,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) @ one_one_real ) @ X )
% 7.75/5.71 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_correct
% 7.75/5.71 thf(fact_5701_ceiling__correct,axiom,
% 7.75/5.71 ! [X: rat] :
% 7.75/5.71 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 7.75/5.71 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_correct
% 7.75/5.71 thf(fact_5702_ceiling__unique,axiom,
% 7.75/5.71 ! [Z: int,X: real] :
% 7.75/5.71 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) )
% 7.75/5.71 => ( ( archim7802044766580827645g_real @ X )
% 7.75/5.71 = Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_unique
% 7.75/5.71 thf(fact_5703_ceiling__unique,axiom,
% 7.75/5.71 ! [Z: int,X: rat] :
% 7.75/5.71 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 7.75/5.71 => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 7.75/5.71 => ( ( archim2889992004027027881ng_rat @ X )
% 7.75/5.71 = Z ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_unique
% 7.75/5.71 thf(fact_5704_ceiling__eq__iff,axiom,
% 7.75/5.71 ! [X: real,A: int] :
% 7.75/5.71 ( ( ( archim7802044766580827645g_real @ X )
% 7.75/5.71 = A )
% 7.75/5.71 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X )
% 7.75/5.71 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_eq_iff
% 7.75/5.71 thf(fact_5705_ceiling__eq__iff,axiom,
% 7.75/5.71 ! [X: rat,A: int] :
% 7.75/5.71 ( ( ( archim2889992004027027881ng_rat @ X )
% 7.75/5.71 = A )
% 7.75/5.71 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 7.75/5.71 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_eq_iff
% 7.75/5.71 thf(fact_5706_ceiling__split,axiom,
% 7.75/5.71 ! [P: int > $o,T: real] :
% 7.75/5.71 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 7.75/5.71 = ( ! [I2: int] :
% 7.75/5.71 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I2 ) @ one_one_real ) @ T )
% 7.75/5.71 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I2 ) ) )
% 7.75/5.71 => ( P @ I2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_split
% 7.75/5.71 thf(fact_5707_ceiling__split,axiom,
% 7.75/5.71 ! [P: int > $o,T: rat] :
% 7.75/5.71 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 7.75/5.71 = ( ! [I2: int] :
% 7.75/5.71 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) @ T )
% 7.75/5.71 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I2 ) ) )
% 7.75/5.71 => ( P @ I2 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_split
% 7.75/5.71 thf(fact_5708_ceiling__less__iff,axiom,
% 7.75/5.71 ! [X: real,Z: int] :
% 7.75/5.71 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 7.75/5.71 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_iff
% 7.75/5.71 thf(fact_5709_ceiling__less__iff,axiom,
% 7.75/5.71 ! [X: rat,Z: int] :
% 7.75/5.71 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 7.75/5.71 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_less_iff
% 7.75/5.71 thf(fact_5710_le__ceiling__iff,axiom,
% 7.75/5.71 ! [Z: int,X: rat] :
% 7.75/5.71 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 7.75/5.71 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % le_ceiling_iff
% 7.75/5.71 thf(fact_5711_le__ceiling__iff,axiom,
% 7.75/5.71 ! [Z: int,X: real] :
% 7.75/5.71 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % le_ceiling_iff
% 7.75/5.71 thf(fact_5712_bset_I3_J,axiom,
% 7.75/5.71 ! [D4: int,T: int,B3: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( X5 = T )
% 7.75/5.71 => ( ( minus_minus_int @ X5 @ D4 )
% 7.75/5.71 = T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(3)
% 7.75/5.71 thf(fact_5713_bset_I4_J,axiom,
% 7.75/5.71 ! [D4: int,T: int,B3: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ( member_int @ T @ B3 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( X5 != T )
% 7.75/5.71 => ( ( minus_minus_int @ X5 @ D4 )
% 7.75/5.71 != T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(4)
% 7.75/5.71 thf(fact_5714_bset_I5_J,axiom,
% 7.75/5.71 ! [D4: int,B3: set_int,T: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ord_less_int @ X5 @ T )
% 7.75/5.71 => ( ord_less_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(5)
% 7.75/5.71 thf(fact_5715_bset_I7_J,axiom,
% 7.75/5.71 ! [D4: int,T: int,B3: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ( member_int @ T @ B3 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ord_less_int @ T @ X5 )
% 7.75/5.71 => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(7)
% 7.75/5.71 thf(fact_5716_aset_I3_J,axiom,
% 7.75/5.71 ! [D4: int,T: int,A2: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( X5 = T )
% 7.75/5.71 => ( ( plus_plus_int @ X5 @ D4 )
% 7.75/5.71 = T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(3)
% 7.75/5.71 thf(fact_5717_aset_I4_J,axiom,
% 7.75/5.71 ! [D4: int,T: int,A2: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ( member_int @ T @ A2 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( X5 != T )
% 7.75/5.71 => ( ( plus_plus_int @ X5 @ D4 )
% 7.75/5.71 != T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(4)
% 7.75/5.71 thf(fact_5718_aset_I5_J,axiom,
% 7.75/5.71 ! [D4: int,T: int,A2: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ( member_int @ T @ A2 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ord_less_int @ X5 @ T )
% 7.75/5.71 => ( ord_less_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(5)
% 7.75/5.71 thf(fact_5719_aset_I7_J,axiom,
% 7.75/5.71 ! [D4: int,A2: set_int,T: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ord_less_int @ T @ X5 )
% 7.75/5.71 => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(7)
% 7.75/5.71 thf(fact_5720_periodic__finite__ex,axiom,
% 7.75/5.71 ! [D2: int,P: int > $o] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D2 )
% 7.75/5.71 => ( ! [X3: int,K2: int] :
% 7.75/5.71 ( ( P @ X3 )
% 7.75/5.71 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 7.75/5.71 => ( ( ? [X7: int] : ( P @ X7 ) )
% 7.75/5.71 = ( ? [X2: int] :
% 7.75/5.71 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 7.75/5.71 & ( P @ X2 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % periodic_finite_ex
% 7.75/5.71 thf(fact_5721_real__of__int__div2,axiom,
% 7.75/5.71 ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % real_of_int_div2
% 7.75/5.71 thf(fact_5722_real__of__int__div3,axiom,
% 7.75/5.71 ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % real_of_int_div3
% 7.75/5.71 thf(fact_5723_ln__one__minus__pos__upper__bound,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_real @ X @ one_one_real )
% 7.75/5.71 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_one_minus_pos_upper_bound
% 7.75/5.71 thf(fact_5724_log__eq__div__ln__mult__log,axiom,
% 7.75/5.71 ! [A: real,B: real,X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.71 => ( ( A != one_one_real )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.71 => ( ( B != one_one_real )
% 7.75/5.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( log @ A @ X )
% 7.75/5.71 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % log_eq_div_ln_mult_log
% 7.75/5.71 thf(fact_5725_ceiling__divide__upper,axiom,
% 7.75/5.71 ! [Q3: real,P4: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 7.75/5.71 => ( ord_less_eq_real @ P4 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P4 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_divide_upper
% 7.75/5.71 thf(fact_5726_ceiling__divide__upper,axiom,
% 7.75/5.71 ! [Q3: rat,P4: rat] :
% 7.75/5.71 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 7.75/5.71 => ( ord_less_eq_rat @ P4 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_divide_upper
% 7.75/5.71 thf(fact_5727_even__of__int__iff,axiom,
% 7.75/5.71 ! [K: int] :
% 7.75/5.71 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 7.75/5.71 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % even_of_int_iff
% 7.75/5.71 thf(fact_5728_bset_I6_J,axiom,
% 7.75/5.71 ! [D4: int,B3: set_int,T: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ord_less_eq_int @ X5 @ T )
% 7.75/5.71 => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(6)
% 7.75/5.71 thf(fact_5729_bset_I8_J,axiom,
% 7.75/5.71 ! [D4: int,T: int,B3: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ B3 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ord_less_eq_int @ T @ X5 )
% 7.75/5.71 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % bset(8)
% 7.75/5.71 thf(fact_5730_aset_I6_J,axiom,
% 7.75/5.71 ! [D4: int,T: int,A2: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ord_less_eq_int @ X5 @ T )
% 7.75/5.71 => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(6)
% 7.75/5.71 thf(fact_5731_aset_I8_J,axiom,
% 7.75/5.71 ! [D4: int,A2: set_int,T: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ! [X5: int] :
% 7.75/5.71 ( ! [Xa2: int] :
% 7.75/5.71 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb2: int] :
% 7.75/5.71 ( ( member_int @ Xb2 @ A2 )
% 7.75/5.71 => ( X5
% 7.75/5.71 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 7.75/5.71 => ( ( ord_less_eq_int @ T @ X5 )
% 7.75/5.71 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % aset(8)
% 7.75/5.71 thf(fact_5732_cpmi,axiom,
% 7.75/5.71 ! [D4: int,P: int > $o,P3: int > $o,B3: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ? [Z4: int] :
% 7.75/5.71 ! [X3: int] :
% 7.75/5.71 ( ( ord_less_int @ X3 @ Z4 )
% 7.75/5.71 => ( ( P @ X3 )
% 7.75/5.71 = ( P3 @ X3 ) ) )
% 7.75/5.71 => ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ B3 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( P @ X3 )
% 7.75/5.71 => ( P @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ( ! [X3: int,K2: int] :
% 7.75/5.71 ( ( P3 @ X3 )
% 7.75/5.71 = ( P3 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 7.75/5.71 => ( ( ? [X7: int] : ( P @ X7 ) )
% 7.75/5.71 = ( ? [X2: int] :
% 7.75/5.71 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 & ( P3 @ X2 ) )
% 7.75/5.71 | ? [X2: int] :
% 7.75/5.71 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 & ? [Y6: int] :
% 7.75/5.71 ( ( member_int @ Y6 @ B3 )
% 7.75/5.71 & ( P @ ( plus_plus_int @ Y6 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % cpmi
% 7.75/5.71 thf(fact_5733_cppi,axiom,
% 7.75/5.71 ! [D4: int,P: int > $o,P3: int > $o,A2: set_int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ D4 )
% 7.75/5.71 => ( ? [Z4: int] :
% 7.75/5.71 ! [X3: int] :
% 7.75/5.71 ( ( ord_less_int @ Z4 @ X3 )
% 7.75/5.71 => ( ( P @ X3 )
% 7.75/5.71 = ( P3 @ X3 ) ) )
% 7.75/5.71 => ( ! [X3: int] :
% 7.75/5.71 ( ! [Xa: int] :
% 7.75/5.71 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 => ! [Xb: int] :
% 7.75/5.71 ( ( member_int @ Xb @ A2 )
% 7.75/5.71 => ( X3
% 7.75/5.71 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 7.75/5.71 => ( ( P @ X3 )
% 7.75/5.71 => ( P @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 7.75/5.71 => ( ! [X3: int,K2: int] :
% 7.75/5.71 ( ( P3 @ X3 )
% 7.75/5.71 = ( P3 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 7.75/5.71 => ( ( ? [X7: int] : ( P @ X7 ) )
% 7.75/5.71 = ( ? [X2: int] :
% 7.75/5.71 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 & ( P3 @ X2 ) )
% 7.75/5.71 | ? [X2: int] :
% 7.75/5.71 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 7.75/5.71 & ? [Y6: int] :
% 7.75/5.71 ( ( member_int @ Y6 @ A2 )
% 7.75/5.71 & ( P @ ( minus_minus_int @ Y6 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % cppi
% 7.75/5.71 thf(fact_5734_ceiling__divide__lower,axiom,
% 7.75/5.71 ! [Q3: real,P4: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 7.75/5.71 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P4 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P4 ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_divide_lower
% 7.75/5.71 thf(fact_5735_ceiling__divide__lower,axiom,
% 7.75/5.71 ! [Q3: rat,P4: rat] :
% 7.75/5.71 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 7.75/5.71 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P4 ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_divide_lower
% 7.75/5.71 thf(fact_5736_ceiling__eq,axiom,
% 7.75/5.71 ! [N: int,X: real] :
% 7.75/5.71 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 7.75/5.71 => ( ( archim7802044766580827645g_real @ X )
% 7.75/5.71 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_eq
% 7.75/5.71 thf(fact_5737_ceiling__eq,axiom,
% 7.75/5.71 ! [N: int,X: rat] :
% 7.75/5.71 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X )
% 7.75/5.71 => ( ( ord_less_eq_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 7.75/5.71 => ( ( archim2889992004027027881ng_rat @ X )
% 7.75/5.71 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ceiling_eq
% 7.75/5.71 thf(fact_5738_ln__one__plus__pos__lower__bound,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.75/5.71 => ( 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 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_one_plus_pos_lower_bound
% 7.75/5.71 thf(fact_5739_member__bound__height,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( 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 ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % member_bound_height
% 7.75/5.71 thf(fact_5740_ln__one__minus__pos__lower__bound,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.71 => ( 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 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % ln_one_minus_pos_lower_bound
% 7.75/5.71 thf(fact_5741_psubsetI,axiom,
% 7.75/5.71 ! [A2: set_nat,B3: set_nat] :
% 7.75/5.71 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 7.75/5.71 => ( ( A2 != B3 )
% 7.75/5.71 => ( ord_less_set_nat @ A2 @ B3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubsetI
% 7.75/5.71 thf(fact_5742_succ__bound__size__univ,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % succ_bound_size_univ
% 7.75/5.71 thf(fact_5743_insert__bound__size__univ,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % insert_bound_size_univ
% 7.75/5.71 thf(fact_5744_pred__bound__size__univ,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pred_bound_size_univ
% 7.75/5.71 thf(fact_5745_succ__bound__height,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % succ_bound_height
% 7.75/5.71 thf(fact_5746_pred__bound__height,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pred_bound_height
% 7.75/5.71 thf(fact_5747_psubsetD,axiom,
% 7.75/5.71 ! [A2: set_nat,B3: set_nat,C: nat] :
% 7.75/5.71 ( ( ord_less_set_nat @ A2 @ B3 )
% 7.75/5.71 => ( ( member_nat @ C @ A2 )
% 7.75/5.71 => ( member_nat @ C @ B3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubsetD
% 7.75/5.71 thf(fact_5748_psubsetD,axiom,
% 7.75/5.71 ! [A2: set_real,B3: set_real,C: real] :
% 7.75/5.71 ( ( ord_less_set_real @ A2 @ B3 )
% 7.75/5.71 => ( ( member_real @ C @ A2 )
% 7.75/5.71 => ( member_real @ C @ B3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubsetD
% 7.75/5.71 thf(fact_5749_psubsetD,axiom,
% 7.75/5.71 ! [A2: set_int,B3: set_int,C: int] :
% 7.75/5.71 ( ( ord_less_set_int @ A2 @ B3 )
% 7.75/5.71 => ( ( member_int @ C @ A2 )
% 7.75/5.71 => ( member_int @ C @ B3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubsetD
% 7.75/5.71 thf(fact_5750_psubsetD,axiom,
% 7.75/5.71 ! [A2: set_VEBT_VEBT,B3: set_VEBT_VEBT,C: vEBT_VEBT] :
% 7.75/5.71 ( ( ord_le3480810397992357184T_VEBT @ A2 @ B3 )
% 7.75/5.71 => ( ( member_VEBT_VEBT @ C @ A2 )
% 7.75/5.71 => ( member_VEBT_VEBT @ C @ B3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubsetD
% 7.75/5.71 thf(fact_5751_psubsetD,axiom,
% 7.75/5.71 ! [A2: set_complex,B3: set_complex,C: complex] :
% 7.75/5.71 ( ( ord_less_set_complex @ A2 @ B3 )
% 7.75/5.71 => ( ( member_complex @ C @ A2 )
% 7.75/5.71 => ( member_complex @ C @ B3 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubsetD
% 7.75/5.71 thf(fact_5752_psubset__imp__ex__mem,axiom,
% 7.75/5.71 ! [A2: set_real,B3: set_real] :
% 7.75/5.71 ( ( ord_less_set_real @ A2 @ B3 )
% 7.75/5.71 => ? [B2: real] : ( member_real @ B2 @ ( minus_minus_set_real @ B3 @ A2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubset_imp_ex_mem
% 7.75/5.71 thf(fact_5753_psubset__imp__ex__mem,axiom,
% 7.75/5.71 ! [A2: set_int,B3: set_int] :
% 7.75/5.71 ( ( ord_less_set_int @ A2 @ B3 )
% 7.75/5.71 => ? [B2: int] : ( member_int @ B2 @ ( minus_minus_set_int @ B3 @ A2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubset_imp_ex_mem
% 7.75/5.71 thf(fact_5754_psubset__imp__ex__mem,axiom,
% 7.75/5.71 ! [A2: set_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 7.75/5.71 ( ( ord_le3480810397992357184T_VEBT @ A2 @ B3 )
% 7.75/5.71 => ? [B2: vEBT_VEBT] : ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ B3 @ A2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubset_imp_ex_mem
% 7.75/5.71 thf(fact_5755_psubset__imp__ex__mem,axiom,
% 7.75/5.71 ! [A2: set_complex,B3: set_complex] :
% 7.75/5.71 ( ( ord_less_set_complex @ A2 @ B3 )
% 7.75/5.71 => ? [B2: complex] : ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B3 @ A2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubset_imp_ex_mem
% 7.75/5.71 thf(fact_5756_psubset__imp__ex__mem,axiom,
% 7.75/5.71 ! [A2: set_nat,B3: set_nat] :
% 7.75/5.71 ( ( ord_less_set_nat @ A2 @ B3 )
% 7.75/5.71 => ? [B2: nat] : ( member_nat @ B2 @ ( minus_minus_set_nat @ B3 @ A2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubset_imp_ex_mem
% 7.75/5.71 thf(fact_5757_psubsetE,axiom,
% 7.75/5.71 ! [A2: set_nat,B3: set_nat] :
% 7.75/5.71 ( ( ord_less_set_nat @ A2 @ B3 )
% 7.75/5.71 => ~ ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 7.75/5.71 => ( ord_less_eq_set_nat @ B3 @ A2 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubsetE
% 7.75/5.71 thf(fact_5758_psubset__eq,axiom,
% 7.75/5.71 ( ord_less_set_nat
% 7.75/5.71 = ( ^ [A6: set_nat,B7: set_nat] :
% 7.75/5.71 ( ( ord_less_eq_set_nat @ A6 @ B7 )
% 7.75/5.71 & ( A6 != B7 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubset_eq
% 7.75/5.71 thf(fact_5759_psubset__imp__subset,axiom,
% 7.75/5.71 ! [A2: set_nat,B3: set_nat] :
% 7.75/5.71 ( ( ord_less_set_nat @ A2 @ B3 )
% 7.75/5.71 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubset_imp_subset
% 7.75/5.71 thf(fact_5760_psubset__subset__trans,axiom,
% 7.75/5.71 ! [A2: set_nat,B3: set_nat,C5: set_nat] :
% 7.75/5.71 ( ( ord_less_set_nat @ A2 @ B3 )
% 7.75/5.71 => ( ( ord_less_eq_set_nat @ B3 @ C5 )
% 7.75/5.71 => ( ord_less_set_nat @ A2 @ C5 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % psubset_subset_trans
% 7.75/5.71 thf(fact_5761_subset__not__subset__eq,axiom,
% 7.75/5.71 ( ord_less_set_nat
% 7.75/5.71 = ( ^ [A6: set_nat,B7: set_nat] :
% 7.75/5.71 ( ( ord_less_eq_set_nat @ A6 @ B7 )
% 7.75/5.71 & ~ ( ord_less_eq_set_nat @ B7 @ A6 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % subset_not_subset_eq
% 7.75/5.71 thf(fact_5762_subset__psubset__trans,axiom,
% 7.75/5.71 ! [A2: set_nat,B3: set_nat,C5: set_nat] :
% 7.75/5.71 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 7.75/5.71 => ( ( ord_less_set_nat @ B3 @ C5 )
% 7.75/5.71 => ( ord_less_set_nat @ A2 @ C5 ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % subset_psubset_trans
% 7.75/5.71 thf(fact_5763_subset__iff__psubset__eq,axiom,
% 7.75/5.71 ( ord_less_eq_set_nat
% 7.75/5.71 = ( ^ [A6: set_nat,B7: set_nat] :
% 7.75/5.71 ( ( ord_less_set_nat @ A6 @ B7 )
% 7.75/5.71 | ( A6 = B7 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % subset_iff_psubset_eq
% 7.75/5.71 thf(fact_5764_insersimp,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,Y: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 7.75/5.71 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % insersimp
% 7.75/5.71 thf(fact_5765_insert__bound__height,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % insert_bound_height
% 7.75/5.71 thf(fact_5766_succ__bound__size__univ_H,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % succ_bound_size_univ'
% 7.75/5.71 thf(fact_5767_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.75/5.71 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.75/5.71 => ( 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 ) ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 7.75/5.71 thf(fact_5768_round__unique,axiom,
% 7.75/5.71 ! [X: real,Y: int] :
% 7.75/5.71 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 7.75/5.71 => ( ( 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 ) ) ) ) )
% 7.75/5.71 => ( ( archim8280529875227126926d_real @ X )
% 7.75/5.71 = Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % round_unique
% 7.75/5.71 thf(fact_5769_round__unique,axiom,
% 7.75/5.71 ! [X: rat,Y: int] :
% 7.75/5.71 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 7.75/5.71 => ( ( 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 ) ) ) ) )
% 7.75/5.71 => ( ( archim7778729529865785530nd_rat @ X )
% 7.75/5.71 = Y ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % round_unique
% 7.75/5.71 thf(fact_5770_pred__bound__size__univ_H,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( ( U
% 7.75/5.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pred_bound_size_univ'
% 7.75/5.71 thf(fact_5771_tanh__ln__real,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.71 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 7.75/5.71 = ( 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 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % tanh_ln_real
% 7.75/5.71 thf(fact_5772_obtain__set__pred,axiom,
% 7.75/5.71 ! [Z: nat,X: nat,A2: set_nat] :
% 7.75/5.71 ( ( ord_less_nat @ Z @ X )
% 7.75/5.71 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 7.75/5.71 => ( ( finite_finite_nat @ A2 )
% 7.75/5.71 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % obtain_set_pred
% 7.75/5.71 thf(fact_5773_set__vebt__finite,axiom,
% 7.75/5.71 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.71 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.71 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % set_vebt_finite
% 7.75/5.71 thf(fact_5774_succ__none__empty,axiom,
% 7.75/5.71 ! [Xs2: set_nat,A: nat] :
% 7.75/5.71 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_1 )
% 7.75/5.71 => ( ( finite_finite_nat @ Xs2 )
% 7.75/5.71 => ~ ? [X5: nat] :
% 7.75/5.71 ( ( member_nat @ X5 @ Xs2 )
% 7.75/5.71 & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % succ_none_empty
% 7.75/5.71 thf(fact_5775_pred__none__empty,axiom,
% 7.75/5.71 ! [Xs2: set_nat,A: nat] :
% 7.75/5.71 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_1 )
% 7.75/5.71 => ( ( finite_finite_nat @ Xs2 )
% 7.75/5.71 => ~ ? [X5: nat] :
% 7.75/5.71 ( ( member_nat @ X5 @ Xs2 )
% 7.75/5.71 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % pred_none_empty
% 7.75/5.71 thf(fact_5776_abs__abs,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 7.75/5.71 = ( abs_abs_real @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_abs
% 7.75/5.71 thf(fact_5777_abs__abs,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 7.75/5.71 = ( abs_abs_int @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_abs
% 7.75/5.71 thf(fact_5778_abs__abs,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 7.75/5.71 = ( abs_abs_Code_integer @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_abs
% 7.75/5.71 thf(fact_5779_abs__abs,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 7.75/5.71 = ( abs_abs_rat @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_abs
% 7.75/5.71 thf(fact_5780_abs__idempotent,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 7.75/5.71 = ( abs_abs_real @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_idempotent
% 7.75/5.71 thf(fact_5781_abs__idempotent,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 7.75/5.71 = ( abs_abs_int @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_idempotent
% 7.75/5.71 thf(fact_5782_abs__idempotent,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 7.75/5.71 = ( abs_abs_Code_integer @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_idempotent
% 7.75/5.71 thf(fact_5783_abs__idempotent,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 7.75/5.71 = ( abs_abs_rat @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_idempotent
% 7.75/5.71 thf(fact_5784_obtain__set__succ,axiom,
% 7.75/5.71 ! [X: nat,Z: nat,A2: set_nat,B3: set_nat] :
% 7.75/5.71 ( ( ord_less_nat @ X @ Z )
% 7.75/5.71 => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 7.75/5.71 => ( ( finite_finite_nat @ B3 )
% 7.75/5.71 => ( ( A2 = B3 )
% 7.75/5.71 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_1 ) ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % obtain_set_succ
% 7.75/5.71 thf(fact_5785_abs__zero,axiom,
% 7.75/5.71 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 7.75/5.71 = zero_z3403309356797280102nteger ) ).
% 7.75/5.71
% 7.75/5.71 % abs_zero
% 7.75/5.71 thf(fact_5786_abs__zero,axiom,
% 7.75/5.71 ( ( abs_abs_real @ zero_zero_real )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % abs_zero
% 7.75/5.71 thf(fact_5787_abs__zero,axiom,
% 7.75/5.71 ( ( abs_abs_rat @ zero_zero_rat )
% 7.75/5.71 = zero_zero_rat ) ).
% 7.75/5.71
% 7.75/5.71 % abs_zero
% 7.75/5.71 thf(fact_5788_abs__zero,axiom,
% 7.75/5.71 ( ( abs_abs_int @ zero_zero_int )
% 7.75/5.71 = zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % abs_zero
% 7.75/5.71 thf(fact_5789_abs__eq__0,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( ( abs_abs_Code_integer @ A )
% 7.75/5.71 = zero_z3403309356797280102nteger )
% 7.75/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_0
% 7.75/5.71 thf(fact_5790_abs__eq__0,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( ( abs_abs_real @ A )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 = ( A = zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_0
% 7.75/5.71 thf(fact_5791_abs__eq__0,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( ( abs_abs_rat @ A )
% 7.75/5.71 = zero_zero_rat )
% 7.75/5.71 = ( A = zero_zero_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_0
% 7.75/5.71 thf(fact_5792_abs__eq__0,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( ( abs_abs_int @ A )
% 7.75/5.71 = zero_zero_int )
% 7.75/5.71 = ( A = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_0
% 7.75/5.71 thf(fact_5793_abs__0__eq,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( zero_z3403309356797280102nteger
% 7.75/5.71 = ( abs_abs_Code_integer @ A ) )
% 7.75/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_0_eq
% 7.75/5.71 thf(fact_5794_abs__0__eq,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( zero_zero_real
% 7.75/5.71 = ( abs_abs_real @ A ) )
% 7.75/5.71 = ( A = zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_0_eq
% 7.75/5.71 thf(fact_5795_abs__0__eq,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( zero_zero_rat
% 7.75/5.71 = ( abs_abs_rat @ A ) )
% 7.75/5.71 = ( A = zero_zero_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_0_eq
% 7.75/5.71 thf(fact_5796_abs__0__eq,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( zero_zero_int
% 7.75/5.71 = ( abs_abs_int @ A ) )
% 7.75/5.71 = ( A = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_0_eq
% 7.75/5.71 thf(fact_5797_abs__0,axiom,
% 7.75/5.71 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 7.75/5.71 = zero_z3403309356797280102nteger ) ).
% 7.75/5.71
% 7.75/5.71 % abs_0
% 7.75/5.71 thf(fact_5798_abs__0,axiom,
% 7.75/5.71 ( ( abs_abs_complex @ zero_zero_complex )
% 7.75/5.71 = zero_zero_complex ) ).
% 7.75/5.71
% 7.75/5.71 % abs_0
% 7.75/5.71 thf(fact_5799_abs__0,axiom,
% 7.75/5.71 ( ( abs_abs_real @ zero_zero_real )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % abs_0
% 7.75/5.71 thf(fact_5800_abs__0,axiom,
% 7.75/5.71 ( ( abs_abs_rat @ zero_zero_rat )
% 7.75/5.71 = zero_zero_rat ) ).
% 7.75/5.71
% 7.75/5.71 % abs_0
% 7.75/5.71 thf(fact_5801_abs__0,axiom,
% 7.75/5.71 ( ( abs_abs_int @ zero_zero_int )
% 7.75/5.71 = zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % abs_0
% 7.75/5.71 thf(fact_5802_abs__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 7.75/5.71 = ( numera6620942414471956472nteger @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_numeral
% 7.75/5.71 thf(fact_5803_abs__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 7.75/5.71 = ( numeral_numeral_real @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_numeral
% 7.75/5.71 thf(fact_5804_abs__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 7.75/5.71 = ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_numeral
% 7.75/5.71 thf(fact_5805_abs__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 7.75/5.71 = ( numeral_numeral_int @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_numeral
% 7.75/5.71 thf(fact_5806_abs__add__abs,axiom,
% 7.75/5.71 ! [A: code_integer,B: code_integer] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 7.75/5.71 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_add_abs
% 7.75/5.71 thf(fact_5807_abs__add__abs,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 7.75/5.71 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_add_abs
% 7.75/5.71 thf(fact_5808_abs__add__abs,axiom,
% 7.75/5.71 ! [A: rat,B: rat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 7.75/5.71 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_add_abs
% 7.75/5.71 thf(fact_5809_abs__add__abs,axiom,
% 7.75/5.71 ! [A: int,B: int] :
% 7.75/5.71 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 7.75/5.71 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_add_abs
% 7.75/5.71 thf(fact_5810_abs__1,axiom,
% 7.75/5.71 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 7.75/5.71 = one_one_Code_integer ) ).
% 7.75/5.71
% 7.75/5.71 % abs_1
% 7.75/5.71 thf(fact_5811_abs__1,axiom,
% 7.75/5.71 ( ( abs_abs_real @ one_one_real )
% 7.75/5.71 = one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % abs_1
% 7.75/5.71 thf(fact_5812_abs__1,axiom,
% 7.75/5.71 ( ( abs_abs_rat @ one_one_rat )
% 7.75/5.71 = one_one_rat ) ).
% 7.75/5.71
% 7.75/5.71 % abs_1
% 7.75/5.71 thf(fact_5813_abs__1,axiom,
% 7.75/5.71 ( ( abs_abs_int @ one_one_int )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % abs_1
% 7.75/5.71 thf(fact_5814_abs__mult__self__eq,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 7.75/5.71 = ( times_times_rat @ A @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_mult_self_eq
% 7.75/5.71 thf(fact_5815_abs__mult__self__eq,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 7.75/5.71 = ( times_times_real @ A @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_mult_self_eq
% 7.75/5.71 thf(fact_5816_abs__mult__self__eq,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 7.75/5.71 = ( times_times_int @ A @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_mult_self_eq
% 7.75/5.71 thf(fact_5817_abs__mult__self__eq,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 7.75/5.71 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_mult_self_eq
% 7.75/5.71 thf(fact_5818_abs__divide,axiom,
% 7.75/5.71 ! [A: complex,B: complex] :
% 7.75/5.71 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 7.75/5.71 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_divide
% 7.75/5.71 thf(fact_5819_abs__divide,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.71 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_divide
% 7.75/5.71 thf(fact_5820_abs__divide,axiom,
% 7.75/5.71 ! [A: rat,B: rat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 7.75/5.71 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_divide
% 7.75/5.71 thf(fact_5821_abs__minus,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 7.75/5.71 = ( abs_abs_int @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus
% 7.75/5.71 thf(fact_5822_abs__minus,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 7.75/5.71 = ( abs_abs_real @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus
% 7.75/5.71 thf(fact_5823_abs__minus,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.71 = ( abs_abs_Code_integer @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus
% 7.75/5.71 thf(fact_5824_abs__minus,axiom,
% 7.75/5.71 ! [A: complex] :
% 7.75/5.71 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 7.75/5.71 = ( abs_abs_complex @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus
% 7.75/5.71 thf(fact_5825_abs__minus,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 7.75/5.71 = ( abs_abs_rat @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus
% 7.75/5.71 thf(fact_5826_abs__minus__cancel,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 7.75/5.71 = ( abs_abs_int @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus_cancel
% 7.75/5.71 thf(fact_5827_abs__minus__cancel,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 7.75/5.71 = ( abs_abs_real @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus_cancel
% 7.75/5.71 thf(fact_5828_abs__minus__cancel,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.71 = ( abs_abs_Code_integer @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus_cancel
% 7.75/5.71 thf(fact_5829_abs__minus__cancel,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 7.75/5.71 = ( abs_abs_rat @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus_cancel
% 7.75/5.71 thf(fact_5830_dvd__abs__iff,axiom,
% 7.75/5.71 ! [M: real,K: real] :
% 7.75/5.71 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 7.75/5.71 = ( dvd_dvd_real @ M @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % dvd_abs_iff
% 7.75/5.71 thf(fact_5831_dvd__abs__iff,axiom,
% 7.75/5.71 ! [M: int,K: int] :
% 7.75/5.71 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 7.75/5.71 = ( dvd_dvd_int @ M @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % dvd_abs_iff
% 7.75/5.71 thf(fact_5832_dvd__abs__iff,axiom,
% 7.75/5.71 ! [M: code_integer,K: code_integer] :
% 7.75/5.71 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 7.75/5.71 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % dvd_abs_iff
% 7.75/5.71 thf(fact_5833_dvd__abs__iff,axiom,
% 7.75/5.71 ! [M: rat,K: rat] :
% 7.75/5.71 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 7.75/5.71 = ( dvd_dvd_rat @ M @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % dvd_abs_iff
% 7.75/5.71 thf(fact_5834_abs__dvd__iff,axiom,
% 7.75/5.71 ! [M: real,K: real] :
% 7.75/5.71 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 7.75/5.71 = ( dvd_dvd_real @ M @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_dvd_iff
% 7.75/5.71 thf(fact_5835_abs__dvd__iff,axiom,
% 7.75/5.71 ! [M: int,K: int] :
% 7.75/5.71 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 7.75/5.71 = ( dvd_dvd_int @ M @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_dvd_iff
% 7.75/5.71 thf(fact_5836_abs__dvd__iff,axiom,
% 7.75/5.71 ! [M: code_integer,K: code_integer] :
% 7.75/5.71 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 7.75/5.71 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_dvd_iff
% 7.75/5.71 thf(fact_5837_abs__dvd__iff,axiom,
% 7.75/5.71 ! [M: rat,K: rat] :
% 7.75/5.71 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 7.75/5.71 = ( dvd_dvd_rat @ M @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_dvd_iff
% 7.75/5.71 thf(fact_5838_abs__of__nat,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 7.75/5.71 = ( semiri4939895301339042750nteger @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nat
% 7.75/5.71 thf(fact_5839_abs__of__nat,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 7.75/5.71 = ( semiri681578069525770553at_rat @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nat
% 7.75/5.71 thf(fact_5840_abs__of__nat,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.71 = ( semiri5074537144036343181t_real @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nat
% 7.75/5.71 thf(fact_5841_abs__of__nat,axiom,
% 7.75/5.71 ! [N: nat] :
% 7.75/5.71 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.71 = ( semiri1314217659103216013at_int @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nat
% 7.75/5.71 thf(fact_5842_abs__bool__eq,axiom,
% 7.75/5.71 ! [P: $o] :
% 7.75/5.71 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 7.75/5.71 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_bool_eq
% 7.75/5.71 thf(fact_5843_abs__bool__eq,axiom,
% 7.75/5.71 ! [P: $o] :
% 7.75/5.71 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 7.75/5.71 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_bool_eq
% 7.75/5.71 thf(fact_5844_abs__bool__eq,axiom,
% 7.75/5.71 ! [P: $o] :
% 7.75/5.71 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 7.75/5.71 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_bool_eq
% 7.75/5.71 thf(fact_5845_abs__bool__eq,axiom,
% 7.75/5.71 ! [P: $o] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 7.75/5.71 = ( zero_n356916108424825756nteger @ P ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_bool_eq
% 7.75/5.71 thf(fact_5846_tanh__0,axiom,
% 7.75/5.71 ( ( tanh_complex @ zero_zero_complex )
% 7.75/5.71 = zero_zero_complex ) ).
% 7.75/5.71
% 7.75/5.71 % tanh_0
% 7.75/5.71 thf(fact_5847_tanh__0,axiom,
% 7.75/5.71 ( ( tanh_real @ zero_zero_real )
% 7.75/5.71 = zero_zero_real ) ).
% 7.75/5.71
% 7.75/5.71 % tanh_0
% 7.75/5.71 thf(fact_5848_tanh__real__zero__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ( tanh_real @ X )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 = ( X = zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % tanh_real_zero_iff
% 7.75/5.71 thf(fact_5849_tanh__real__less__iff,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ord_less_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 7.75/5.71 = ( ord_less_real @ X @ Y ) ) ).
% 7.75/5.71
% 7.75/5.71 % tanh_real_less_iff
% 7.75/5.71 thf(fact_5850_abs__of__nonneg,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.71 => ( ( abs_abs_Code_integer @ A )
% 7.75/5.71 = A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nonneg
% 7.75/5.71 thf(fact_5851_abs__of__nonneg,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.71 => ( ( abs_abs_real @ A )
% 7.75/5.71 = A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nonneg
% 7.75/5.71 thf(fact_5852_abs__of__nonneg,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.71 => ( ( abs_abs_rat @ A )
% 7.75/5.71 = A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nonneg
% 7.75/5.71 thf(fact_5853_abs__of__nonneg,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.71 => ( ( abs_abs_int @ A )
% 7.75/5.71 = A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nonneg
% 7.75/5.71 thf(fact_5854_abs__le__self__iff,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 7.75/5.71 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_self_iff
% 7.75/5.71 thf(fact_5855_abs__le__self__iff,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 7.75/5.71 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_self_iff
% 7.75/5.71 thf(fact_5856_abs__le__self__iff,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 7.75/5.71 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_self_iff
% 7.75/5.71 thf(fact_5857_abs__le__self__iff,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 7.75/5.71 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_self_iff
% 7.75/5.71 thf(fact_5858_abs__le__zero__iff,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 7.75/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_zero_iff
% 7.75/5.71 thf(fact_5859_abs__le__zero__iff,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 7.75/5.71 = ( A = zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_zero_iff
% 7.75/5.71 thf(fact_5860_abs__le__zero__iff,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 7.75/5.71 = ( A = zero_zero_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_zero_iff
% 7.75/5.71 thf(fact_5861_abs__le__zero__iff,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 7.75/5.71 = ( A = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_zero_iff
% 7.75/5.71 thf(fact_5862_zero__less__abs__iff,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 7.75/5.71 = ( A != zero_z3403309356797280102nteger ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_abs_iff
% 7.75/5.71 thf(fact_5863_zero__less__abs__iff,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 7.75/5.71 = ( A != zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_abs_iff
% 7.75/5.71 thf(fact_5864_zero__less__abs__iff,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 7.75/5.71 = ( A != zero_zero_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_abs_iff
% 7.75/5.71 thf(fact_5865_zero__less__abs__iff,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 7.75/5.71 = ( A != zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_abs_iff
% 7.75/5.71 thf(fact_5866_abs__neg__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.71 = ( numeral_numeral_int @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_neg_numeral
% 7.75/5.71 thf(fact_5867_abs__neg__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.71 = ( numeral_numeral_real @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_neg_numeral
% 7.75/5.71 thf(fact_5868_abs__neg__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.71 = ( numera6620942414471956472nteger @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_neg_numeral
% 7.75/5.71 thf(fact_5869_abs__neg__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.71 = ( numeral_numeral_rat @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_neg_numeral
% 7.75/5.71 thf(fact_5870_abs__neg__one,axiom,
% 7.75/5.71 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % abs_neg_one
% 7.75/5.71 thf(fact_5871_abs__neg__one,axiom,
% 7.75/5.71 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.71 = one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % abs_neg_one
% 7.75/5.71 thf(fact_5872_abs__neg__one,axiom,
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.71 = one_one_Code_integer ) ).
% 7.75/5.71
% 7.75/5.71 % abs_neg_one
% 7.75/5.71 thf(fact_5873_abs__neg__one,axiom,
% 7.75/5.71 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.71 = one_one_rat ) ).
% 7.75/5.71
% 7.75/5.71 % abs_neg_one
% 7.75/5.71 thf(fact_5874_infinite__Icc__iff,axiom,
% 7.75/5.71 ! [A: rat,B: rat] :
% 7.75/5.71 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 7.75/5.71 = ( ord_less_rat @ A @ B ) ) ).
% 7.75/5.71
% 7.75/5.71 % infinite_Icc_iff
% 7.75/5.71 thf(fact_5875_infinite__Icc__iff,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 7.75/5.71 = ( ord_less_real @ A @ B ) ) ).
% 7.75/5.71
% 7.75/5.71 % infinite_Icc_iff
% 7.75/5.71 thf(fact_5876_abs__power__minus,axiom,
% 7.75/5.71 ! [A: int,N: nat] :
% 7.75/5.71 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 7.75/5.71 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_power_minus
% 7.75/5.71 thf(fact_5877_abs__power__minus,axiom,
% 7.75/5.71 ! [A: real,N: nat] :
% 7.75/5.71 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 7.75/5.71 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_power_minus
% 7.75/5.71 thf(fact_5878_abs__power__minus,axiom,
% 7.75/5.71 ! [A: code_integer,N: nat] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 7.75/5.71 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_power_minus
% 7.75/5.71 thf(fact_5879_abs__power__minus,axiom,
% 7.75/5.71 ! [A: rat,N: nat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 7.75/5.71 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_power_minus
% 7.75/5.71 thf(fact_5880_round__0,axiom,
% 7.75/5.71 ( ( archim8280529875227126926d_real @ zero_zero_real )
% 7.75/5.71 = zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % round_0
% 7.75/5.71 thf(fact_5881_round__0,axiom,
% 7.75/5.71 ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 7.75/5.71 = zero_zero_int ) ).
% 7.75/5.71
% 7.75/5.71 % round_0
% 7.75/5.71 thf(fact_5882_round__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 7.75/5.71 = ( numeral_numeral_int @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % round_numeral
% 7.75/5.71 thf(fact_5883_round__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 7.75/5.71 = ( numeral_numeral_int @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % round_numeral
% 7.75/5.71 thf(fact_5884_tanh__real__pos__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 7.75/5.71 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % tanh_real_pos_iff
% 7.75/5.71 thf(fact_5885_tanh__real__neg__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % tanh_real_neg_iff
% 7.75/5.71 thf(fact_5886_tanh__real__nonpos__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 7.75/5.71 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % tanh_real_nonpos_iff
% 7.75/5.71 thf(fact_5887_tanh__real__nonneg__iff,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 7.75/5.71 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 7.75/5.71
% 7.75/5.71 % tanh_real_nonneg_iff
% 7.75/5.71 thf(fact_5888_round__1,axiom,
% 7.75/5.71 ( ( archim8280529875227126926d_real @ one_one_real )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % round_1
% 7.75/5.71 thf(fact_5889_round__1,axiom,
% 7.75/5.71 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % round_1
% 7.75/5.71 thf(fact_5890_divide__le__0__abs__iff,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 7.75/5.71 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.71 | ( B = zero_zero_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % divide_le_0_abs_iff
% 7.75/5.71 thf(fact_5891_divide__le__0__abs__iff,axiom,
% 7.75/5.71 ! [A: rat,B: rat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 7.75/5.71 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.71 | ( B = zero_zero_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % divide_le_0_abs_iff
% 7.75/5.71 thf(fact_5892_zero__le__divide__abs__iff,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 7.75/5.71 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.71 | ( B = zero_zero_real ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_le_divide_abs_iff
% 7.75/5.71 thf(fact_5893_zero__le__divide__abs__iff,axiom,
% 7.75/5.71 ! [A: rat,B: rat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 7.75/5.71 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.71 | ( B = zero_zero_rat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_le_divide_abs_iff
% 7.75/5.71 thf(fact_5894_abs__of__nonpos,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.71 => ( ( abs_abs_real @ A )
% 7.75/5.71 = ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nonpos
% 7.75/5.71 thf(fact_5895_abs__of__nonpos,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.71 => ( ( abs_abs_Code_integer @ A )
% 7.75/5.71 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nonpos
% 7.75/5.71 thf(fact_5896_abs__of__nonpos,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 7.75/5.71 => ( ( abs_abs_rat @ A )
% 7.75/5.71 = ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nonpos
% 7.75/5.71 thf(fact_5897_abs__of__nonpos,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 7.75/5.71 => ( ( abs_abs_int @ A )
% 7.75/5.71 = ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_of_nonpos
% 7.75/5.71 thf(fact_5898_artanh__minus__real,axiom,
% 7.75/5.71 ! [X: real] :
% 7.75/5.71 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.75/5.71 => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 7.75/5.71 = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % artanh_minus_real
% 7.75/5.71 thf(fact_5899_zero__less__power__abs__iff,axiom,
% 7.75/5.71 ! [A: code_integer,N: nat] :
% 7.75/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 7.75/5.71 = ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.71 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_power_abs_iff
% 7.75/5.71 thf(fact_5900_zero__less__power__abs__iff,axiom,
% 7.75/5.71 ! [A: real,N: nat] :
% 7.75/5.71 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 7.75/5.71 = ( ( A != zero_zero_real )
% 7.75/5.71 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_power_abs_iff
% 7.75/5.71 thf(fact_5901_zero__less__power__abs__iff,axiom,
% 7.75/5.71 ! [A: rat,N: nat] :
% 7.75/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 7.75/5.71 = ( ( A != zero_zero_rat )
% 7.75/5.71 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_power_abs_iff
% 7.75/5.71 thf(fact_5902_zero__less__power__abs__iff,axiom,
% 7.75/5.71 ! [A: int,N: nat] :
% 7.75/5.71 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 7.75/5.71 = ( ( A != zero_zero_int )
% 7.75/5.71 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % zero_less_power_abs_iff
% 7.75/5.71 thf(fact_5903_abs__power2,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.71 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_power2
% 7.75/5.71 thf(fact_5904_abs__power2,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.71 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_power2
% 7.75/5.71 thf(fact_5905_abs__power2,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.71 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_power2
% 7.75/5.71 thf(fact_5906_abs__power2,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.71 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_power2
% 7.75/5.71 thf(fact_5907_power2__abs,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.71 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power2_abs
% 7.75/5.71 thf(fact_5908_power2__abs,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.71 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power2_abs
% 7.75/5.71 thf(fact_5909_power2__abs,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.71 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power2_abs
% 7.75/5.71 thf(fact_5910_power2__abs,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.71 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power2_abs
% 7.75/5.71 thf(fact_5911_round__neg__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % round_neg_numeral
% 7.75/5.71 thf(fact_5912_round__neg__numeral,axiom,
% 7.75/5.71 ! [N: num] :
% 7.75/5.71 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % round_neg_numeral
% 7.75/5.71 thf(fact_5913_power__even__abs__numeral,axiom,
% 7.75/5.71 ! [W: num,A: rat] :
% 7.75/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.71 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.71 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_even_abs_numeral
% 7.75/5.71 thf(fact_5914_power__even__abs__numeral,axiom,
% 7.75/5.71 ! [W: num,A: real] :
% 7.75/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.71 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.71 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_even_abs_numeral
% 7.75/5.71 thf(fact_5915_power__even__abs__numeral,axiom,
% 7.75/5.71 ! [W: num,A: int] :
% 7.75/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.71 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.71 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_even_abs_numeral
% 7.75/5.71 thf(fact_5916_power__even__abs__numeral,axiom,
% 7.75/5.71 ! [W: num,A: code_integer] :
% 7.75/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.71 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 7.75/5.71 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_even_abs_numeral
% 7.75/5.71 thf(fact_5917_abs__eq__0__iff,axiom,
% 7.75/5.71 ! [A: code_integer] :
% 7.75/5.71 ( ( ( abs_abs_Code_integer @ A )
% 7.75/5.71 = zero_z3403309356797280102nteger )
% 7.75/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_0_iff
% 7.75/5.71 thf(fact_5918_abs__eq__0__iff,axiom,
% 7.75/5.71 ! [A: complex] :
% 7.75/5.71 ( ( ( abs_abs_complex @ A )
% 7.75/5.71 = zero_zero_complex )
% 7.75/5.71 = ( A = zero_zero_complex ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_0_iff
% 7.75/5.71 thf(fact_5919_abs__eq__0__iff,axiom,
% 7.75/5.71 ! [A: real] :
% 7.75/5.71 ( ( ( abs_abs_real @ A )
% 7.75/5.71 = zero_zero_real )
% 7.75/5.71 = ( A = zero_zero_real ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_0_iff
% 7.75/5.71 thf(fact_5920_abs__eq__0__iff,axiom,
% 7.75/5.71 ! [A: rat] :
% 7.75/5.71 ( ( ( abs_abs_rat @ A )
% 7.75/5.71 = zero_zero_rat )
% 7.75/5.71 = ( A = zero_zero_rat ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_0_iff
% 7.75/5.71 thf(fact_5921_abs__eq__0__iff,axiom,
% 7.75/5.71 ! [A: int] :
% 7.75/5.71 ( ( ( abs_abs_int @ A )
% 7.75/5.71 = zero_zero_int )
% 7.75/5.71 = ( A = zero_zero_int ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_0_iff
% 7.75/5.71 thf(fact_5922_abs__le__D1,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 7.75/5.71 => ( ord_less_eq_real @ A @ B ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_D1
% 7.75/5.71 thf(fact_5923_abs__le__D1,axiom,
% 7.75/5.71 ! [A: code_integer,B: code_integer] :
% 7.75/5.71 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 7.75/5.71 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_D1
% 7.75/5.71 thf(fact_5924_abs__le__D1,axiom,
% 7.75/5.71 ! [A: rat,B: rat] :
% 7.75/5.71 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 7.75/5.71 => ( ord_less_eq_rat @ A @ B ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_D1
% 7.75/5.71 thf(fact_5925_abs__le__D1,axiom,
% 7.75/5.71 ! [A: int,B: int] :
% 7.75/5.71 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 7.75/5.71 => ( ord_less_eq_int @ A @ B ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_le_D1
% 7.75/5.71 thf(fact_5926_abs__ge__self,axiom,
% 7.75/5.71 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_ge_self
% 7.75/5.71 thf(fact_5927_abs__ge__self,axiom,
% 7.75/5.71 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_ge_self
% 7.75/5.71 thf(fact_5928_abs__ge__self,axiom,
% 7.75/5.71 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_ge_self
% 7.75/5.71 thf(fact_5929_abs__ge__self,axiom,
% 7.75/5.71 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_ge_self
% 7.75/5.71 thf(fact_5930_abs__one,axiom,
% 7.75/5.71 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 7.75/5.71 = one_one_Code_integer ) ).
% 7.75/5.71
% 7.75/5.71 % abs_one
% 7.75/5.71 thf(fact_5931_abs__one,axiom,
% 7.75/5.71 ( ( abs_abs_real @ one_one_real )
% 7.75/5.71 = one_one_real ) ).
% 7.75/5.71
% 7.75/5.71 % abs_one
% 7.75/5.71 thf(fact_5932_abs__one,axiom,
% 7.75/5.71 ( ( abs_abs_rat @ one_one_rat )
% 7.75/5.71 = one_one_rat ) ).
% 7.75/5.71
% 7.75/5.71 % abs_one
% 7.75/5.71 thf(fact_5933_abs__one,axiom,
% 7.75/5.71 ( ( abs_abs_int @ one_one_int )
% 7.75/5.71 = one_one_int ) ).
% 7.75/5.71
% 7.75/5.71 % abs_one
% 7.75/5.71 thf(fact_5934_abs__mult,axiom,
% 7.75/5.71 ! [A: rat,B: rat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.71 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_mult
% 7.75/5.71 thf(fact_5935_abs__mult,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 7.75/5.71 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_mult
% 7.75/5.71 thf(fact_5936_abs__mult,axiom,
% 7.75/5.71 ! [A: int,B: int] :
% 7.75/5.71 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 7.75/5.71 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_mult
% 7.75/5.71 thf(fact_5937_abs__mult,axiom,
% 7.75/5.71 ! [A: code_integer,B: code_integer] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 7.75/5.71 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_mult
% 7.75/5.71 thf(fact_5938_abs__mult,axiom,
% 7.75/5.71 ! [A: complex,B: complex] :
% 7.75/5.71 ( ( abs_abs_complex @ ( times_times_complex @ A @ B ) )
% 7.75/5.71 = ( times_times_complex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_mult
% 7.75/5.71 thf(fact_5939_abs__minus__commute,axiom,
% 7.75/5.71 ! [A: code_integer,B: code_integer] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 7.75/5.71 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus_commute
% 7.75/5.71 thf(fact_5940_abs__minus__commute,axiom,
% 7.75/5.71 ! [A: rat,B: rat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 7.75/5.71 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus_commute
% 7.75/5.71 thf(fact_5941_abs__minus__commute,axiom,
% 7.75/5.71 ! [A: real,B: real] :
% 7.75/5.71 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 7.75/5.71 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus_commute
% 7.75/5.71 thf(fact_5942_abs__minus__commute,axiom,
% 7.75/5.71 ! [A: int,B: int] :
% 7.75/5.71 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 7.75/5.71 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_minus_commute
% 7.75/5.71 thf(fact_5943_abs__eq__iff,axiom,
% 7.75/5.71 ! [X: int,Y: int] :
% 7.75/5.71 ( ( ( abs_abs_int @ X )
% 7.75/5.71 = ( abs_abs_int @ Y ) )
% 7.75/5.71 = ( ( X = Y )
% 7.75/5.71 | ( X
% 7.75/5.71 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_iff
% 7.75/5.71 thf(fact_5944_abs__eq__iff,axiom,
% 7.75/5.71 ! [X: real,Y: real] :
% 7.75/5.71 ( ( ( abs_abs_real @ X )
% 7.75/5.71 = ( abs_abs_real @ Y ) )
% 7.75/5.71 = ( ( X = Y )
% 7.75/5.71 | ( X
% 7.75/5.71 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_iff
% 7.75/5.71 thf(fact_5945_abs__eq__iff,axiom,
% 7.75/5.71 ! [X: code_integer,Y: code_integer] :
% 7.75/5.71 ( ( ( abs_abs_Code_integer @ X )
% 7.75/5.71 = ( abs_abs_Code_integer @ Y ) )
% 7.75/5.71 = ( ( X = Y )
% 7.75/5.71 | ( X
% 7.75/5.71 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_iff
% 7.75/5.71 thf(fact_5946_abs__eq__iff,axiom,
% 7.75/5.71 ! [X: rat,Y: rat] :
% 7.75/5.71 ( ( ( abs_abs_rat @ X )
% 7.75/5.71 = ( abs_abs_rat @ Y ) )
% 7.75/5.71 = ( ( X = Y )
% 7.75/5.71 | ( X
% 7.75/5.71 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_eq_iff
% 7.75/5.71 thf(fact_5947_power__abs,axiom,
% 7.75/5.71 ! [A: rat,N: nat] :
% 7.75/5.71 ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 7.75/5.71 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_abs
% 7.75/5.71 thf(fact_5948_power__abs,axiom,
% 7.75/5.71 ! [A: real,N: nat] :
% 7.75/5.71 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 7.75/5.71 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_abs
% 7.75/5.71 thf(fact_5949_power__abs,axiom,
% 7.75/5.71 ! [A: int,N: nat] :
% 7.75/5.71 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 7.75/5.71 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_abs
% 7.75/5.71 thf(fact_5950_power__abs,axiom,
% 7.75/5.71 ! [A: code_integer,N: nat] :
% 7.75/5.71 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.71 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % power_abs
% 7.75/5.71 thf(fact_5951_dvd__if__abs__eq,axiom,
% 7.75/5.71 ! [L: real,K: real] :
% 7.75/5.71 ( ( ( abs_abs_real @ L )
% 7.75/5.71 = ( abs_abs_real @ K ) )
% 7.75/5.71 => ( dvd_dvd_real @ L @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % dvd_if_abs_eq
% 7.75/5.71 thf(fact_5952_dvd__if__abs__eq,axiom,
% 7.75/5.71 ! [L: int,K: int] :
% 7.75/5.71 ( ( ( abs_abs_int @ L )
% 7.75/5.71 = ( abs_abs_int @ K ) )
% 7.75/5.71 => ( dvd_dvd_int @ L @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % dvd_if_abs_eq
% 7.75/5.71 thf(fact_5953_dvd__if__abs__eq,axiom,
% 7.75/5.71 ! [L: code_integer,K: code_integer] :
% 7.75/5.71 ( ( ( abs_abs_Code_integer @ L )
% 7.75/5.71 = ( abs_abs_Code_integer @ K ) )
% 7.75/5.71 => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % dvd_if_abs_eq
% 7.75/5.71 thf(fact_5954_dvd__if__abs__eq,axiom,
% 7.75/5.71 ! [L: rat,K: rat] :
% 7.75/5.71 ( ( ( abs_abs_rat @ L )
% 7.75/5.71 = ( abs_abs_rat @ K ) )
% 7.75/5.71 => ( dvd_dvd_rat @ L @ K ) ) ).
% 7.75/5.71
% 7.75/5.71 % dvd_if_abs_eq
% 7.75/5.71 thf(fact_5955_finite__nat__set__iff__bounded,axiom,
% 7.75/5.71 ( finite_finite_nat
% 7.75/5.71 = ( ^ [N8: set_nat] :
% 7.75/5.71 ? [M4: nat] :
% 7.75/5.71 ! [X2: nat] :
% 7.75/5.71 ( ( member_nat @ X2 @ N8 )
% 7.75/5.71 => ( ord_less_nat @ X2 @ M4 ) ) ) ) ).
% 7.75/5.71
% 7.75/5.71 % finite_nat_set_iff_bounded
% 7.75/5.71 thf(fact_5956_bounded__nat__set__is__finite,axiom,
% 7.75/5.71 ! [N4: set_nat,N: nat] :
% 7.75/5.71 ( ! [X3: nat] :
% 7.75/5.71 ( ( member_nat @ X3 @ N4 )
% 7.75/5.71 => ( ord_less_nat @ X3 @ N ) )
% 7.75/5.71 => ( finite_finite_nat @ N4 ) ) ).
% 7.75/5.71
% 7.75/5.71 % bounded_nat_set_is_finite
% 7.75/5.71 thf(fact_5957_finite__set__decode,axiom,
% 7.75/5.71 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 7.75/5.71
% 7.75/5.71 % finite_set_decode
% 7.75/5.71 thf(fact_5958_abs__ge__zero,axiom,
% 7.75/5.71 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_ge_zero
% 7.75/5.71 thf(fact_5959_abs__ge__zero,axiom,
% 7.75/5.71 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_ge_zero
% 7.75/5.71 thf(fact_5960_abs__ge__zero,axiom,
% 7.75/5.71 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_ge_zero
% 7.75/5.71 thf(fact_5961_abs__ge__zero,axiom,
% 7.75/5.71 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 7.75/5.71
% 7.75/5.71 % abs_ge_zero
% 7.75/5.71 thf(fact_5962_abs__not__less__zero,axiom,
% 7.75/5.72 ! [A: code_integer] :
% 7.75/5.72 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 7.75/5.72
% 7.75/5.72 % abs_not_less_zero
% 7.75/5.72 thf(fact_5963_abs__not__less__zero,axiom,
% 7.75/5.72 ! [A: real] :
% 7.75/5.72 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % abs_not_less_zero
% 7.75/5.72 thf(fact_5964_abs__not__less__zero,axiom,
% 7.75/5.72 ! [A: rat] :
% 7.75/5.72 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 7.75/5.72
% 7.75/5.72 % abs_not_less_zero
% 7.75/5.72 thf(fact_5965_abs__not__less__zero,axiom,
% 7.75/5.72 ! [A: int] :
% 7.75/5.72 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 7.75/5.72
% 7.75/5.72 % abs_not_less_zero
% 7.75/5.72 thf(fact_5966_abs__of__pos,axiom,
% 7.75/5.72 ! [A: code_integer] :
% 7.75/5.72 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.72 => ( ( abs_abs_Code_integer @ A )
% 7.75/5.72 = A ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_of_pos
% 7.75/5.72 thf(fact_5967_abs__of__pos,axiom,
% 7.75/5.72 ! [A: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ( abs_abs_real @ A )
% 7.75/5.72 = A ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_of_pos
% 7.75/5.72 thf(fact_5968_abs__of__pos,axiom,
% 7.75/5.72 ! [A: rat] :
% 7.75/5.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.72 => ( ( abs_abs_rat @ A )
% 7.75/5.72 = A ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_of_pos
% 7.75/5.72 thf(fact_5969_abs__of__pos,axiom,
% 7.75/5.72 ! [A: int] :
% 7.75/5.72 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.72 => ( ( abs_abs_int @ A )
% 7.75/5.72 = A ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_of_pos
% 7.75/5.72 thf(fact_5970_abs__triangle__ineq,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq
% 7.75/5.72 thf(fact_5971_abs__triangle__ineq,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq
% 7.75/5.72 thf(fact_5972_abs__triangle__ineq,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq
% 7.75/5.72 thf(fact_5973_abs__triangle__ineq,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq
% 7.75/5.72 thf(fact_5974_abs__mult__less,axiom,
% 7.75/5.72 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 7.75/5.72 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 7.75/5.72 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 7.75/5.72 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_mult_less
% 7.75/5.72 thf(fact_5975_abs__mult__less,axiom,
% 7.75/5.72 ! [A: real,C: real,B: real,D2: real] :
% 7.75/5.72 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 7.75/5.72 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D2 )
% 7.75/5.72 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_mult_less
% 7.75/5.72 thf(fact_5976_abs__mult__less,axiom,
% 7.75/5.72 ! [A: rat,C: rat,B: rat,D2: rat] :
% 7.75/5.72 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 7.75/5.72 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 7.75/5.72 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_mult_less
% 7.75/5.72 thf(fact_5977_abs__mult__less,axiom,
% 7.75/5.72 ! [A: int,C: int,B: int,D2: int] :
% 7.75/5.72 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 7.75/5.72 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 7.75/5.72 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_mult_less
% 7.75/5.72 thf(fact_5978_abs__triangle__ineq2__sym,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq2_sym
% 7.75/5.72 thf(fact_5979_abs__triangle__ineq2__sym,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq2_sym
% 7.75/5.72 thf(fact_5980_abs__triangle__ineq2__sym,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq2_sym
% 7.75/5.72 thf(fact_5981_abs__triangle__ineq2__sym,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq2_sym
% 7.75/5.72 thf(fact_5982_abs__triangle__ineq3,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq3
% 7.75/5.72 thf(fact_5983_abs__triangle__ineq3,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq3
% 7.75/5.72 thf(fact_5984_abs__triangle__ineq3,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq3
% 7.75/5.72 thf(fact_5985_abs__triangle__ineq3,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq3
% 7.75/5.72 thf(fact_5986_abs__triangle__ineq2,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq2
% 7.75/5.72 thf(fact_5987_abs__triangle__ineq2,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq2
% 7.75/5.72 thf(fact_5988_abs__triangle__ineq2,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq2
% 7.75/5.72 thf(fact_5989_abs__triangle__ineq2,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq2
% 7.75/5.72 thf(fact_5990_nonzero__abs__divide,axiom,
% 7.75/5.72 ! [B: real,A: real] :
% 7.75/5.72 ( ( B != zero_zero_real )
% 7.75/5.72 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.72 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nonzero_abs_divide
% 7.75/5.72 thf(fact_5991_nonzero__abs__divide,axiom,
% 7.75/5.72 ! [B: rat,A: rat] :
% 7.75/5.72 ( ( B != zero_zero_rat )
% 7.75/5.72 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 7.75/5.72 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nonzero_abs_divide
% 7.75/5.72 thf(fact_5992_abs__ge__minus__self,axiom,
% 7.75/5.72 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_ge_minus_self
% 7.75/5.72 thf(fact_5993_abs__ge__minus__self,axiom,
% 7.75/5.72 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_ge_minus_self
% 7.75/5.72 thf(fact_5994_abs__ge__minus__self,axiom,
% 7.75/5.72 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_ge_minus_self
% 7.75/5.72 thf(fact_5995_abs__ge__minus__self,axiom,
% 7.75/5.72 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_ge_minus_self
% 7.75/5.72 thf(fact_5996_abs__le__iff,axiom,
% 7.75/5.72 ! [A: real,B: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 7.75/5.72 = ( ( ord_less_eq_real @ A @ B )
% 7.75/5.72 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_iff
% 7.75/5.72 thf(fact_5997_abs__le__iff,axiom,
% 7.75/5.72 ! [A: code_integer,B: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 7.75/5.72 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.72 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_iff
% 7.75/5.72 thf(fact_5998_abs__le__iff,axiom,
% 7.75/5.72 ! [A: rat,B: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 7.75/5.72 = ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.72 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_iff
% 7.75/5.72 thf(fact_5999_abs__le__iff,axiom,
% 7.75/5.72 ! [A: int,B: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 7.75/5.72 = ( ( ord_less_eq_int @ A @ B )
% 7.75/5.72 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_iff
% 7.75/5.72 thf(fact_6000_abs__le__D2,axiom,
% 7.75/5.72 ! [A: real,B: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 7.75/5.72 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_D2
% 7.75/5.72 thf(fact_6001_abs__le__D2,axiom,
% 7.75/5.72 ! [A: code_integer,B: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 7.75/5.72 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_D2
% 7.75/5.72 thf(fact_6002_abs__le__D2,axiom,
% 7.75/5.72 ! [A: rat,B: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 7.75/5.72 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_D2
% 7.75/5.72 thf(fact_6003_abs__le__D2,axiom,
% 7.75/5.72 ! [A: int,B: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 7.75/5.72 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_D2
% 7.75/5.72 thf(fact_6004_abs__leI,axiom,
% 7.75/5.72 ! [A: real,B: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.72 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 7.75/5.72 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_leI
% 7.75/5.72 thf(fact_6005_abs__leI,axiom,
% 7.75/5.72 ! [A: code_integer,B: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ A @ B )
% 7.75/5.72 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 7.75/5.72 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_leI
% 7.75/5.72 thf(fact_6006_abs__leI,axiom,
% 7.75/5.72 ! [A: rat,B: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ A @ B )
% 7.75/5.72 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 7.75/5.72 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_leI
% 7.75/5.72 thf(fact_6007_abs__leI,axiom,
% 7.75/5.72 ! [A: int,B: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ A @ B )
% 7.75/5.72 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 7.75/5.72 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_leI
% 7.75/5.72 thf(fact_6008_abs__less__iff,axiom,
% 7.75/5.72 ! [A: int,B: int] :
% 7.75/5.72 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 7.75/5.72 = ( ( ord_less_int @ A @ B )
% 7.75/5.72 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_less_iff
% 7.75/5.72 thf(fact_6009_abs__less__iff,axiom,
% 7.75/5.72 ! [A: real,B: real] :
% 7.75/5.72 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 7.75/5.72 = ( ( ord_less_real @ A @ B )
% 7.75/5.72 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_less_iff
% 7.75/5.72 thf(fact_6010_abs__less__iff,axiom,
% 7.75/5.72 ! [A: code_integer,B: code_integer] :
% 7.75/5.72 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 7.75/5.72 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.75/5.72 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_less_iff
% 7.75/5.72 thf(fact_6011_abs__less__iff,axiom,
% 7.75/5.72 ! [A: rat,B: rat] :
% 7.75/5.72 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 7.75/5.72 = ( ( ord_less_rat @ A @ B )
% 7.75/5.72 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_less_iff
% 7.75/5.72 thf(fact_6012_infinite__Icc,axiom,
% 7.75/5.72 ! [A: rat,B: rat] :
% 7.75/5.72 ( ( ord_less_rat @ A @ B )
% 7.75/5.72 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % infinite_Icc
% 7.75/5.72 thf(fact_6013_infinite__Icc,axiom,
% 7.75/5.72 ! [A: real,B: real] :
% 7.75/5.72 ( ( ord_less_real @ A @ B )
% 7.75/5.72 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % infinite_Icc
% 7.75/5.72 thf(fact_6014_tanh__real__lt__1,axiom,
% 7.75/5.72 ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 7.75/5.72
% 7.75/5.72 % tanh_real_lt_1
% 7.75/5.72 thf(fact_6015_dense__eq0__I,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ! [E2: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ E2 )
% 7.75/5.72 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 7.75/5.72 => ( X = zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % dense_eq0_I
% 7.75/5.72 thf(fact_6016_dense__eq0__I,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ! [E2: rat] :
% 7.75/5.72 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 7.75/5.72 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 7.75/5.72 => ( X = zero_zero_rat ) ) ).
% 7.75/5.72
% 7.75/5.72 % dense_eq0_I
% 7.75/5.72 thf(fact_6017_abs__mult__pos,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 7.75/5.72 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_mult_pos
% 7.75/5.72 thf(fact_6018_abs__mult__pos,axiom,
% 7.75/5.72 ! [X: code_integer,Y: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 7.75/5.72 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 7.75/5.72 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_mult_pos
% 7.75/5.72 thf(fact_6019_abs__mult__pos,axiom,
% 7.75/5.72 ! [X: rat,Y: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.72 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 7.75/5.72 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_mult_pos
% 7.75/5.72 thf(fact_6020_abs__mult__pos,axiom,
% 7.75/5.72 ! [X: int,Y: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.72 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 7.75/5.72 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_mult_pos
% 7.75/5.72 thf(fact_6021_abs__eq__mult,axiom,
% 7.75/5.72 ! [A: real,B: real] :
% 7.75/5.72 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.72 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 7.75/5.72 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.72 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 7.75/5.72 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 7.75/5.72 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_eq_mult
% 7.75/5.72 thf(fact_6022_abs__eq__mult,axiom,
% 7.75/5.72 ! [A: code_integer,B: code_integer] :
% 7.75/5.72 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.72 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 7.75/5.72 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.72 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 7.75/5.72 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 7.75/5.72 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_eq_mult
% 7.75/5.72 thf(fact_6023_abs__eq__mult,axiom,
% 7.75/5.72 ! [A: rat,B: rat] :
% 7.75/5.72 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.72 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 7.75/5.72 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.72 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 7.75/5.72 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.72 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_eq_mult
% 7.75/5.72 thf(fact_6024_abs__eq__mult,axiom,
% 7.75/5.72 ! [A: int,B: int] :
% 7.75/5.72 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.72 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 7.75/5.72 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.72 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 7.75/5.72 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 7.75/5.72 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_eq_mult
% 7.75/5.72 thf(fact_6025_abs__minus__le__zero,axiom,
% 7.75/5.72 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % abs_minus_le_zero
% 7.75/5.72 thf(fact_6026_abs__minus__le__zero,axiom,
% 7.75/5.72 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 7.75/5.72
% 7.75/5.72 % abs_minus_le_zero
% 7.75/5.72 thf(fact_6027_abs__minus__le__zero,axiom,
% 7.75/5.72 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 7.75/5.72
% 7.75/5.72 % abs_minus_le_zero
% 7.75/5.72 thf(fact_6028_abs__minus__le__zero,axiom,
% 7.75/5.72 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 7.75/5.72
% 7.75/5.72 % abs_minus_le_zero
% 7.75/5.72 thf(fact_6029_abs__eq__iff_H,axiom,
% 7.75/5.72 ! [A: real,B: real] :
% 7.75/5.72 ( ( ( abs_abs_real @ A )
% 7.75/5.72 = B )
% 7.75/5.72 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.72 & ( ( A = B )
% 7.75/5.72 | ( A
% 7.75/5.72 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_eq_iff'
% 7.75/5.72 thf(fact_6030_abs__eq__iff_H,axiom,
% 7.75/5.72 ! [A: code_integer,B: code_integer] :
% 7.75/5.72 ( ( ( abs_abs_Code_integer @ A )
% 7.75/5.72 = B )
% 7.75/5.72 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 7.75/5.72 & ( ( A = B )
% 7.75/5.72 | ( A
% 7.75/5.72 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_eq_iff'
% 7.75/5.72 thf(fact_6031_abs__eq__iff_H,axiom,
% 7.75/5.72 ! [A: rat,B: rat] :
% 7.75/5.72 ( ( ( abs_abs_rat @ A )
% 7.75/5.72 = B )
% 7.75/5.72 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.72 & ( ( A = B )
% 7.75/5.72 | ( A
% 7.75/5.72 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_eq_iff'
% 7.75/5.72 thf(fact_6032_abs__eq__iff_H,axiom,
% 7.75/5.72 ! [A: int,B: int] :
% 7.75/5.72 ( ( ( abs_abs_int @ A )
% 7.75/5.72 = B )
% 7.75/5.72 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.72 & ( ( A = B )
% 7.75/5.72 | ( A
% 7.75/5.72 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_eq_iff'
% 7.75/5.72 thf(fact_6033_eq__abs__iff_H,axiom,
% 7.75/5.72 ! [A: real,B: real] :
% 7.75/5.72 ( ( A
% 7.75/5.72 = ( abs_abs_real @ B ) )
% 7.75/5.72 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.72 & ( ( B = A )
% 7.75/5.72 | ( B
% 7.75/5.72 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % eq_abs_iff'
% 7.75/5.72 thf(fact_6034_eq__abs__iff_H,axiom,
% 7.75/5.72 ! [A: code_integer,B: code_integer] :
% 7.75/5.72 ( ( A
% 7.75/5.72 = ( abs_abs_Code_integer @ B ) )
% 7.75/5.72 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.72 & ( ( B = A )
% 7.75/5.72 | ( B
% 7.75/5.72 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % eq_abs_iff'
% 7.75/5.72 thf(fact_6035_eq__abs__iff_H,axiom,
% 7.75/5.72 ! [A: rat,B: rat] :
% 7.75/5.72 ( ( A
% 7.75/5.72 = ( abs_abs_rat @ B ) )
% 7.75/5.72 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.72 & ( ( B = A )
% 7.75/5.72 | ( B
% 7.75/5.72 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % eq_abs_iff'
% 7.75/5.72 thf(fact_6036_eq__abs__iff_H,axiom,
% 7.75/5.72 ! [A: int,B: int] :
% 7.75/5.72 ( ( A
% 7.75/5.72 = ( abs_abs_int @ B ) )
% 7.75/5.72 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 7.75/5.72 & ( ( B = A )
% 7.75/5.72 | ( B
% 7.75/5.72 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % eq_abs_iff'
% 7.75/5.72 thf(fact_6037_zero__le__power__abs,axiom,
% 7.75/5.72 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_le_power_abs
% 7.75/5.72 thf(fact_6038_zero__le__power__abs,axiom,
% 7.75/5.72 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_le_power_abs
% 7.75/5.72 thf(fact_6039_zero__le__power__abs,axiom,
% 7.75/5.72 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_le_power_abs
% 7.75/5.72 thf(fact_6040_zero__le__power__abs,axiom,
% 7.75/5.72 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_le_power_abs
% 7.75/5.72 thf(fact_6041_abs__div__pos,axiom,
% 7.75/5.72 ! [Y: real,X: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.72 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 7.75/5.72 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_div_pos
% 7.75/5.72 thf(fact_6042_abs__div__pos,axiom,
% 7.75/5.72 ! [Y: rat,X: rat] :
% 7.75/5.72 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 7.75/5.72 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 7.75/5.72 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_div_pos
% 7.75/5.72 thf(fact_6043_abs__if__raw,axiom,
% 7.75/5.72 ( abs_abs_int
% 7.75/5.72 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_if_raw
% 7.75/5.72 thf(fact_6044_abs__if__raw,axiom,
% 7.75/5.72 ( abs_abs_real
% 7.75/5.72 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_if_raw
% 7.75/5.72 thf(fact_6045_abs__if__raw,axiom,
% 7.75/5.72 ( abs_abs_Code_integer
% 7.75/5.72 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_if_raw
% 7.75/5.72 thf(fact_6046_abs__if__raw,axiom,
% 7.75/5.72 ( abs_abs_rat
% 7.75/5.72 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_if_raw
% 7.75/5.72 thf(fact_6047_abs__of__neg,axiom,
% 7.75/5.72 ! [A: int] :
% 7.75/5.72 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.72 => ( ( abs_abs_int @ A )
% 7.75/5.72 = ( uminus_uminus_int @ A ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_of_neg
% 7.75/5.72 thf(fact_6048_abs__of__neg,axiom,
% 7.75/5.72 ! [A: real] :
% 7.75/5.72 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.72 => ( ( abs_abs_real @ A )
% 7.75/5.72 = ( uminus_uminus_real @ A ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_of_neg
% 7.75/5.72 thf(fact_6049_abs__of__neg,axiom,
% 7.75/5.72 ! [A: code_integer] :
% 7.75/5.72 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.72 => ( ( abs_abs_Code_integer @ A )
% 7.75/5.72 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_of_neg
% 7.75/5.72 thf(fact_6050_abs__of__neg,axiom,
% 7.75/5.72 ! [A: rat] :
% 7.75/5.72 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.72 => ( ( abs_abs_rat @ A )
% 7.75/5.72 = ( uminus_uminus_rat @ A ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_of_neg
% 7.75/5.72 thf(fact_6051_abs__if,axiom,
% 7.75/5.72 ( abs_abs_int
% 7.75/5.72 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_if
% 7.75/5.72 thf(fact_6052_abs__if,axiom,
% 7.75/5.72 ( abs_abs_real
% 7.75/5.72 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_if
% 7.75/5.72 thf(fact_6053_abs__if,axiom,
% 7.75/5.72 ( abs_abs_Code_integer
% 7.75/5.72 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_if
% 7.75/5.72 thf(fact_6054_abs__if,axiom,
% 7.75/5.72 ( abs_abs_rat
% 7.75/5.72 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_if
% 7.75/5.72 thf(fact_6055_abs__diff__triangle__ineq,axiom,
% 7.75/5.72 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_triangle_ineq
% 7.75/5.72 thf(fact_6056_abs__diff__triangle__ineq,axiom,
% 7.75/5.72 ! [A: real,B: real,C: real,D2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D2 ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_triangle_ineq
% 7.75/5.72 thf(fact_6057_abs__diff__triangle__ineq,axiom,
% 7.75/5.72 ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_triangle_ineq
% 7.75/5.72 thf(fact_6058_abs__diff__triangle__ineq,axiom,
% 7.75/5.72 ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_triangle_ineq
% 7.75/5.72 thf(fact_6059_abs__triangle__ineq4,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq4
% 7.75/5.72 thf(fact_6060_abs__triangle__ineq4,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq4
% 7.75/5.72 thf(fact_6061_abs__triangle__ineq4,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq4
% 7.75/5.72 thf(fact_6062_abs__triangle__ineq4,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_triangle_ineq4
% 7.75/5.72 thf(fact_6063_abs__diff__le__iff,axiom,
% 7.75/5.72 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 7.75/5.72 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 7.75/5.72 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_le_iff
% 7.75/5.72 thf(fact_6064_abs__diff__le__iff,axiom,
% 7.75/5.72 ! [X: real,A: real,R2: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 7.75/5.72 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 7.75/5.72 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_le_iff
% 7.75/5.72 thf(fact_6065_abs__diff__le__iff,axiom,
% 7.75/5.72 ! [X: rat,A: rat,R2: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 7.75/5.72 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 7.75/5.72 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_le_iff
% 7.75/5.72 thf(fact_6066_abs__diff__le__iff,axiom,
% 7.75/5.72 ! [X: int,A: int,R2: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 7.75/5.72 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 7.75/5.72 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_le_iff
% 7.75/5.72 thf(fact_6067_abs__diff__less__iff,axiom,
% 7.75/5.72 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 7.75/5.72 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 7.75/5.72 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 7.75/5.72 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_less_iff
% 7.75/5.72 thf(fact_6068_abs__diff__less__iff,axiom,
% 7.75/5.72 ! [X: real,A: real,R2: real] :
% 7.75/5.72 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 7.75/5.72 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 7.75/5.72 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_less_iff
% 7.75/5.72 thf(fact_6069_abs__diff__less__iff,axiom,
% 7.75/5.72 ! [X: rat,A: rat,R2: rat] :
% 7.75/5.72 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 7.75/5.72 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 7.75/5.72 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_less_iff
% 7.75/5.72 thf(fact_6070_abs__diff__less__iff,axiom,
% 7.75/5.72 ! [X: int,A: int,R2: int] :
% 7.75/5.72 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 7.75/5.72 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 7.75/5.72 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_diff_less_iff
% 7.75/5.72 thf(fact_6071_abs__real__def,axiom,
% 7.75/5.72 ( abs_abs_real
% 7.75/5.72 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_real_def
% 7.75/5.72 thf(fact_6072_lemma__interval__lt,axiom,
% 7.75/5.72 ! [A: real,X: real,B: real] :
% 7.75/5.72 ( ( ord_less_real @ A @ X )
% 7.75/5.72 => ( ( ord_less_real @ X @ B )
% 7.75/5.72 => ? [D3: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 7.75/5.72 & ! [Y4: real] :
% 7.75/5.72 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D3 )
% 7.75/5.72 => ( ( ord_less_real @ A @ Y4 )
% 7.75/5.72 & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % lemma_interval_lt
% 7.75/5.72 thf(fact_6073_subset__eq__atLeast0__atMost__finite,axiom,
% 7.75/5.72 ! [N4: set_nat,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 7.75/5.72 => ( finite_finite_nat @ N4 ) ) ).
% 7.75/5.72
% 7.75/5.72 % subset_eq_atLeast0_atMost_finite
% 7.75/5.72 thf(fact_6074_tanh__real__gt__neg1,axiom,
% 7.75/5.72 ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % tanh_real_gt_neg1
% 7.75/5.72 thf(fact_6075_abs__add__one__gt__zero,axiom,
% 7.75/5.72 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_add_one_gt_zero
% 7.75/5.72 thf(fact_6076_abs__add__one__gt__zero,axiom,
% 7.75/5.72 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_add_one_gt_zero
% 7.75/5.72 thf(fact_6077_abs__add__one__gt__zero,axiom,
% 7.75/5.72 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_add_one_gt_zero
% 7.75/5.72 thf(fact_6078_abs__add__one__gt__zero,axiom,
% 7.75/5.72 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_add_one_gt_zero
% 7.75/5.72 thf(fact_6079_of__int__leD,axiom,
% 7.75/5.72 ! [N: int,X: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 7.75/5.72 => ( ( N = zero_zero_int )
% 7.75/5.72 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_leD
% 7.75/5.72 thf(fact_6080_of__int__leD,axiom,
% 7.75/5.72 ! [N: int,X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 7.75/5.72 => ( ( N = zero_zero_int )
% 7.75/5.72 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_leD
% 7.75/5.72 thf(fact_6081_of__int__leD,axiom,
% 7.75/5.72 ! [N: int,X: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 7.75/5.72 => ( ( N = zero_zero_int )
% 7.75/5.72 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_leD
% 7.75/5.72 thf(fact_6082_of__int__leD,axiom,
% 7.75/5.72 ! [N: int,X: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 7.75/5.72 => ( ( N = zero_zero_int )
% 7.75/5.72 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_leD
% 7.75/5.72 thf(fact_6083_of__int__lessD,axiom,
% 7.75/5.72 ! [N: int,X: code_integer] :
% 7.75/5.72 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 7.75/5.72 => ( ( N = zero_zero_int )
% 7.75/5.72 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_lessD
% 7.75/5.72 thf(fact_6084_of__int__lessD,axiom,
% 7.75/5.72 ! [N: int,X: real] :
% 7.75/5.72 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 7.75/5.72 => ( ( N = zero_zero_int )
% 7.75/5.72 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_lessD
% 7.75/5.72 thf(fact_6085_of__int__lessD,axiom,
% 7.75/5.72 ! [N: int,X: rat] :
% 7.75/5.72 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 7.75/5.72 => ( ( N = zero_zero_int )
% 7.75/5.72 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_lessD
% 7.75/5.72 thf(fact_6086_of__int__lessD,axiom,
% 7.75/5.72 ! [N: int,X: int] :
% 7.75/5.72 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 7.75/5.72 => ( ( N = zero_zero_int )
% 7.75/5.72 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_lessD
% 7.75/5.72 thf(fact_6087_lemma__interval,axiom,
% 7.75/5.72 ! [A: real,X: real,B: real] :
% 7.75/5.72 ( ( ord_less_real @ A @ X )
% 7.75/5.72 => ( ( ord_less_real @ X @ B )
% 7.75/5.72 => ? [D3: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ D3 )
% 7.75/5.72 & ! [Y4: real] :
% 7.75/5.72 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D3 )
% 7.75/5.72 => ( ( ord_less_eq_real @ A @ Y4 )
% 7.75/5.72 & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % lemma_interval
% 7.75/5.72 thf(fact_6088_of__int__round__abs__le,axiom,
% 7.75/5.72 ! [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 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_round_abs_le
% 7.75/5.72 thf(fact_6089_of__int__round__abs__le,axiom,
% 7.75/5.72 ! [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 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_round_abs_le
% 7.75/5.72 thf(fact_6090_round__unique_H,axiom,
% 7.75/5.72 ! [X: real,N: int] :
% 7.75/5.72 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.72 => ( ( archim8280529875227126926d_real @ X )
% 7.75/5.72 = N ) ) ).
% 7.75/5.72
% 7.75/5.72 % round_unique'
% 7.75/5.72 thf(fact_6091_round__unique_H,axiom,
% 7.75/5.72 ! [X: rat,N: int] :
% 7.75/5.72 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 7.75/5.72 => ( ( archim7778729529865785530nd_rat @ X )
% 7.75/5.72 = N ) ) ).
% 7.75/5.72
% 7.75/5.72 % round_unique'
% 7.75/5.72 thf(fact_6092_abs__le__square__iff,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_square_iff
% 7.75/5.72 thf(fact_6093_abs__le__square__iff,axiom,
% 7.75/5.72 ! [X: code_integer,Y: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 7.75/5.72 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_square_iff
% 7.75/5.72 thf(fact_6094_abs__le__square__iff,axiom,
% 7.75/5.72 ! [X: rat,Y: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 7.75/5.72 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_square_iff
% 7.75/5.72 thf(fact_6095_abs__le__square__iff,axiom,
% 7.75/5.72 ! [X: int,Y: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 7.75/5.72 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_le_square_iff
% 7.75/5.72 thf(fact_6096_abs__square__eq__1,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.72 = one_one_rat )
% 7.75/5.72 = ( ( abs_abs_rat @ X )
% 7.75/5.72 = one_one_rat ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_eq_1
% 7.75/5.72 thf(fact_6097_abs__square__eq__1,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.72 = one_one_real )
% 7.75/5.72 = ( ( abs_abs_real @ X )
% 7.75/5.72 = one_one_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_eq_1
% 7.75/5.72 thf(fact_6098_abs__square__eq__1,axiom,
% 7.75/5.72 ! [X: int] :
% 7.75/5.72 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.72 = one_one_int )
% 7.75/5.72 = ( ( abs_abs_int @ X )
% 7.75/5.72 = one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_eq_1
% 7.75/5.72 thf(fact_6099_abs__square__eq__1,axiom,
% 7.75/5.72 ! [X: code_integer] :
% 7.75/5.72 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.72 = one_one_Code_integer )
% 7.75/5.72 = ( ( abs_abs_Code_integer @ X )
% 7.75/5.72 = one_one_Code_integer ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_eq_1
% 7.75/5.72 thf(fact_6100_power__even__abs,axiom,
% 7.75/5.72 ! [N: nat,A: rat] :
% 7.75/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 7.75/5.72 = ( power_power_rat @ A @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power_even_abs
% 7.75/5.72 thf(fact_6101_power__even__abs,axiom,
% 7.75/5.72 ! [N: nat,A: real] :
% 7.75/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 7.75/5.72 = ( power_power_real @ A @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power_even_abs
% 7.75/5.72 thf(fact_6102_power__even__abs,axiom,
% 7.75/5.72 ! [N: nat,A: int] :
% 7.75/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 7.75/5.72 = ( power_power_int @ A @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power_even_abs
% 7.75/5.72 thf(fact_6103_power__even__abs,axiom,
% 7.75/5.72 ! [N: nat,A: code_integer] :
% 7.75/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 7.75/5.72 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power_even_abs
% 7.75/5.72 thf(fact_6104_power2__le__iff__abs__le,axiom,
% 7.75/5.72 ! [Y: real,X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.72 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power2_le_iff_abs_le
% 7.75/5.72 thf(fact_6105_power2__le__iff__abs__le,axiom,
% 7.75/5.72 ! [Y: code_integer,X: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 7.75/5.72 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.72 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power2_le_iff_abs_le
% 7.75/5.72 thf(fact_6106_power2__le__iff__abs__le,axiom,
% 7.75/5.72 ! [Y: rat,X: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 7.75/5.72 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.72 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power2_le_iff_abs_le
% 7.75/5.72 thf(fact_6107_power2__le__iff__abs__le,axiom,
% 7.75/5.72 ! [Y: int,X: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.72 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.72 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power2_le_iff_abs_le
% 7.75/5.72 thf(fact_6108_abs__square__le__1,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 7.75/5.72 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_le_1
% 7.75/5.72 thf(fact_6109_abs__square__le__1,axiom,
% 7.75/5.72 ! [X: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 7.75/5.72 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_le_1
% 7.75/5.72 thf(fact_6110_abs__square__le__1,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 7.75/5.72 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_le_1
% 7.75/5.72 thf(fact_6111_abs__square__le__1,axiom,
% 7.75/5.72 ! [X: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 7.75/5.72 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_le_1
% 7.75/5.72 thf(fact_6112_abs__square__less__1,axiom,
% 7.75/5.72 ! [X: code_integer] :
% 7.75/5.72 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 7.75/5.72 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_less_1
% 7.75/5.72 thf(fact_6113_abs__square__less__1,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 7.75/5.72 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_less_1
% 7.75/5.72 thf(fact_6114_abs__square__less__1,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 7.75/5.72 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_less_1
% 7.75/5.72 thf(fact_6115_abs__square__less__1,axiom,
% 7.75/5.72 ! [X: int] :
% 7.75/5.72 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 7.75/5.72 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_square_less_1
% 7.75/5.72 thf(fact_6116_power__mono__even,axiom,
% 7.75/5.72 ! [N: nat,A: real,B: real] :
% 7.75/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 7.75/5.72 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power_mono_even
% 7.75/5.72 thf(fact_6117_power__mono__even,axiom,
% 7.75/5.72 ! [N: nat,A: code_integer,B: code_integer] :
% 7.75/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 7.75/5.72 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power_mono_even
% 7.75/5.72 thf(fact_6118_power__mono__even,axiom,
% 7.75/5.72 ! [N: nat,A: rat,B: rat] :
% 7.75/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 7.75/5.72 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power_mono_even
% 7.75/5.72 thf(fact_6119_power__mono__even,axiom,
% 7.75/5.72 ! [N: nat,A: int,B: int] :
% 7.75/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 7.75/5.72 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % power_mono_even
% 7.75/5.72 thf(fact_6120_pred__bound__height_H,axiom,
% 7.75/5.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.72 => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % pred_bound_height'
% 7.75/5.72 thf(fact_6121_succ_H__bound__height,axiom,
% 7.75/5.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.72 => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % succ'_bound_height
% 7.75/5.72 thf(fact_6122_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.75/5.72 => ( 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 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 7.75/5.72 thf(fact_6123_of__int__round__le,axiom,
% 7.75/5.72 ! [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 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_round_le
% 7.75/5.72 thf(fact_6124_of__int__round__le,axiom,
% 7.75/5.72 ! [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 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_round_le
% 7.75/5.72 thf(fact_6125_of__int__round__ge,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_round_ge
% 7.75/5.72 thf(fact_6126_of__int__round__ge,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_round_ge
% 7.75/5.72 thf(fact_6127_of__int__round__gt,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_round_gt
% 7.75/5.72 thf(fact_6128_of__int__round__gt,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_round_gt
% 7.75/5.72 thf(fact_6129_abs__ln__one__plus__x__minus__x__bound,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.72 => ( 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 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_ln_one_plus_x_minus_x_bound
% 7.75/5.72 thf(fact_6130_abs__sqrt__wlog,axiom,
% 7.75/5.72 ! [P: real > real > $o,X: real] :
% 7.75/5.72 ( ! [X3: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 7.75/5.72 => ( P @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.72 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_sqrt_wlog
% 7.75/5.72 thf(fact_6131_abs__sqrt__wlog,axiom,
% 7.75/5.72 ! [P: code_integer > code_integer > $o,X: code_integer] :
% 7.75/5.72 ( ! [X3: code_integer] :
% 7.75/5.72 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 7.75/5.72 => ( P @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.72 => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_sqrt_wlog
% 7.75/5.72 thf(fact_6132_abs__sqrt__wlog,axiom,
% 7.75/5.72 ! [P: rat > rat > $o,X: rat] :
% 7.75/5.72 ( ! [X3: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 7.75/5.72 => ( P @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.72 => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_sqrt_wlog
% 7.75/5.72 thf(fact_6133_abs__sqrt__wlog,axiom,
% 7.75/5.72 ! [P: int > int > $o,X: int] :
% 7.75/5.72 ( ! [X3: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 7.75/5.72 => ( P @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.72 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_sqrt_wlog
% 7.75/5.72 thf(fact_6134_arctan__double,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.75/5.72 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 7.75/5.72 = ( 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 ) ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % arctan_double
% 7.75/5.72 thf(fact_6135_ceiling__log__eq__powr__iff,axiom,
% 7.75/5.72 ! [X: real,B: real,K: nat] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 7.75/5.72 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 7.75/5.72 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 7.75/5.72 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ceiling_log_eq_powr_iff
% 7.75/5.72 thf(fact_6136_floor__log__nat__eq__powr__iff,axiom,
% 7.75/5.72 ! [B: nat,K: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 7.75/5.72 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.72 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 7.75/5.72 = ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.72 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 7.75/5.72 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_log_nat_eq_powr_iff
% 7.75/5.72 thf(fact_6137_height__compose__summary,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % height_compose_summary
% 7.75/5.72 thf(fact_6138_central__binomial__lower__bound,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.72 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % central_binomial_lower_bound
% 7.75/5.72 thf(fact_6139_deg__deg__n,axiom,
% 7.75/5.72 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 7.75/5.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 7.75/5.72 => ( Deg = N ) ) ).
% 7.75/5.72
% 7.75/5.72 % deg_deg_n
% 7.75/5.72 thf(fact_6140_deg__SUcn__Node,axiom,
% 7.75/5.72 ! [Tree: vEBT_VEBT,N: nat] :
% 7.75/5.72 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 7.75/5.72 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.72 ( Tree
% 7.75/5.72 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % deg_SUcn_Node
% 7.75/5.72 thf(fact_6141_VEBT_Oinject_I1_J,axiom,
% 7.75/5.72 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 7.75/5.72 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 7.75/5.72 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 7.75/5.72 = ( ( X11 = Y11 )
% 7.75/5.72 & ( X12 = Y12 )
% 7.75/5.72 & ( X13 = Y13 )
% 7.75/5.72 & ( X14 = Y14 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT.inject(1)
% 7.75/5.72 thf(fact_6142_powr__0,axiom,
% 7.75/5.72 ! [Z: real] :
% 7.75/5.72 ( ( powr_real @ zero_zero_real @ Z )
% 7.75/5.72 = zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % powr_0
% 7.75/5.72 thf(fact_6143_powr__eq__0__iff,axiom,
% 7.75/5.72 ! [W: real,Z: real] :
% 7.75/5.72 ( ( ( powr_real @ W @ Z )
% 7.75/5.72 = zero_zero_real )
% 7.75/5.72 = ( W = zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_eq_0_iff
% 7.75/5.72 thf(fact_6144_powr__one__eq__one,axiom,
% 7.75/5.72 ! [A: real] :
% 7.75/5.72 ( ( powr_real @ one_one_real @ A )
% 7.75/5.72 = one_one_real ) ).
% 7.75/5.72
% 7.75/5.72 % powr_one_eq_one
% 7.75/5.72 thf(fact_6145_zdvd1__eq,axiom,
% 7.75/5.72 ! [X: int] :
% 7.75/5.72 ( ( dvd_dvd_int @ X @ one_one_int )
% 7.75/5.72 = ( ( abs_abs_int @ X )
% 7.75/5.72 = one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % zdvd1_eq
% 7.75/5.72 thf(fact_6146_of__int__floor__cancel,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = X )
% 7.75/5.72 = ( ? [N3: int] :
% 7.75/5.72 ( X
% 7.75/5.72 = ( ring_1_of_int_real @ N3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_int_floor_cancel
% 7.75/5.72 thf(fact_6147_arctan__eq__zero__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( arctan @ X )
% 7.75/5.72 = zero_zero_real )
% 7.75/5.72 = ( X = zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % arctan_eq_zero_iff
% 7.75/5.72 thf(fact_6148_arctan__zero__zero,axiom,
% 7.75/5.72 ( ( arctan @ zero_zero_real )
% 7.75/5.72 = zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % arctan_zero_zero
% 7.75/5.72 thf(fact_6149_powr__zero__eq__one,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( X = zero_zero_real )
% 7.75/5.72 => ( ( powr_real @ X @ zero_zero_real )
% 7.75/5.72 = zero_zero_real ) )
% 7.75/5.72 & ( ( X != zero_zero_real )
% 7.75/5.72 => ( ( powr_real @ X @ zero_zero_real )
% 7.75/5.72 = one_one_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_zero_eq_one
% 7.75/5.72 thf(fact_6150_floor__zero,axiom,
% 7.75/5.72 ( ( archim3151403230148437115or_rat @ zero_zero_rat )
% 7.75/5.72 = zero_zero_int ) ).
% 7.75/5.72
% 7.75/5.72 % floor_zero
% 7.75/5.72 thf(fact_6151_floor__zero,axiom,
% 7.75/5.72 ( ( archim6058952711729229775r_real @ zero_zero_real )
% 7.75/5.72 = zero_zero_int ) ).
% 7.75/5.72
% 7.75/5.72 % floor_zero
% 7.75/5.72 thf(fact_6152_floor__numeral,axiom,
% 7.75/5.72 ! [V: num] :
% 7.75/5.72 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 7.75/5.72 = ( numeral_numeral_int @ V ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_numeral
% 7.75/5.72 thf(fact_6153_floor__numeral,axiom,
% 7.75/5.72 ! [V: num] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 7.75/5.72 = ( numeral_numeral_int @ V ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_numeral
% 7.75/5.72 thf(fact_6154_zabs__less__one__iff,axiom,
% 7.75/5.72 ! [Z: int] :
% 7.75/5.72 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 7.75/5.72 = ( Z = zero_zero_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % zabs_less_one_iff
% 7.75/5.72 thf(fact_6155_floor__one,axiom,
% 7.75/5.72 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 7.75/5.72 = one_one_int ) ).
% 7.75/5.72
% 7.75/5.72 % floor_one
% 7.75/5.72 thf(fact_6156_floor__one,axiom,
% 7.75/5.72 ( ( archim6058952711729229775r_real @ one_one_real )
% 7.75/5.72 = one_one_int ) ).
% 7.75/5.72
% 7.75/5.72 % floor_one
% 7.75/5.72 thf(fact_6157_powr__gt__zero,axiom,
% 7.75/5.72 ! [X: real,A: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 7.75/5.72 = ( X != zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_gt_zero
% 7.75/5.72 thf(fact_6158_powr__nonneg__iff,axiom,
% 7.75/5.72 ! [A: real,X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 7.75/5.72 = ( A = zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_nonneg_iff
% 7.75/5.72 thf(fact_6159_powr__less__cancel__iff,axiom,
% 7.75/5.72 ! [X: real,A: real,B: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 7.75/5.72 = ( ord_less_real @ A @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_less_cancel_iff
% 7.75/5.72 thf(fact_6160_arctan__less__zero__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 7.75/5.72 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % arctan_less_zero_iff
% 7.75/5.72 thf(fact_6161_zero__less__arctan__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 7.75/5.72 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_less_arctan_iff
% 7.75/5.72 thf(fact_6162_arctan__le__zero__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 7.75/5.72 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % arctan_le_zero_iff
% 7.75/5.72 thf(fact_6163_zero__le__arctan__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_le_arctan_iff
% 7.75/5.72 thf(fact_6164_powr__eq__one__iff,axiom,
% 7.75/5.72 ! [A: real,X: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ A )
% 7.75/5.72 => ( ( ( powr_real @ A @ X )
% 7.75/5.72 = one_one_real )
% 7.75/5.72 = ( X = zero_zero_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_eq_one_iff
% 7.75/5.72 thf(fact_6165_powr__one,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( powr_real @ X @ one_one_real )
% 7.75/5.72 = X ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_one
% 7.75/5.72 thf(fact_6166_powr__one__gt__zero__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( powr_real @ X @ one_one_real )
% 7.75/5.72 = X )
% 7.75/5.72 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_one_gt_zero_iff
% 7.75/5.72 thf(fact_6167_powr__le__cancel__iff,axiom,
% 7.75/5.72 ! [X: real,A: real,B: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 7.75/5.72 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_le_cancel_iff
% 7.75/5.72 thf(fact_6168_numeral__powr__numeral__real,axiom,
% 7.75/5.72 ! [M: num,N: num] :
% 7.75/5.72 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.72 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % numeral_powr_numeral_real
% 7.75/5.72 thf(fact_6169_zero__le__floor,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( ord_less_eq_rat @ zero_zero_rat @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_le_floor
% 7.75/5.72 thf(fact_6170_zero__le__floor,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_le_floor
% 7.75/5.72 thf(fact_6171_numeral__le__floor,axiom,
% 7.75/5.72 ! [V: num,X: rat] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % numeral_le_floor
% 7.75/5.72 thf(fact_6172_numeral__le__floor,axiom,
% 7.75/5.72 ! [V: num,X: real] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % numeral_le_floor
% 7.75/5.72 thf(fact_6173_floor__less__zero,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 7.75/5.72 = ( ord_less_rat @ X @ zero_zero_rat ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_zero
% 7.75/5.72 thf(fact_6174_floor__less__zero,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 7.75/5.72 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_zero
% 7.75/5.72 thf(fact_6175_floor__less__numeral,axiom,
% 7.75/5.72 ! [X: rat,V: num] :
% 7.75/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.72 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_numeral
% 7.75/5.72 thf(fact_6176_floor__less__numeral,axiom,
% 7.75/5.72 ! [X: real,V: num] :
% 7.75/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.72 = ( ord_less_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_numeral
% 7.75/5.72 thf(fact_6177_zero__less__floor,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_less_floor
% 7.75/5.72 thf(fact_6178_zero__less__floor,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_less_floor
% 7.75/5.72 thf(fact_6179_floor__le__zero,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 7.75/5.72 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_zero
% 7.75/5.72 thf(fact_6180_floor__le__zero,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 7.75/5.72 = ( ord_less_real @ X @ one_one_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_zero
% 7.75/5.72 thf(fact_6181_one__le__floor,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % one_le_floor
% 7.75/5.72 thf(fact_6182_one__le__floor,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % one_le_floor
% 7.75/5.72 thf(fact_6183_floor__less__one,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 7.75/5.72 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_one
% 7.75/5.72 thf(fact_6184_floor__less__one,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 7.75/5.72 = ( ord_less_real @ X @ one_one_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_one
% 7.75/5.72 thf(fact_6185_floor__neg__numeral,axiom,
% 7.75/5.72 ! [V: num] :
% 7.75/5.72 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_neg_numeral
% 7.75/5.72 thf(fact_6186_floor__neg__numeral,axiom,
% 7.75/5.72 ! [V: num] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_neg_numeral
% 7.75/5.72 thf(fact_6187_floor__diff__numeral,axiom,
% 7.75/5.72 ! [X: rat,V: num] :
% 7.75/5.72 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.72 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_diff_numeral
% 7.75/5.72 thf(fact_6188_floor__diff__numeral,axiom,
% 7.75/5.72 ! [X: real,V: num] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.72 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_diff_numeral
% 7.75/5.72 thf(fact_6189_floor__numeral__power,axiom,
% 7.75/5.72 ! [X: num,N: nat] :
% 7.75/5.72 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 7.75/5.72 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_numeral_power
% 7.75/5.72 thf(fact_6190_floor__numeral__power,axiom,
% 7.75/5.72 ! [X: num,N: nat] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 7.75/5.72 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_numeral_power
% 7.75/5.72 thf(fact_6191_floor__diff__one,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 7.75/5.72 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_diff_one
% 7.75/5.72 thf(fact_6192_floor__diff__one,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ one_one_real ) )
% 7.75/5.72 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_diff_one
% 7.75/5.72 thf(fact_6193_log__powr__cancel,axiom,
% 7.75/5.72 ! [A: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ( A != one_one_real )
% 7.75/5.72 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 7.75/5.72 = Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_powr_cancel
% 7.75/5.72 thf(fact_6194_powr__log__cancel,axiom,
% 7.75/5.72 ! [A: real,X: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ( A != one_one_real )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( powr_real @ A @ ( log @ A @ X ) )
% 7.75/5.72 = X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_log_cancel
% 7.75/5.72 thf(fact_6195_floor__divide__eq__div__numeral,axiom,
% 7.75/5.72 ! [A: num,B: num] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 7.75/5.72 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_eq_div_numeral
% 7.75/5.72 thf(fact_6196_powr__numeral,axiom,
% 7.75/5.72 ! [X: real,N: num] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 7.75/5.72 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_numeral
% 7.75/5.72 thf(fact_6197_numeral__less__floor,axiom,
% 7.75/5.72 ! [V: num,X: rat] :
% 7.75/5.72 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % numeral_less_floor
% 7.75/5.72 thf(fact_6198_numeral__less__floor,axiom,
% 7.75/5.72 ! [V: num,X: real] :
% 7.75/5.72 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % numeral_less_floor
% 7.75/5.72 thf(fact_6199_floor__le__numeral,axiom,
% 7.75/5.72 ! [X: rat,V: num] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.72 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_numeral
% 7.75/5.72 thf(fact_6200_floor__le__numeral,axiom,
% 7.75/5.72 ! [X: real,V: num] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.72 = ( ord_less_real @ X @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_numeral
% 7.75/5.72 thf(fact_6201_one__less__floor,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % one_less_floor
% 7.75/5.72 thf(fact_6202_one__less__floor,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % one_less_floor
% 7.75/5.72 thf(fact_6203_floor__le__one,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 7.75/5.72 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_one
% 7.75/5.72 thf(fact_6204_floor__le__one,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 7.75/5.72 = ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_one
% 7.75/5.72 thf(fact_6205_neg__numeral__le__floor,axiom,
% 7.75/5.72 ! [V: num,X: rat] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % neg_numeral_le_floor
% 7.75/5.72 thf(fact_6206_neg__numeral__le__floor,axiom,
% 7.75/5.72 ! [V: num,X: real] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % neg_numeral_le_floor
% 7.75/5.72 thf(fact_6207_floor__less__neg__numeral,axiom,
% 7.75/5.72 ! [X: rat,V: num] :
% 7.75/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.72 = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_neg_numeral
% 7.75/5.72 thf(fact_6208_floor__less__neg__numeral,axiom,
% 7.75/5.72 ! [X: real,V: num] :
% 7.75/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.72 = ( ord_less_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_neg_numeral
% 7.75/5.72 thf(fact_6209_floor__one__divide__eq__div__numeral,axiom,
% 7.75/5.72 ! [B: num] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 7.75/5.72 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_one_divide_eq_div_numeral
% 7.75/5.72 thf(fact_6210_floor__minus__divide__eq__div__numeral,axiom,
% 7.75/5.72 ! [A: num,B: num] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 7.75/5.72 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_minus_divide_eq_div_numeral
% 7.75/5.72 thf(fact_6211_neg__numeral__less__floor,axiom,
% 7.75/5.72 ! [V: num,X: rat] :
% 7.75/5.72 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % neg_numeral_less_floor
% 7.75/5.72 thf(fact_6212_neg__numeral__less__floor,axiom,
% 7.75/5.72 ! [V: num,X: real] :
% 7.75/5.72 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % neg_numeral_less_floor
% 7.75/5.72 thf(fact_6213_floor__le__neg__numeral,axiom,
% 7.75/5.72 ! [X: rat,V: num] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.72 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_neg_numeral
% 7.75/5.72 thf(fact_6214_floor__le__neg__numeral,axiom,
% 7.75/5.72 ! [X: real,V: num] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.72 = ( ord_less_real @ X @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_neg_numeral
% 7.75/5.72 thf(fact_6215_square__powr__half,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.72 = ( abs_abs_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % square_powr_half
% 7.75/5.72 thf(fact_6216_floor__minus__one__divide__eq__div__numeral,axiom,
% 7.75/5.72 ! [B: num] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 7.75/5.72 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_minus_one_divide_eq_div_numeral
% 7.75/5.72 thf(fact_6217_powr__powr,axiom,
% 7.75/5.72 ! [X: real,A: real,B: real] :
% 7.75/5.72 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 7.75/5.72 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_powr
% 7.75/5.72 thf(fact_6218_arctan__monotone,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ X @ Y )
% 7.75/5.72 => ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % arctan_monotone
% 7.75/5.72 thf(fact_6219_arctan__less__iff,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 7.75/5.72 = ( ord_less_real @ X @ Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % arctan_less_iff
% 7.75/5.72 thf(fact_6220_floor__less__cancel,axiom,
% 7.75/5.72 ! [X: rat,Y: rat] :
% 7.75/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) )
% 7.75/5.72 => ( ord_less_rat @ X @ Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_cancel
% 7.75/5.72 thf(fact_6221_floor__less__cancel,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) )
% 7.75/5.72 => ( ord_less_real @ X @ Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_cancel
% 7.75/5.72 thf(fact_6222_powr__non__neg,axiom,
% 7.75/5.72 ! [A: real,X: real] :
% 7.75/5.72 ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % powr_non_neg
% 7.75/5.72 thf(fact_6223_powr__less__mono2__neg,axiom,
% 7.75/5.72 ! [A: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ X @ Y )
% 7.75/5.72 => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_less_mono2_neg
% 7.75/5.72 thf(fact_6224_powr__ge__pzero,axiom,
% 7.75/5.72 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_ge_pzero
% 7.75/5.72 thf(fact_6225_powr__mono2,axiom,
% 7.75/5.72 ! [A: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ X @ Y )
% 7.75/5.72 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_mono2
% 7.75/5.72 thf(fact_6226_powr__less__mono,axiom,
% 7.75/5.72 ! [A: real,B: real,X: real] :
% 7.75/5.72 ( ( ord_less_real @ A @ B )
% 7.75/5.72 => ( ( ord_less_real @ one_one_real @ X )
% 7.75/5.72 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_less_mono
% 7.75/5.72 thf(fact_6227_powr__less__cancel,axiom,
% 7.75/5.72 ! [X: real,A: real,B: real] :
% 7.75/5.72 ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 7.75/5.72 => ( ( ord_less_real @ one_one_real @ X )
% 7.75/5.72 => ( ord_less_real @ A @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_less_cancel
% 7.75/5.72 thf(fact_6228_powr__mono,axiom,
% 7.75/5.72 ! [A: real,B: real,X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ A @ B )
% 7.75/5.72 => ( ( ord_less_eq_real @ one_one_real @ X )
% 7.75/5.72 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_mono
% 7.75/5.72 thf(fact_6229_abs__zmult__eq__1,axiom,
% 7.75/5.72 ! [M: int,N: int] :
% 7.75/5.72 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 7.75/5.72 = one_one_int )
% 7.75/5.72 => ( ( abs_abs_int @ M )
% 7.75/5.72 = one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_zmult_eq_1
% 7.75/5.72 thf(fact_6230_abs__div,axiom,
% 7.75/5.72 ! [Y: int,X: int] :
% 7.75/5.72 ( ( dvd_dvd_int @ Y @ X )
% 7.75/5.72 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 7.75/5.72 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_div
% 7.75/5.72 thf(fact_6231_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 7.75/5.72 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 7.75/5.72 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.naive_member.simps(2)
% 7.75/5.72 thf(fact_6232_floor__less__iff,axiom,
% 7.75/5.72 ! [X: rat,Z: int] :
% 7.75/5.72 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 7.75/5.72 = ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_iff
% 7.75/5.72 thf(fact_6233_floor__less__iff,axiom,
% 7.75/5.72 ! [X: real,Z: int] :
% 7.75/5.72 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 7.75/5.72 = ( ord_less_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_less_iff
% 7.75/5.72 thf(fact_6234_floor__add__int,axiom,
% 7.75/5.72 ! [X: rat,Z: int] :
% 7.75/5.72 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 7.75/5.72 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_add_int
% 7.75/5.72 thf(fact_6235_floor__add__int,axiom,
% 7.75/5.72 ! [X: real,Z: int] :
% 7.75/5.72 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 7.75/5.72 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_add_int
% 7.75/5.72 thf(fact_6236_int__add__floor,axiom,
% 7.75/5.72 ! [Z: int,X: rat] :
% 7.75/5.72 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % int_add_floor
% 7.75/5.72 thf(fact_6237_int__add__floor,axiom,
% 7.75/5.72 ! [Z: int,X: real] :
% 7.75/5.72 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % int_add_floor
% 7.75/5.72 thf(fact_6238_le__floor__add,axiom,
% 7.75/5.72 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % le_floor_add
% 7.75/5.72 thf(fact_6239_le__floor__add,axiom,
% 7.75/5.72 ! [X: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % le_floor_add
% 7.75/5.72 thf(fact_6240_powr__mono2_H,axiom,
% 7.75/5.72 ! [A: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ X @ Y )
% 7.75/5.72 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_mono2'
% 7.75/5.72 thf(fact_6241_powr__less__mono2,axiom,
% 7.75/5.72 ! [A: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ X @ Y )
% 7.75/5.72 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_less_mono2
% 7.75/5.72 thf(fact_6242_floor__power,axiom,
% 7.75/5.72 ! [X: real,N: nat] :
% 7.75/5.72 ( ( X
% 7.75/5.72 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 7.75/5.72 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X @ N ) )
% 7.75/5.72 = ( power_power_int @ ( archim6058952711729229775r_real @ X ) @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_power
% 7.75/5.72 thf(fact_6243_powr__inj,axiom,
% 7.75/5.72 ! [A: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ( A != one_one_real )
% 7.75/5.72 => ( ( ( powr_real @ A @ X )
% 7.75/5.72 = ( powr_real @ A @ Y ) )
% 7.75/5.72 = ( X = Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_inj
% 7.75/5.72 thf(fact_6244_gr__one__powr,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.72 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % gr_one_powr
% 7.75/5.72 thf(fact_6245_floor__divide__of__int__eq,axiom,
% 7.75/5.72 ! [K: int,L: int] :
% 7.75/5.72 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 7.75/5.72 = ( divide_divide_int @ K @ L ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_of_int_eq
% 7.75/5.72 thf(fact_6246_floor__divide__of__int__eq,axiom,
% 7.75/5.72 ! [K: int,L: int] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 7.75/5.72 = ( divide_divide_int @ K @ L ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_of_int_eq
% 7.75/5.72 thf(fact_6247_powr__le1,axiom,
% 7.75/5.72 ! [A: real,X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.75/5.72 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_le1
% 7.75/5.72 thf(fact_6248_powr__mono__both,axiom,
% 7.75/5.72 ! [A: real,B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ( ord_less_eq_real @ A @ B )
% 7.75/5.72 => ( ( ord_less_eq_real @ one_one_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ X @ Y )
% 7.75/5.72 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_mono_both
% 7.75/5.72 thf(fact_6249_ge__one__powr__ge__zero,axiom,
% 7.75/5.72 ! [X: real,A: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ one_one_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ge_one_powr_ge_zero
% 7.75/5.72 thf(fact_6250_powr__divide,axiom,
% 7.75/5.72 ! [X: real,Y: real,A: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.72 => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 7.75/5.72 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_divide
% 7.75/5.72 thf(fact_6251_powr__mult,axiom,
% 7.75/5.72 ! [X: real,Y: real,A: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.75/5.72 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 7.75/5.72 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_mult
% 7.75/5.72 thf(fact_6252_divide__powr__uminus,axiom,
% 7.75/5.72 ! [A: real,B: real,C: real] :
% 7.75/5.72 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 7.75/5.72 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % divide_powr_uminus
% 7.75/5.72 thf(fact_6253_log__base__powr,axiom,
% 7.75/5.72 ! [A: real,B: real,X: real] :
% 7.75/5.72 ( ( A != zero_zero_real )
% 7.75/5.72 => ( ( log @ ( powr_real @ A @ B ) @ X )
% 7.75/5.72 = ( divide_divide_real @ ( log @ A @ X ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_base_powr
% 7.75/5.72 thf(fact_6254_log__powr,axiom,
% 7.75/5.72 ! [X: real,B: real,Y: real] :
% 7.75/5.72 ( ( X != zero_zero_real )
% 7.75/5.72 => ( ( log @ B @ ( powr_real @ X @ Y ) )
% 7.75/5.72 = ( times_times_real @ Y @ ( log @ B @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_powr
% 7.75/5.72 thf(fact_6255_ln__powr,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( X != zero_zero_real )
% 7.75/5.72 => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 7.75/5.72 = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ln_powr
% 7.75/5.72 thf(fact_6256_zabs__def,axiom,
% 7.75/5.72 ( abs_abs_int
% 7.75/5.72 = ( ^ [I2: int] : ( if_int @ ( ord_less_int @ I2 @ zero_zero_int ) @ ( uminus_uminus_int @ I2 ) @ I2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % zabs_def
% 7.75/5.72 thf(fact_6257_powr__add,axiom,
% 7.75/5.72 ! [X: real,A: real,B: real] :
% 7.75/5.72 ( ( powr_real @ X @ ( plus_plus_real @ A @ B ) )
% 7.75/5.72 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_add
% 7.75/5.72 thf(fact_6258_abs__mod__less,axiom,
% 7.75/5.72 ! [L: int,K: int] :
% 7.75/5.72 ( ( L != zero_zero_int )
% 7.75/5.72 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % abs_mod_less
% 7.75/5.72 thf(fact_6259_powr__diff,axiom,
% 7.75/5.72 ! [W: real,Z1: real,Z22: real] :
% 7.75/5.72 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 7.75/5.72 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_diff
% 7.75/5.72 thf(fact_6260_dvd__imp__le__int,axiom,
% 7.75/5.72 ! [I: int,D2: int] :
% 7.75/5.72 ( ( I != zero_zero_int )
% 7.75/5.72 => ( ( dvd_dvd_int @ D2 @ I )
% 7.75/5.72 => ( ord_less_eq_int @ ( abs_abs_int @ D2 ) @ ( abs_abs_int @ I ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % dvd_imp_le_int
% 7.75/5.72 thf(fact_6261_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,
% 7.75/5.72 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 7.75/5.72 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(2)
% 7.75/5.72 thf(fact_6262_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 7.75/5.72 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 7.75/5.72 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.membermima.simps(2)
% 7.75/5.72 thf(fact_6263_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I4_J,axiom,
% 7.75/5.72 ! [Uy: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 7.75/5.72 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va2 ) @ Vb )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(4)
% 7.75/5.72 thf(fact_6264_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I4_J,axiom,
% 7.75/5.72 ! [Uy: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 7.75/5.72 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va2 ) @ Vb )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(4)
% 7.75/5.72 thf(fact_6265_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I3_J,axiom,
% 7.75/5.72 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 7.75/5.72 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va2 )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(3)
% 7.75/5.72 thf(fact_6266_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I3_J,axiom,
% 7.75/5.72 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 7.75/5.72 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va2 )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(3)
% 7.75/5.72 thf(fact_6267_one__add__floor,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 7.75/5.72 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % one_add_floor
% 7.75/5.72 thf(fact_6268_one__add__floor,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 7.75/5.72 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % one_add_floor
% 7.75/5.72 thf(fact_6269_floor__log__eq__powr__iff,axiom,
% 7.75/5.72 ! [X: real,B: real,K: int] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 7.75/5.72 = K )
% 7.75/5.72 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 7.75/5.72 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_log_eq_powr_iff
% 7.75/5.72 thf(fact_6270_floor__divide__of__nat__eq,axiom,
% 7.75/5.72 ! [M: nat,N: nat] :
% 7.75/5.72 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 7.75/5.72 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_of_nat_eq
% 7.75/5.72 thf(fact_6271_floor__divide__of__nat__eq,axiom,
% 7.75/5.72 ! [M: nat,N: nat] :
% 7.75/5.72 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 7.75/5.72 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_of_nat_eq
% 7.75/5.72 thf(fact_6272_powr__realpow,axiom,
% 7.75/5.72 ! [X: real,N: nat] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.72 = ( power_power_real @ X @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_realpow
% 7.75/5.72 thf(fact_6273_less__log__iff,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ Y @ ( log @ B @ X ) )
% 7.75/5.72 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % less_log_iff
% 7.75/5.72 thf(fact_6274_log__less__iff,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ ( log @ B @ X ) @ Y )
% 7.75/5.72 = ( ord_less_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_less_iff
% 7.75/5.72 thf(fact_6275_less__powr__iff,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y ) )
% 7.75/5.72 = ( ord_less_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % less_powr_iff
% 7.75/5.72 thf(fact_6276_powr__less__iff,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X )
% 7.75/5.72 = ( ord_less_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_less_iff
% 7.75/5.72 thf(fact_6277_ceiling__altdef,axiom,
% 7.75/5.72 ( archim7802044766580827645g_real
% 7.75/5.72 = ( ^ [X2: real] :
% 7.75/5.72 ( if_int
% 7.75/5.72 @ ( X2
% 7.75/5.72 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) )
% 7.75/5.72 @ ( archim6058952711729229775r_real @ X2 )
% 7.75/5.72 @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ceiling_altdef
% 7.75/5.72 thf(fact_6278_ceiling__diff__floor__le__1,axiom,
% 7.75/5.72 ! [X: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) @ one_one_int ) ).
% 7.75/5.72
% 7.75/5.72 % ceiling_diff_floor_le_1
% 7.75/5.72 thf(fact_6279_floor__eq,axiom,
% 7.75/5.72 ! [N: int,X: real] :
% 7.75/5.72 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 7.75/5.72 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 7.75/5.72 => ( ( archim6058952711729229775r_real @ X )
% 7.75/5.72 = N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_eq
% 7.75/5.72 thf(fact_6280_real__of__int__floor__add__one__gt,axiom,
% 7.75/5.72 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % real_of_int_floor_add_one_gt
% 7.75/5.72 thf(fact_6281_real__of__int__floor__add__one__ge,axiom,
% 7.75/5.72 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % real_of_int_floor_add_one_ge
% 7.75/5.72 thf(fact_6282_real__of__int__floor__gt__diff__one,axiom,
% 7.75/5.72 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % real_of_int_floor_gt_diff_one
% 7.75/5.72 thf(fact_6283_real__of__int__floor__ge__diff__one,axiom,
% 7.75/5.72 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % real_of_int_floor_ge_diff_one
% 7.75/5.72 thf(fact_6284_zdvd__mult__cancel1,axiom,
% 7.75/5.72 ! [M: int,N: int] :
% 7.75/5.72 ( ( M != zero_zero_int )
% 7.75/5.72 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 7.75/5.72 = ( ( abs_abs_int @ N )
% 7.75/5.72 = one_one_int ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % zdvd_mult_cancel1
% 7.75/5.72 thf(fact_6285_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,
% 7.75/5.72 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 7.75/5.72 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(3)
% 7.75/5.72 thf(fact_6286_floor__split,axiom,
% 7.75/5.72 ! [P: int > $o,T: rat] :
% 7.75/5.72 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 7.75/5.72 = ( ! [I2: int] :
% 7.75/5.72 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I2 ) @ T )
% 7.75/5.72 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) ) )
% 7.75/5.72 => ( P @ I2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_split
% 7.75/5.72 thf(fact_6287_floor__split,axiom,
% 7.75/5.72 ! [P: int > $o,T: real] :
% 7.75/5.72 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 7.75/5.72 = ( ! [I2: int] :
% 7.75/5.72 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I2 ) @ T )
% 7.75/5.72 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I2 ) @ one_one_real ) ) )
% 7.75/5.72 => ( P @ I2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_split
% 7.75/5.72 thf(fact_6288_floor__eq__iff,axiom,
% 7.75/5.72 ! [X: rat,A: int] :
% 7.75/5.72 ( ( ( archim3151403230148437115or_rat @ X )
% 7.75/5.72 = A )
% 7.75/5.72 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 7.75/5.72 & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_eq_iff
% 7.75/5.72 thf(fact_6289_floor__eq__iff,axiom,
% 7.75/5.72 ! [X: real,A: int] :
% 7.75/5.72 ( ( ( archim6058952711729229775r_real @ X )
% 7.75/5.72 = A )
% 7.75/5.72 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X )
% 7.75/5.72 & ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_eq_iff
% 7.75/5.72 thf(fact_6290_floor__unique,axiom,
% 7.75/5.72 ! [Z: int,X: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 7.75/5.72 => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 7.75/5.72 => ( ( archim3151403230148437115or_rat @ X )
% 7.75/5.72 = Z ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_unique
% 7.75/5.72 thf(fact_6291_floor__unique,axiom,
% 7.75/5.72 ! [Z: int,X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X )
% 7.75/5.72 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 7.75/5.72 => ( ( archim6058952711729229775r_real @ X )
% 7.75/5.72 = Z ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_unique
% 7.75/5.72 thf(fact_6292_powr__minus__divide,axiom,
% 7.75/5.72 ! [X: real,A: real] :
% 7.75/5.72 ( ( powr_real @ X @ ( uminus_uminus_real @ A ) )
% 7.75/5.72 = ( divide_divide_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_minus_divide
% 7.75/5.72 thf(fact_6293_less__floor__iff,axiom,
% 7.75/5.72 ! [Z: int,X: rat] :
% 7.75/5.72 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 7.75/5.72 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % less_floor_iff
% 7.75/5.72 thf(fact_6294_less__floor__iff,axiom,
% 7.75/5.72 ! [Z: int,X: real] :
% 7.75/5.72 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % less_floor_iff
% 7.75/5.72 thf(fact_6295_floor__le__iff,axiom,
% 7.75/5.72 ! [X: rat,Z: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 7.75/5.72 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_iff
% 7.75/5.72 thf(fact_6296_floor__le__iff,axiom,
% 7.75/5.72 ! [X: real,Z: int] :
% 7.75/5.72 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 7.75/5.72 = ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_le_iff
% 7.75/5.72 thf(fact_6297_le__mult__floor,axiom,
% 7.75/5.72 ! [A: rat,B: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 7.75/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 7.75/5.72 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % le_mult_floor
% 7.75/5.72 thf(fact_6298_le__mult__floor,axiom,
% 7.75/5.72 ! [A: real,B: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 7.75/5.72 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % le_mult_floor
% 7.75/5.72 thf(fact_6299_binomial__antimono,axiom,
% 7.75/5.72 ! [K: nat,K4: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ K @ K4 )
% 7.75/5.72 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 7.75/5.72 => ( ( ord_less_eq_nat @ K4 @ N )
% 7.75/5.72 => ( ord_less_eq_nat @ ( binomial @ N @ K4 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_antimono
% 7.75/5.72 thf(fact_6300_binomial__maximum,axiom,
% 7.75/5.72 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_maximum
% 7.75/5.72 thf(fact_6301_binomial__maximum_H,axiom,
% 7.75/5.72 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_maximum'
% 7.75/5.72 thf(fact_6302_binomial__mono,axiom,
% 7.75/5.72 ! [K: nat,K4: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ K @ K4 )
% 7.75/5.72 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) @ N )
% 7.75/5.72 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K4 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_mono
% 7.75/5.72 thf(fact_6303_floor__correct,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 7.75/5.72 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_correct
% 7.75/5.72 thf(fact_6304_floor__correct,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X )
% 7.75/5.72 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_correct
% 7.75/5.72 thf(fact_6305_powr__neg__one,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.72 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_neg_one
% 7.75/5.72 thf(fact_6306_powr__mult__base,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 7.75/5.72 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_mult_base
% 7.75/5.72 thf(fact_6307_le__log__iff,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % le_log_iff
% 7.75/5.72 thf(fact_6308_log__le__iff,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 7.75/5.72 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_le_iff
% 7.75/5.72 thf(fact_6309_le__powr__iff,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % le_powr_iff
% 7.75/5.72 thf(fact_6310_powr__le__iff,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ B )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 7.75/5.72 = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_le_iff
% 7.75/5.72 thf(fact_6311_floor__eq2,axiom,
% 7.75/5.72 ! [N: int,X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 7.75/5.72 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 7.75/5.72 => ( ( archim6058952711729229775r_real @ X )
% 7.75/5.72 = N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_eq2
% 7.75/5.72 thf(fact_6312_floor__divide__real__eq__div,axiom,
% 7.75/5.72 ! [B: int,A: real] :
% 7.75/5.72 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.75/5.72 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 7.75/5.72 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_real_eq_div
% 7.75/5.72 thf(fact_6313_even__abs__add__iff,axiom,
% 7.75/5.72 ! [K: int,L: int] :
% 7.75/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 7.75/5.72 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % even_abs_add_iff
% 7.75/5.72 thf(fact_6314_even__add__abs__iff,axiom,
% 7.75/5.72 ! [K: int,L: int] :
% 7.75/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 7.75/5.72 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % even_add_abs_iff
% 7.75/5.72 thf(fact_6315_floor__divide__lower,axiom,
% 7.75/5.72 ! [Q3: rat,P4: rat] :
% 7.75/5.72 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 7.75/5.72 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q3 ) ) ) @ Q3 ) @ P4 ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_lower
% 7.75/5.72 thf(fact_6316_floor__divide__lower,axiom,
% 7.75/5.72 ! [Q3: real,P4: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 7.75/5.72 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P4 @ Q3 ) ) ) @ Q3 ) @ P4 ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_lower
% 7.75/5.72 thf(fact_6317_binomial__less__binomial__Suc,axiom,
% 7.75/5.72 ! [K: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.72 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_less_binomial_Suc
% 7.75/5.72 thf(fact_6318_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,
% 7.75/5.72 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 7.75/5.72 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X )
% 7.75/5.72 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(2)
% 7.75/5.72 thf(fact_6319_binomial__strict__antimono,axiom,
% 7.75/5.72 ! [K: nat,K4: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_nat @ K @ K4 )
% 7.75/5.72 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 7.75/5.72 => ( ( ord_less_eq_nat @ K4 @ N )
% 7.75/5.72 => ( ord_less_nat @ ( binomial @ N @ K4 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_strict_antimono
% 7.75/5.72 thf(fact_6320_binomial__strict__mono,axiom,
% 7.75/5.72 ! [K: nat,K4: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_nat @ K @ K4 )
% 7.75/5.72 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) @ N )
% 7.75/5.72 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K4 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_strict_mono
% 7.75/5.72 thf(fact_6321_central__binomial__odd,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.72 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % central_binomial_odd
% 7.75/5.72 thf(fact_6322_ln__powr__bound,axiom,
% 7.75/5.72 ! [X: real,A: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ one_one_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ln_powr_bound
% 7.75/5.72 thf(fact_6323_ln__powr__bound2,axiom,
% 7.75/5.72 ! [X: real,A: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ X )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.72 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ln_powr_bound2
% 7.75/5.72 thf(fact_6324_log__add__eq__powr,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.72 => ( ( B != one_one_real )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y )
% 7.75/5.72 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_add_eq_powr
% 7.75/5.72 thf(fact_6325_add__log__eq__powr,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.72 => ( ( B != one_one_real )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( plus_plus_real @ Y @ ( log @ B @ X ) )
% 7.75/5.72 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_log_eq_powr
% 7.75/5.72 thf(fact_6326_minus__log__eq__powr,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.72 => ( ( B != one_one_real )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( minus_minus_real @ Y @ ( log @ B @ X ) )
% 7.75/5.72 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % minus_log_eq_powr
% 7.75/5.72 thf(fact_6327_nat__intermed__int__val,axiom,
% 7.75/5.72 ! [M: nat,N: nat,F: nat > int,K: int] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ( ord_less_eq_nat @ M @ I3 )
% 7.75/5.72 & ( ord_less_nat @ I3 @ N ) )
% 7.75/5.72 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 7.75/5.72 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.72 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 7.75/5.72 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 7.75/5.72 => ? [I3: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ M @ I3 )
% 7.75/5.72 & ( ord_less_eq_nat @ I3 @ N )
% 7.75/5.72 & ( ( F @ I3 )
% 7.75/5.72 = K ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nat_intermed_int_val
% 7.75/5.72 thf(fact_6328_incr__lemma,axiom,
% 7.75/5.72 ! [D2: int,Z: int,X: int] :
% 7.75/5.72 ( ( ord_less_int @ zero_zero_int @ D2 )
% 7.75/5.72 => ( 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 ) @ D2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % incr_lemma
% 7.75/5.72 thf(fact_6329_decr__lemma,axiom,
% 7.75/5.72 ! [D2: int,X: int,Z: int] :
% 7.75/5.72 ( ( ord_less_int @ zero_zero_int @ D2 )
% 7.75/5.72 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 7.75/5.72
% 7.75/5.72 % decr_lemma
% 7.75/5.72 thf(fact_6330_floor__divide__upper,axiom,
% 7.75/5.72 ! [Q3: rat,P4: rat] :
% 7.75/5.72 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 7.75/5.72 => ( ord_less_rat @ P4 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_upper
% 7.75/5.72 thf(fact_6331_floor__divide__upper,axiom,
% 7.75/5.72 ! [Q3: real,P4: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 7.75/5.72 => ( ord_less_real @ P4 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P4 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_divide_upper
% 7.75/5.72 thf(fact_6332_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,
% 7.75/5.72 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.72 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.72 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(4)
% 7.75/5.72 thf(fact_6333_round__def,axiom,
% 7.75/5.72 ( archim7778729529865785530nd_rat
% 7.75/5.72 = ( ^ [X2: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % round_def
% 7.75/5.72 thf(fact_6334_round__def,axiom,
% 7.75/5.72 ( archim8280529875227126926d_real
% 7.75/5.72 = ( ^ [X2: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % round_def
% 7.75/5.72 thf(fact_6335_log__minus__eq__powr,axiom,
% 7.75/5.72 ! [B: real,X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ B )
% 7.75/5.72 => ( ( B != one_one_real )
% 7.75/5.72 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y )
% 7.75/5.72 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_minus_eq_powr
% 7.75/5.72 thf(fact_6336_nat__ivt__aux,axiom,
% 7.75/5.72 ! [N: nat,F: nat > int,K: int] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ N )
% 7.75/5.72 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 7.75/5.72 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 7.75/5.72 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 7.75/5.72 => ? [I3: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ I3 @ N )
% 7.75/5.72 & ( ( F @ I3 )
% 7.75/5.72 = K ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nat_ivt_aux
% 7.75/5.72 thf(fact_6337_powr__neg__numeral,axiom,
% 7.75/5.72 ! [X: real,N: num] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.72 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_neg_numeral
% 7.75/5.72 thf(fact_6338_nat0__intermed__int__val,axiom,
% 7.75/5.72 ! [N: nat,F: nat > int,K: int] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ N )
% 7.75/5.72 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 7.75/5.72 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 7.75/5.72 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 7.75/5.72 => ? [I3: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ I3 @ N )
% 7.75/5.72 & ( ( F @ I3 )
% 7.75/5.72 = K ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nat0_intermed_int_val
% 7.75/5.72 thf(fact_6339_arctan__add,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.75/5.72 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 7.75/5.72 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 7.75/5.72 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % arctan_add
% 7.75/5.72 thf(fact_6340_floor__log2__div2,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.75/5.72 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 7.75/5.72 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_log2_div2
% 7.75/5.72 thf(fact_6341_floor__log__nat__eq__if,axiom,
% 7.75/5.72 ! [B: nat,N: nat,K: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 7.75/5.72 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 7.75/5.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 7.75/5.72 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 7.75/5.72 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_log_nat_eq_if
% 7.75/5.72 thf(fact_6342_zero__less__binomial__iff,axiom,
% 7.75/5.72 ! [N: nat,K: nat] :
% 7.75/5.72 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 7.75/5.72 = ( ord_less_eq_nat @ K @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_less_binomial_iff
% 7.75/5.72 thf(fact_6343_choose__two,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.72 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % choose_two
% 7.75/5.72 thf(fact_6344_both__member__options__ding,axiom,
% 7.75/5.72 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 7.75/5.72 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 7.75/5.72 => ( ( 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 ) ) ) ) )
% 7.75/5.72 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % both_member_options_ding
% 7.75/5.72 thf(fact_6345_binomial__n__0,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( binomial @ N @ zero_zero_nat )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_n_0
% 7.75/5.72 thf(fact_6346_binomial__Suc__Suc,axiom,
% 7.75/5.72 ! [N: nat,K: nat] :
% 7.75/5.72 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 7.75/5.72 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_Suc_Suc
% 7.75/5.72 thf(fact_6347_binomial__eq__0__iff,axiom,
% 7.75/5.72 ! [N: nat,K: nat] :
% 7.75/5.72 ( ( ( binomial @ N @ K )
% 7.75/5.72 = zero_zero_nat )
% 7.75/5.72 = ( ord_less_nat @ N @ K ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_eq_0_iff
% 7.75/5.72 thf(fact_6348_intind,axiom,
% 7.75/5.72 ! [I: nat,N: nat,P: nat > $o,X: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I @ N )
% 7.75/5.72 => ( ( P @ X )
% 7.75/5.72 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % intind
% 7.75/5.72 thf(fact_6349_intind,axiom,
% 7.75/5.72 ! [I: nat,N: nat,P: vEBT_VEBTi > $o,X: vEBT_VEBTi] :
% 7.75/5.72 ( ( ord_less_nat @ I @ N )
% 7.75/5.72 => ( ( P @ X )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBTi @ ( replicate_VEBT_VEBTi @ N @ X ) @ I ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % intind
% 7.75/5.72 thf(fact_6350_intind,axiom,
% 7.75/5.72 ! [I: nat,N: nat,P: int > $o,X: int] :
% 7.75/5.72 ( ( ord_less_nat @ I @ N )
% 7.75/5.72 => ( ( P @ X )
% 7.75/5.72 => ( P @ ( nth_int @ ( replicate_int @ N @ X ) @ I ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % intind
% 7.75/5.72 thf(fact_6351_intind,axiom,
% 7.75/5.72 ! [I: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 7.75/5.72 ( ( ord_less_nat @ I @ N )
% 7.75/5.72 => ( ( P @ X )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % intind
% 7.75/5.72 thf(fact_6352_binomial__Suc__n,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( binomial @ ( suc @ N ) @ N )
% 7.75/5.72 = ( suc @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_Suc_n
% 7.75/5.72 thf(fact_6353_binomial__n__n,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( binomial @ N @ N )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_n_n
% 7.75/5.72 thf(fact_6354_binomial__0__Suc,axiom,
% 7.75/5.72 ! [K: nat] :
% 7.75/5.72 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 7.75/5.72 = zero_zero_nat ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_0_Suc
% 7.75/5.72 thf(fact_6355_binomial__1,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_1
% 7.75/5.72 thf(fact_6356_nth__replicate,axiom,
% 7.75/5.72 ! [I: nat,N: nat,X: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I @ N )
% 7.75/5.72 => ( ( nth_nat @ ( replicate_nat @ N @ X ) @ I )
% 7.75/5.72 = X ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_replicate
% 7.75/5.72 thf(fact_6357_nth__replicate,axiom,
% 7.75/5.72 ! [I: nat,N: nat,X: vEBT_VEBTi] :
% 7.75/5.72 ( ( ord_less_nat @ I @ N )
% 7.75/5.72 => ( ( nth_VEBT_VEBTi @ ( replicate_VEBT_VEBTi @ N @ X ) @ I )
% 7.75/5.72 = X ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_replicate
% 7.75/5.72 thf(fact_6358_nth__replicate,axiom,
% 7.75/5.72 ! [I: nat,N: nat,X: int] :
% 7.75/5.72 ( ( ord_less_nat @ I @ N )
% 7.75/5.72 => ( ( nth_int @ ( replicate_int @ N @ X ) @ I )
% 7.75/5.72 = X ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_replicate
% 7.75/5.72 thf(fact_6359_nth__replicate,axiom,
% 7.75/5.72 ! [I: nat,N: nat,X: vEBT_VEBT] :
% 7.75/5.72 ( ( ord_less_nat @ I @ N )
% 7.75/5.72 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I )
% 7.75/5.72 = X ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_replicate
% 7.75/5.72 thf(fact_6360_choose__one,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( binomial @ N @ one_one_nat )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % choose_one
% 7.75/5.72 thf(fact_6361_binomial__eq__0,axiom,
% 7.75/5.72 ! [N: nat,K: nat] :
% 7.75/5.72 ( ( ord_less_nat @ N @ K )
% 7.75/5.72 => ( ( binomial @ N @ K )
% 7.75/5.72 = zero_zero_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_eq_0
% 7.75/5.72 thf(fact_6362_Suc__times__binomial,axiom,
% 7.75/5.72 ! [K: nat,N: nat] :
% 7.75/5.72 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 7.75/5.72 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Suc_times_binomial
% 7.75/5.72 thf(fact_6363_Suc__times__binomial__eq,axiom,
% 7.75/5.72 ! [N: nat,K: nat] :
% 7.75/5.72 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 7.75/5.72 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Suc_times_binomial_eq
% 7.75/5.72 thf(fact_6364_choose__mult__lemma,axiom,
% 7.75/5.72 ! [M: nat,R2: nat,K: nat] :
% 7.75/5.72 ( ( 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 ) )
% 7.75/5.72 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % choose_mult_lemma
% 7.75/5.72 thf(fact_6365_binomial__le__pow,axiom,
% 7.75/5.72 ! [R2: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ R2 @ N )
% 7.75/5.72 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_le_pow
% 7.75/5.72 thf(fact_6366_zero__less__binomial,axiom,
% 7.75/5.72 ! [K: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.72 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % zero_less_binomial
% 7.75/5.72 thf(fact_6367_Suc__times__binomial__add,axiom,
% 7.75/5.72 ! [A: nat,B: nat] :
% 7.75/5.72 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 7.75/5.72 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Suc_times_binomial_add
% 7.75/5.72 thf(fact_6368_binomial__Suc__Suc__eq__times,axiom,
% 7.75/5.72 ! [N: nat,K: nat] :
% 7.75/5.72 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 7.75/5.72 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_Suc_Suc_eq_times
% 7.75/5.72 thf(fact_6369_choose__mult,axiom,
% 7.75/5.72 ! [K: nat,M: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ K @ M )
% 7.75/5.72 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.72 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 7.75/5.72 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % choose_mult
% 7.75/5.72 thf(fact_6370_binomial__absorb__comp,axiom,
% 7.75/5.72 ! [N: nat,K: nat] :
% 7.75/5.72 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 7.75/5.72 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_absorb_comp
% 7.75/5.72 thf(fact_6371_binomial__absorption,axiom,
% 7.75/5.72 ! [K: nat,N: nat] :
% 7.75/5.72 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 7.75/5.72 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_absorption
% 7.75/5.72 thf(fact_6372_binomial__ge__n__over__k__pow__k,axiom,
% 7.75/5.72 ! [K: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.72 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_ge_n_over_k_pow_k
% 7.75/5.72 thf(fact_6373_binomial__ge__n__over__k__pow__k,axiom,
% 7.75/5.72 ! [K: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.72 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_ge_n_over_k_pow_k
% 7.75/5.72 thf(fact_6374_binomial__le__pow2,axiom,
% 7.75/5.72 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_le_pow2
% 7.75/5.72 thf(fact_6375_choose__reduce__nat,axiom,
% 7.75/5.72 ! [N: nat,K: nat] :
% 7.75/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.72 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.72 => ( ( binomial @ N @ K )
% 7.75/5.72 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % choose_reduce_nat
% 7.75/5.72 thf(fact_6376_times__binomial__minus1__eq,axiom,
% 7.75/5.72 ! [K: nat,N: nat] :
% 7.75/5.72 ( ( ord_less_nat @ zero_zero_nat @ K )
% 7.75/5.72 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 7.75/5.72 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % times_binomial_minus1_eq
% 7.75/5.72 thf(fact_6377_binomial__addition__formula,axiom,
% 7.75/5.72 ! [N: nat,K: nat] :
% 7.75/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.72 => ( ( binomial @ N @ ( suc @ K ) )
% 7.75/5.72 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % binomial_addition_formula
% 7.75/5.72 thf(fact_6378_in__children__def,axiom,
% 7.75/5.72 ( vEBT_V5917875025757280293ildren
% 7.75/5.72 = ( ^ [N3: nat,TreeList3: list_VEBT_VEBT,X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X2 @ N3 ) ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_children_def
% 7.75/5.72 thf(fact_6379_heaphelp,axiom,
% 7.75/5.72 ! [Xa3: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Xb3: vEBT_VEBTi,N: nat,Xc: vEBT_VEBTi,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn
% 7.75/5.72 @ ( times_times_assn
% 7.75/5.72 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa3 @ Tree_is ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ Xb3 ) )
% 7.75/5.72 @ ( pure_assn
% 7.75/5.72 @ ( ( none_P5556105721700978146at_nat = none_P5556105721700978146at_nat )
% 7.75/5.72 & ( N = N ) ) ) )
% 7.75/5.72 @ ( pure_assn
% 7.75/5.72 @ ( Xc
% 7.75/5.72 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ N @ Xa3 @ Xb3 ) ) ) )
% 7.75/5.72 @ H2 )
% 7.75/5.72 => ( rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ none_P5556105721700978146at_nat @ N @ TreeList @ Summary ) @ Xc ) @ H2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % heaphelp
% 7.75/5.72 thf(fact_6380_heaphelp,axiom,
% 7.75/5.72 ! [Xa3: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Xb3: vEBT_VEBTi,N: nat,Xc: vEBT_VEBTi,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn
% 7.75/5.72 @ ( times_times_assn
% 7.75/5.72 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa3 @ Tree_is ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ Xb3 ) )
% 7.75/5.72 @ ( pure_assn
% 7.75/5.72 @ ( ( none_nat = none_nat )
% 7.75/5.72 & ( N = N ) ) ) )
% 7.75/5.72 @ ( pure_assn
% 7.75/5.72 @ ( Xc
% 7.75/5.72 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ N @ Xa3 @ Xb3 ) ) ) )
% 7.75/5.72 @ H2 )
% 7.75/5.72 => ( rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ none_P5556105721700978146at_nat @ N @ TreeList @ Summary ) @ Xc ) @ H2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % heaphelp
% 7.75/5.72 thf(fact_6381_heaphelp,axiom,
% 7.75/5.72 ! [Xa3: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Xb3: vEBT_VEBTi,N: nat,Xc: vEBT_VEBTi,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn
% 7.75/5.72 @ ( times_times_assn
% 7.75/5.72 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa3 @ Tree_is ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ Xb3 ) )
% 7.75/5.72 @ ( pure_assn
% 7.75/5.72 @ ( ( none_num = none_num )
% 7.75/5.72 & ( N = N ) ) ) )
% 7.75/5.72 @ ( pure_assn
% 7.75/5.72 @ ( Xc
% 7.75/5.72 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ N @ Xa3 @ Xb3 ) ) ) )
% 7.75/5.72 @ H2 )
% 7.75/5.72 => ( rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ none_P5556105721700978146at_nat @ N @ TreeList @ Summary ) @ Xc ) @ H2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % heaphelp
% 7.75/5.72 thf(fact_6382_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I4_J,axiom,
% 7.75/5.72 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 7.75/5.72 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(4)
% 7.75/5.72 thf(fact_6383_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I4_J,axiom,
% 7.75/5.72 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 7.75/5.72 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(4)
% 7.75/5.72 thf(fact_6384_vebt__insert_Osimps_I3_J,axiom,
% 7.75/5.72 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 7.75/5.72 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 7.75/5.72 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 7.75/5.72
% 7.75/5.72 % vebt_insert.simps(3)
% 7.75/5.72 thf(fact_6385_height__compose__child,axiom,
% 7.75/5.72 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.72 => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % height_compose_child
% 7.75/5.72 thf(fact_6386_Rep__assn__inject,axiom,
% 7.75/5.72 ! [X: assn,Y: assn] :
% 7.75/5.72 ( ( ( rep_assn @ X )
% 7.75/5.72 = ( rep_assn @ Y ) )
% 7.75/5.72 = ( X = Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % Rep_assn_inject
% 7.75/5.72 thf(fact_6387_List_Ofinite__set,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % List.finite_set
% 7.75/5.72 thf(fact_6388_List_Ofinite__set,axiom,
% 7.75/5.72 ! [Xs2: list_real] : ( finite_finite_real @ ( set_real2 @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % List.finite_set
% 7.75/5.72 thf(fact_6389_List_Ofinite__set,axiom,
% 7.75/5.72 ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % List.finite_set
% 7.75/5.72 thf(fact_6390_List_Ofinite__set,axiom,
% 7.75/5.72 ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % List.finite_set
% 7.75/5.72 thf(fact_6391_List_Ofinite__set,axiom,
% 7.75/5.72 ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % List.finite_set
% 7.75/5.72 thf(fact_6392_List_Ofinite__set,axiom,
% 7.75/5.72 ! [Xs2: list_Code_integer] : ( finite6017078050557962740nteger @ ( set_Code_integer2 @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % List.finite_set
% 7.75/5.72 thf(fact_6393_in__set__replicate,axiom,
% 7.75/5.72 ! [X: complex,N: nat,Y: complex] :
% 7.75/5.72 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 7.75/5.72 = ( ( X = Y )
% 7.75/5.72 & ( N != zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_replicate
% 7.75/5.72 thf(fact_6394_in__set__replicate,axiom,
% 7.75/5.72 ! [X: nat,N: nat,Y: nat] :
% 7.75/5.72 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 7.75/5.72 = ( ( X = Y )
% 7.75/5.72 & ( N != zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_replicate
% 7.75/5.72 thf(fact_6395_in__set__replicate,axiom,
% 7.75/5.72 ! [X: real,N: nat,Y: real] :
% 7.75/5.72 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 7.75/5.72 = ( ( X = Y )
% 7.75/5.72 & ( N != zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_replicate
% 7.75/5.72 thf(fact_6396_in__set__replicate,axiom,
% 7.75/5.72 ! [X: int,N: nat,Y: int] :
% 7.75/5.72 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 7.75/5.72 = ( ( X = Y )
% 7.75/5.72 & ( N != zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_replicate
% 7.75/5.72 thf(fact_6397_in__set__replicate,axiom,
% 7.75/5.72 ! [X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 7.75/5.72 = ( ( X = Y )
% 7.75/5.72 & ( N != zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_replicate
% 7.75/5.72 thf(fact_6398_Bex__set__replicate,axiom,
% 7.75/5.72 ! [N: nat,A: nat,P: nat > $o] :
% 7.75/5.72 ( ( ? [X2: nat] :
% 7.75/5.72 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 7.75/5.72 & ( P @ X2 ) ) )
% 7.75/5.72 = ( ( P @ A )
% 7.75/5.72 & ( N != zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Bex_set_replicate
% 7.75/5.72 thf(fact_6399_Bex__set__replicate,axiom,
% 7.75/5.72 ! [N: nat,A: real,P: real > $o] :
% 7.75/5.72 ( ( ? [X2: real] :
% 7.75/5.72 ( ( member_real @ X2 @ ( set_real2 @ ( replicate_real @ N @ A ) ) )
% 7.75/5.72 & ( P @ X2 ) ) )
% 7.75/5.72 = ( ( P @ A )
% 7.75/5.72 & ( N != zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Bex_set_replicate
% 7.75/5.72 thf(fact_6400_Bex__set__replicate,axiom,
% 7.75/5.72 ! [N: nat,A: int,P: int > $o] :
% 7.75/5.72 ( ( ? [X2: int] :
% 7.75/5.72 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 7.75/5.72 & ( P @ X2 ) ) )
% 7.75/5.72 = ( ( P @ A )
% 7.75/5.72 & ( N != zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Bex_set_replicate
% 7.75/5.72 thf(fact_6401_Bex__set__replicate,axiom,
% 7.75/5.72 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 7.75/5.72 ( ( ? [X2: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 7.75/5.72 & ( P @ X2 ) ) )
% 7.75/5.72 = ( ( P @ A )
% 7.75/5.72 & ( N != zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Bex_set_replicate
% 7.75/5.72 thf(fact_6402_Ball__set__replicate,axiom,
% 7.75/5.72 ! [N: nat,A: nat,P: nat > $o] :
% 7.75/5.72 ( ( ! [X2: nat] :
% 7.75/5.72 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ( P @ A )
% 7.75/5.72 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Ball_set_replicate
% 7.75/5.72 thf(fact_6403_Ball__set__replicate,axiom,
% 7.75/5.72 ! [N: nat,A: real,P: real > $o] :
% 7.75/5.72 ( ( ! [X2: real] :
% 7.75/5.72 ( ( member_real @ X2 @ ( set_real2 @ ( replicate_real @ N @ A ) ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ( P @ A )
% 7.75/5.72 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Ball_set_replicate
% 7.75/5.72 thf(fact_6404_Ball__set__replicate,axiom,
% 7.75/5.72 ! [N: nat,A: int,P: int > $o] :
% 7.75/5.72 ( ( ! [X2: int] :
% 7.75/5.72 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ( P @ A )
% 7.75/5.72 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Ball_set_replicate
% 7.75/5.72 thf(fact_6405_Ball__set__replicate,axiom,
% 7.75/5.72 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 7.75/5.72 ( ( ! [X2: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ( P @ A )
% 7.75/5.72 | ( N = zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Ball_set_replicate
% 7.75/5.72 thf(fact_6406_mod__pure__star__dist,axiom,
% 7.75/5.72 ! [P: assn,B: $o,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( times_times_assn @ P @ ( pure_assn @ B ) ) @ H2 )
% 7.75/5.72 = ( ( rep_assn @ P @ H2 )
% 7.75/5.72 & B ) ) ).
% 7.75/5.72
% 7.75/5.72 % mod_pure_star_dist
% 7.75/5.72 thf(fact_6407_ent__pure__post__iff,axiom,
% 7.75/5.72 ! [P: assn,Q: assn,B: $o] :
% 7.75/5.72 ( ( entails @ P @ ( times_times_assn @ Q @ ( pure_assn @ B ) ) )
% 7.75/5.72 = ( ! [H: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ P @ H )
% 7.75/5.72 => B )
% 7.75/5.72 & ( entails @ P @ Q ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ent_pure_post_iff
% 7.75/5.72 thf(fact_6408_ent__pure__post__iff__sng,axiom,
% 7.75/5.72 ! [P: assn,B: $o] :
% 7.75/5.72 ( ( entails @ P @ ( pure_assn @ B ) )
% 7.75/5.72 = ( ! [H: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ P @ H )
% 7.75/5.72 => B )
% 7.75/5.72 & ( entails @ P @ one_one_assn ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ent_pure_post_iff_sng
% 7.75/5.72 thf(fact_6409_mod__starE,axiom,
% 7.75/5.72 ! [A: assn,B: assn,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H2 )
% 7.75/5.72 => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A @ X_1 )
% 7.75/5.72 => ! [H_2: produc3658429121746597890et_nat] :
% 7.75/5.72 ~ ( rep_assn @ B @ H_2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % mod_starE
% 7.75/5.72 thf(fact_6410_mod__starD,axiom,
% 7.75/5.72 ! [A2: assn,B3: assn,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( times_times_assn @ A2 @ B3 ) @ H2 )
% 7.75/5.72 => ? [H1: produc3658429121746597890et_nat,H22: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ A2 @ H1 )
% 7.75/5.72 & ( rep_assn @ B3 @ H22 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % mod_starD
% 7.75/5.72 thf(fact_6411_entails__def,axiom,
% 7.75/5.72 ( entails
% 7.75/5.72 = ( ^ [P2: assn,Q2: assn] :
% 7.75/5.72 ! [H: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ P2 @ H )
% 7.75/5.72 => ( rep_assn @ Q2 @ H ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % entails_def
% 7.75/5.72 thf(fact_6412_entailsI,axiom,
% 7.75/5.72 ! [P: assn,Q: assn] :
% 7.75/5.72 ( ! [H3: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ P @ H3 )
% 7.75/5.72 => ( rep_assn @ Q @ H3 ) )
% 7.75/5.72 => ( entails @ P @ Q ) ) ).
% 7.75/5.72
% 7.75/5.72 % entailsI
% 7.75/5.72 thf(fact_6413_entailsD,axiom,
% 7.75/5.72 ! [P: assn,Q: assn,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( entails @ P @ Q )
% 7.75/5.72 => ( ( rep_assn @ P @ H2 )
% 7.75/5.72 => ( rep_assn @ Q @ H2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % entailsD
% 7.75/5.72 thf(fact_6414_ent__fwd,axiom,
% 7.75/5.72 ! [P: assn,H2: produc3658429121746597890et_nat,Q: assn] :
% 7.75/5.72 ( ( rep_assn @ P @ H2 )
% 7.75/5.72 => ( ( entails @ P @ Q )
% 7.75/5.72 => ( rep_assn @ Q @ H2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ent_fwd
% 7.75/5.72 thf(fact_6415_finite__list,axiom,
% 7.75/5.72 ! [A2: set_VEBT_VEBT] :
% 7.75/5.72 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.72 => ? [Xs3: list_VEBT_VEBT] :
% 7.75/5.72 ( ( set_VEBT_VEBT2 @ Xs3 )
% 7.75/5.72 = A2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_list
% 7.75/5.72 thf(fact_6416_finite__list,axiom,
% 7.75/5.72 ! [A2: set_real] :
% 7.75/5.72 ( ( finite_finite_real @ A2 )
% 7.75/5.72 => ? [Xs3: list_real] :
% 7.75/5.72 ( ( set_real2 @ Xs3 )
% 7.75/5.72 = A2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_list
% 7.75/5.72 thf(fact_6417_finite__list,axiom,
% 7.75/5.72 ! [A2: set_nat] :
% 7.75/5.72 ( ( finite_finite_nat @ A2 )
% 7.75/5.72 => ? [Xs3: list_nat] :
% 7.75/5.72 ( ( set_nat2 @ Xs3 )
% 7.75/5.72 = A2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_list
% 7.75/5.72 thf(fact_6418_finite__list,axiom,
% 7.75/5.72 ! [A2: set_int] :
% 7.75/5.72 ( ( finite_finite_int @ A2 )
% 7.75/5.72 => ? [Xs3: list_int] :
% 7.75/5.72 ( ( set_int2 @ Xs3 )
% 7.75/5.72 = A2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_list
% 7.75/5.72 thf(fact_6419_finite__list,axiom,
% 7.75/5.72 ! [A2: set_complex] :
% 7.75/5.72 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.72 => ? [Xs3: list_complex] :
% 7.75/5.72 ( ( set_complex2 @ Xs3 )
% 7.75/5.72 = A2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_list
% 7.75/5.72 thf(fact_6420_finite__list,axiom,
% 7.75/5.72 ! [A2: set_Code_integer] :
% 7.75/5.72 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.72 => ? [Xs3: list_Code_integer] :
% 7.75/5.72 ( ( set_Code_integer2 @ Xs3 )
% 7.75/5.72 = A2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_list
% 7.75/5.72 thf(fact_6421_subset__code_I1_J,axiom,
% 7.75/5.72 ! [Xs2: list_complex,B3: set_complex] :
% 7.75/5.72 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B3 )
% 7.75/5.72 = ( ! [X2: complex] :
% 7.75/5.72 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 7.75/5.72 => ( member_complex @ X2 @ B3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % subset_code(1)
% 7.75/5.72 thf(fact_6422_subset__code_I1_J,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 7.75/5.72 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B3 )
% 7.75/5.72 = ( ! [X2: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.75/5.72 => ( member_VEBT_VEBT @ X2 @ B3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % subset_code(1)
% 7.75/5.72 thf(fact_6423_subset__code_I1_J,axiom,
% 7.75/5.72 ! [Xs2: list_real,B3: set_real] :
% 7.75/5.72 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B3 )
% 7.75/5.72 = ( ! [X2: real] :
% 7.75/5.72 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 7.75/5.72 => ( member_real @ X2 @ B3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % subset_code(1)
% 7.75/5.72 thf(fact_6424_subset__code_I1_J,axiom,
% 7.75/5.72 ! [Xs2: list_int,B3: set_int] :
% 7.75/5.72 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B3 )
% 7.75/5.72 = ( ! [X2: int] :
% 7.75/5.72 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 7.75/5.72 => ( member_int @ X2 @ B3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % subset_code(1)
% 7.75/5.72 thf(fact_6425_subset__code_I1_J,axiom,
% 7.75/5.72 ! [Xs2: list_nat,B3: set_nat] :
% 7.75/5.72 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B3 )
% 7.75/5.72 = ( ! [X2: nat] :
% 7.75/5.72 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 7.75/5.72 => ( member_nat @ X2 @ B3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % subset_code(1)
% 7.75/5.72 thf(fact_6426_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_complex,Xs4: list_complex,Xsi: list_complex,Xsi2: list_complex,A2: complex > complex > assn,A7: complex > complex > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: complex,Xi: complex] :
% 7.75/5.72 ( ( member_complex @ X3 @ ( set_complex2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_complex @ Xi @ ( set_complex2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L4260503343685368993omplex @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L4260503343685368993omplex @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6427_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_complex,Xs4: list_complex,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A2: complex > vEBT_VEBT > assn,A7: complex > vEBT_VEBT > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: complex,Xi: vEBT_VEBT] :
% 7.75/5.72 ( ( member_complex @ X3 @ ( set_complex2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_VEBT_VEBT @ Xi @ ( set_VEBT_VEBT2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L8524933119956041985T_VEBT @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L8524933119956041985T_VEBT @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6428_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_complex,Xs4: list_complex,Xsi: list_nat,Xsi2: list_nat,A2: complex > nat > assn,A7: complex > nat > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: complex,Xi: nat] :
% 7.75/5.72 ( ( member_complex @ X3 @ ( set_complex2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_nat @ Xi @ ( set_nat2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L137475477348087235ex_nat @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L137475477348087235ex_nat @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6429_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_complex,Xs4: list_complex,Xsi: list_real,Xsi2: list_real,A2: complex > real > assn,A7: complex > real > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: complex,Xi: real] :
% 7.75/5.72 ( ( member_complex @ X3 @ ( set_complex2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_real @ Xi @ ( set_real2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L2479436891206192927x_real @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L2479436891206192927x_real @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6430_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_complex,Xs4: list_complex,Xsi: list_int,Xsi2: list_int,A2: complex > int > assn,A7: complex > int > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: complex,Xi: int] :
% 7.75/5.72 ( ( member_complex @ X3 @ ( set_complex2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_int @ Xi @ ( set_int2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L134985006839036959ex_int @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L134985006839036959ex_int @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6431_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_complex,Xsi2: list_complex,A2: vEBT_VEBT > complex > assn,A7: vEBT_VEBT > complex > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: vEBT_VEBT,Xi: complex] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_complex @ Xi @ ( set_complex2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L2162147798726695391omplex @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L2162147798726695391omplex @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6432_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A2: vEBT_VEBT > vEBT_VEBT > assn,A7: vEBT_VEBT > vEBT_VEBT > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: vEBT_VEBT,Xi: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_VEBT_VEBT @ Xi @ ( set_VEBT_VEBT2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L1279224858307276611T_VEBT @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L1279224858307276611T_VEBT @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6433_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_nat,Xsi2: list_nat,A2: vEBT_VEBT > nat > assn,A7: vEBT_VEBT > nat > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: vEBT_VEBT,Xi: nat] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_nat @ Xi @ ( set_nat2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L8296926524756676353BT_nat @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L8296926524756676353BT_nat @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6434_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_real,Xsi2: list_real,A2: vEBT_VEBT > real > assn,A7: vEBT_VEBT > real > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: vEBT_VEBT,Xi: real] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_real @ Xi @ ( set_real2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L5781919052683127133T_real @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L5781919052683127133T_real @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6435_list__assn__cong,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,Xs4: list_VEBT_VEBT,Xsi: list_int,Xsi2: list_int,A2: vEBT_VEBT > int > assn,A7: vEBT_VEBT > int > assn] :
% 7.75/5.72 ( ( Xs2 = Xs4 )
% 7.75/5.72 => ( ( Xsi = Xsi2 )
% 7.75/5.72 => ( ! [X3: vEBT_VEBT,Xi: int] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs4 ) )
% 7.75/5.72 => ( ( member_int @ Xi @ ( set_int2 @ Xsi2 ) )
% 7.75/5.72 => ( ( A2 @ X3 @ Xi )
% 7.75/5.72 = ( A7 @ X3 @ Xi ) ) ) )
% 7.75/5.72 => ( ( vEBT_L8294436054247626077BT_int @ A2 @ Xs2 @ Xsi )
% 7.75/5.72 = ( vEBT_L8294436054247626077BT_int @ A7 @ Xs4 @ Xsi2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_assn_cong
% 7.75/5.72 thf(fact_6436_vebt__insert_Osimps_I2_J,axiom,
% 7.75/5.72 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 7.75/5.72 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 7.75/5.72 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 7.75/5.72
% 7.75/5.72 % vebt_insert.simps(2)
% 7.75/5.72 thf(fact_6437_set__n__deg__not__0,axiom,
% 7.75/5.72 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 7.75/5.72 ( ! [X3: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.72 => ( vEBT_invar_vebt @ X3 @ N ) )
% 7.75/5.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 7.75/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.72 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % set_n_deg_not_0
% 7.75/5.72 thf(fact_6438_arcosh__def,axiom,
% 7.75/5.72 ( arcosh_real
% 7.75/5.72 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % arcosh_def
% 7.75/5.72 thf(fact_6439_round__altdef,axiom,
% 7.75/5.72 ( archim7778729529865785530nd_rat
% 7.75/5.72 = ( ^ [X2: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X2 ) ) @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim3151403230148437115or_rat @ X2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % round_altdef
% 7.75/5.72 thf(fact_6440_round__altdef,axiom,
% 7.75/5.72 ( archim8280529875227126926d_real
% 7.75/5.72 = ( ^ [X2: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X2 ) ) @ ( archim7802044766580827645g_real @ X2 ) @ ( archim6058952711729229775r_real @ X2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % round_altdef
% 7.75/5.72 thf(fact_6441_vebt__member_Osimps_I2_J,axiom,
% 7.75/5.72 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 7.75/5.72 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 7.75/5.72
% 7.75/5.72 % vebt_member.simps(2)
% 7.75/5.72 thf(fact_6442_arsinh__def,axiom,
% 7.75/5.72 ( arsinh_real
% 7.75/5.72 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % arsinh_def
% 7.75/5.72 thf(fact_6443_invar__vebt_Ointros_I3_J,axiom,
% 7.75/5.72 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 7.75/5.72 ( ! [X3: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.72 => ( vEBT_invar_vebt @ X3 @ N ) )
% 7.75/5.72 => ( ( vEBT_invar_vebt @ Summary @ M )
% 7.75/5.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 7.75/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.72 => ( ( M
% 7.75/5.72 = ( suc @ N ) )
% 7.75/5.72 => ( ( Deg
% 7.75/5.72 = ( plus_plus_nat @ N @ M ) )
% 7.75/5.72 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 7.75/5.72 => ( ! [X3: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.72 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 7.75/5.72 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % invar_vebt.intros(3)
% 7.75/5.72 thf(fact_6444_inthall,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBTi,P: vEBT_VEBTi > $o,N: nat] :
% 7.75/5.72 ( ! [X3: vEBT_VEBTi] :
% 7.75/5.72 ( ( member_VEBT_VEBTi @ X3 @ ( set_VEBT_VEBTi2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBTi @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % inthall
% 7.75/5.72 thf(fact_6445_inthall,axiom,
% 7.75/5.72 ! [Xs2: list_complex,P: complex > $o,N: nat] :
% 7.75/5.72 ( ! [X3: complex] :
% 7.75/5.72 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % inthall
% 7.75/5.72 thf(fact_6446_inthall,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 7.75/5.72 ( ! [X3: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % inthall
% 7.75/5.72 thf(fact_6447_inthall,axiom,
% 7.75/5.72 ! [Xs2: list_real,P: real > $o,N: nat] :
% 7.75/5.72 ( ! [X3: real] :
% 7.75/5.72 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % inthall
% 7.75/5.72 thf(fact_6448_inthall,axiom,
% 7.75/5.72 ! [Xs2: list_o,P: $o > $o,N: nat] :
% 7.75/5.72 ( ! [X3: $o] :
% 7.75/5.72 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % inthall
% 7.75/5.72 thf(fact_6449_inthall,axiom,
% 7.75/5.72 ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 7.75/5.72 ( ! [X3: nat] :
% 7.75/5.72 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % inthall
% 7.75/5.72 thf(fact_6450_inthall,axiom,
% 7.75/5.72 ! [Xs2: list_int,P: int > $o,N: nat] :
% 7.75/5.72 ( ! [X3: int] :
% 7.75/5.72 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % inthall
% 7.75/5.72 thf(fact_6451_length__replicate,axiom,
% 7.75/5.72 ! [N: nat,X: vEBT_VEBT] :
% 7.75/5.72 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % length_replicate
% 7.75/5.72 thf(fact_6452_length__replicate,axiom,
% 7.75/5.72 ! [N: nat,X: real] :
% 7.75/5.72 ( ( size_size_list_real @ ( replicate_real @ N @ X ) )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % length_replicate
% 7.75/5.72 thf(fact_6453_length__replicate,axiom,
% 7.75/5.72 ! [N: nat,X: $o] :
% 7.75/5.72 ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % length_replicate
% 7.75/5.72 thf(fact_6454_length__replicate,axiom,
% 7.75/5.72 ! [N: nat,X: nat] :
% 7.75/5.72 ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % length_replicate
% 7.75/5.72 thf(fact_6455_length__replicate,axiom,
% 7.75/5.72 ! [N: nat,X: int] :
% 7.75/5.72 ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % length_replicate
% 7.75/5.72 thf(fact_6456_of__real__eq__0__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( real_V1803761363581548252l_real @ X )
% 7.75/5.72 = zero_zero_real )
% 7.75/5.72 = ( X = zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_eq_0_iff
% 7.75/5.72 thf(fact_6457_of__real__eq__0__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( real_V4546457046886955230omplex @ X )
% 7.75/5.72 = zero_zero_complex )
% 7.75/5.72 = ( X = zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_eq_0_iff
% 7.75/5.72 thf(fact_6458_of__real__0,axiom,
% 7.75/5.72 ( ( real_V1803761363581548252l_real @ zero_zero_real )
% 7.75/5.72 = zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_0
% 7.75/5.72 thf(fact_6459_of__real__0,axiom,
% 7.75/5.72 ( ( real_V4546457046886955230omplex @ zero_zero_real )
% 7.75/5.72 = zero_zero_complex ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_0
% 7.75/5.72 thf(fact_6460_of__real__eq__1__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( real_V1803761363581548252l_real @ X )
% 7.75/5.72 = one_one_real )
% 7.75/5.72 = ( X = one_one_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_eq_1_iff
% 7.75/5.72 thf(fact_6461_of__real__eq__1__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( real_V4546457046886955230omplex @ X )
% 7.75/5.72 = one_one_complex )
% 7.75/5.72 = ( X = one_one_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_eq_1_iff
% 7.75/5.72 thf(fact_6462_of__real__1,axiom,
% 7.75/5.72 ( ( real_V1803761363581548252l_real @ one_one_real )
% 7.75/5.72 = one_one_real ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_1
% 7.75/5.72 thf(fact_6463_of__real__1,axiom,
% 7.75/5.72 ( ( real_V4546457046886955230omplex @ one_one_real )
% 7.75/5.72 = one_one_complex ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_1
% 7.75/5.72 thf(fact_6464_of__real__numeral,axiom,
% 7.75/5.72 ! [W: num] :
% 7.75/5.72 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 7.75/5.72 = ( numeral_numeral_real @ W ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_numeral
% 7.75/5.72 thf(fact_6465_of__real__numeral,axiom,
% 7.75/5.72 ! [W: num] :
% 7.75/5.72 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 7.75/5.72 = ( numera6690914467698888265omplex @ W ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_numeral
% 7.75/5.72 thf(fact_6466_of__real__mult,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( real_V1803761363581548252l_real @ ( times_times_real @ X @ Y ) )
% 7.75/5.72 = ( times_times_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_mult
% 7.75/5.72 thf(fact_6467_of__real__mult,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( real_V4546457046886955230omplex @ ( times_times_real @ X @ Y ) )
% 7.75/5.72 = ( times_times_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_mult
% 7.75/5.72 thf(fact_6468_of__real__divide,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y ) )
% 7.75/5.72 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_divide
% 7.75/5.72 thf(fact_6469_of__real__divide,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y ) )
% 7.75/5.72 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_divide
% 7.75/5.72 thf(fact_6470_of__real__add,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X @ Y ) )
% 7.75/5.72 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_add
% 7.75/5.72 thf(fact_6471_of__real__add,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X @ Y ) )
% 7.75/5.72 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_add
% 7.75/5.72 thf(fact_6472_of__real__power,axiom,
% 7.75/5.72 ! [X: real,N: nat] :
% 7.75/5.72 ( ( real_V1803761363581548252l_real @ ( power_power_real @ X @ N ) )
% 7.75/5.72 = ( power_power_real @ ( real_V1803761363581548252l_real @ X ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_power
% 7.75/5.72 thf(fact_6473_of__real__power,axiom,
% 7.75/5.72 ! [X: real,N: nat] :
% 7.75/5.72 ( ( real_V4546457046886955230omplex @ ( power_power_real @ X @ N ) )
% 7.75/5.72 = ( power_power_complex @ ( real_V4546457046886955230omplex @ X ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_power
% 7.75/5.72 thf(fact_6474_frac__of__int,axiom,
% 7.75/5.72 ! [Z: int] :
% 7.75/5.72 ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z ) )
% 7.75/5.72 = zero_zero_rat ) ).
% 7.75/5.72
% 7.75/5.72 % frac_of_int
% 7.75/5.72 thf(fact_6475_frac__of__int,axiom,
% 7.75/5.72 ! [Z: int] :
% 7.75/5.72 ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z ) )
% 7.75/5.72 = zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % frac_of_int
% 7.75/5.72 thf(fact_6476_of__real__neg__numeral,axiom,
% 7.75/5.72 ! [W: num] :
% 7.75/5.72 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_neg_numeral
% 7.75/5.72 thf(fact_6477_of__real__neg__numeral,axiom,
% 7.75/5.72 ! [W: num] :
% 7.75/5.72 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 7.75/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % of_real_neg_numeral
% 7.75/5.72 thf(fact_6478_norm__of__real__add1,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ one_one_real ) )
% 7.75/5.72 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % norm_of_real_add1
% 7.75/5.72 thf(fact_6479_norm__of__real__add1,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ one_one_complex ) )
% 7.75/5.72 = ( abs_abs_real @ ( plus_plus_real @ X @ one_one_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % norm_of_real_add1
% 7.75/5.72 thf(fact_6480_norm__of__real__addn,axiom,
% 7.75/5.72 ! [X: real,B: num] :
% 7.75/5.72 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( numeral_numeral_real @ B ) ) )
% 7.75/5.72 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % norm_of_real_addn
% 7.75/5.72 thf(fact_6481_norm__of__real__addn,axiom,
% 7.75/5.72 ! [X: real,B: num] :
% 7.75/5.72 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( numera6690914467698888265omplex @ B ) ) )
% 7.75/5.72 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % norm_of_real_addn
% 7.75/5.72 thf(fact_6482_Ex__list__of__length,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ? [Xs3: list_real] :
% 7.75/5.72 ( ( size_size_list_real @ Xs3 )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % Ex_list_of_length
% 7.75/5.72 thf(fact_6483_Ex__list__of__length,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ? [Xs3: list_o] :
% 7.75/5.72 ( ( size_size_list_o @ Xs3 )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % Ex_list_of_length
% 7.75/5.72 thf(fact_6484_Ex__list__of__length,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ? [Xs3: list_nat] :
% 7.75/5.72 ( ( size_size_list_nat @ Xs3 )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % Ex_list_of_length
% 7.75/5.72 thf(fact_6485_Ex__list__of__length,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ? [Xs3: list_int] :
% 7.75/5.72 ( ( size_size_list_int @ Xs3 )
% 7.75/5.72 = N ) ).
% 7.75/5.72
% 7.75/5.72 % Ex_list_of_length
% 7.75/5.72 thf(fact_6486_neq__if__length__neq,axiom,
% 7.75/5.72 ! [Xs2: list_real,Ys: list_real] :
% 7.75/5.72 ( ( ( size_size_list_real @ Xs2 )
% 7.75/5.72 != ( size_size_list_real @ Ys ) )
% 7.75/5.72 => ( Xs2 != Ys ) ) ).
% 7.75/5.72
% 7.75/5.72 % neq_if_length_neq
% 7.75/5.72 thf(fact_6487_neq__if__length__neq,axiom,
% 7.75/5.72 ! [Xs2: list_o,Ys: list_o] :
% 7.75/5.72 ( ( ( size_size_list_o @ Xs2 )
% 7.75/5.72 != ( size_size_list_o @ Ys ) )
% 7.75/5.72 => ( Xs2 != Ys ) ) ).
% 7.75/5.72
% 7.75/5.72 % neq_if_length_neq
% 7.75/5.72 thf(fact_6488_neq__if__length__neq,axiom,
% 7.75/5.72 ! [Xs2: list_nat,Ys: list_nat] :
% 7.75/5.72 ( ( ( size_size_list_nat @ Xs2 )
% 7.75/5.72 != ( size_size_list_nat @ Ys ) )
% 7.75/5.72 => ( Xs2 != Ys ) ) ).
% 7.75/5.72
% 7.75/5.72 % neq_if_length_neq
% 7.75/5.72 thf(fact_6489_neq__if__length__neq,axiom,
% 7.75/5.72 ! [Xs2: list_int,Ys: list_int] :
% 7.75/5.72 ( ( ( size_size_list_int @ Xs2 )
% 7.75/5.72 != ( size_size_list_int @ Ys ) )
% 7.75/5.72 => ( Xs2 != Ys ) ) ).
% 7.75/5.72
% 7.75/5.72 % neq_if_length_neq
% 7.75/5.72 thf(fact_6490_size__neq__size__imp__neq,axiom,
% 7.75/5.72 ! [X: list_real,Y: list_real] :
% 7.75/5.72 ( ( ( size_size_list_real @ X )
% 7.75/5.72 != ( size_size_list_real @ Y ) )
% 7.75/5.72 => ( X != Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % size_neq_size_imp_neq
% 7.75/5.72 thf(fact_6491_size__neq__size__imp__neq,axiom,
% 7.75/5.72 ! [X: list_o,Y: list_o] :
% 7.75/5.72 ( ( ( size_size_list_o @ X )
% 7.75/5.72 != ( size_size_list_o @ Y ) )
% 7.75/5.72 => ( X != Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % size_neq_size_imp_neq
% 7.75/5.72 thf(fact_6492_size__neq__size__imp__neq,axiom,
% 7.75/5.72 ! [X: list_nat,Y: list_nat] :
% 7.75/5.72 ( ( ( size_size_list_nat @ X )
% 7.75/5.72 != ( size_size_list_nat @ Y ) )
% 7.75/5.72 => ( X != Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % size_neq_size_imp_neq
% 7.75/5.72 thf(fact_6493_size__neq__size__imp__neq,axiom,
% 7.75/5.72 ! [X: list_int,Y: list_int] :
% 7.75/5.72 ( ( ( size_size_list_int @ X )
% 7.75/5.72 != ( size_size_list_int @ Y ) )
% 7.75/5.72 => ( X != Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % size_neq_size_imp_neq
% 7.75/5.72 thf(fact_6494_size__neq__size__imp__neq,axiom,
% 7.75/5.72 ! [X: num,Y: num] :
% 7.75/5.72 ( ( ( size_size_num @ X )
% 7.75/5.72 != ( size_size_num @ Y ) )
% 7.75/5.72 => ( X != Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % size_neq_size_imp_neq
% 7.75/5.72 thf(fact_6495_length__induct,axiom,
% 7.75/5.72 ! [P: list_real > $o,Xs2: list_real] :
% 7.75/5.72 ( ! [Xs3: list_real] :
% 7.75/5.72 ( ! [Ys2: list_real] :
% 7.75/5.72 ( ( ord_less_nat @ ( size_size_list_real @ Ys2 ) @ ( size_size_list_real @ Xs3 ) )
% 7.75/5.72 => ( P @ Ys2 ) )
% 7.75/5.72 => ( P @ Xs3 ) )
% 7.75/5.72 => ( P @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_induct
% 7.75/5.72 thf(fact_6496_length__induct,axiom,
% 7.75/5.72 ! [P: list_o > $o,Xs2: list_o] :
% 7.75/5.72 ( ! [Xs3: list_o] :
% 7.75/5.72 ( ! [Ys2: list_o] :
% 7.75/5.72 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 7.75/5.72 => ( P @ Ys2 ) )
% 7.75/5.72 => ( P @ Xs3 ) )
% 7.75/5.72 => ( P @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_induct
% 7.75/5.72 thf(fact_6497_length__induct,axiom,
% 7.75/5.72 ! [P: list_nat > $o,Xs2: list_nat] :
% 7.75/5.72 ( ! [Xs3: list_nat] :
% 7.75/5.72 ( ! [Ys2: list_nat] :
% 7.75/5.72 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 7.75/5.72 => ( P @ Ys2 ) )
% 7.75/5.72 => ( P @ Xs3 ) )
% 7.75/5.72 => ( P @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_induct
% 7.75/5.72 thf(fact_6498_length__induct,axiom,
% 7.75/5.72 ! [P: list_int > $o,Xs2: list_int] :
% 7.75/5.72 ( ! [Xs3: list_int] :
% 7.75/5.72 ( ! [Ys2: list_int] :
% 7.75/5.72 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 7.75/5.72 => ( P @ Ys2 ) )
% 7.75/5.72 => ( P @ Xs3 ) )
% 7.75/5.72 => ( P @ Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_induct
% 7.75/5.72 thf(fact_6499_finite__maxlen,axiom,
% 7.75/5.72 ! [M7: set_list_real] :
% 7.75/5.72 ( ( finite306553202115118035t_real @ M7 )
% 7.75/5.72 => ? [N2: nat] :
% 7.75/5.72 ! [X5: list_real] :
% 7.75/5.72 ( ( member_list_real @ X5 @ M7 )
% 7.75/5.72 => ( ord_less_nat @ ( size_size_list_real @ X5 ) @ N2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_maxlen
% 7.75/5.72 thf(fact_6500_finite__maxlen,axiom,
% 7.75/5.72 ! [M7: set_list_o] :
% 7.75/5.72 ( ( finite_finite_list_o @ M7 )
% 7.75/5.72 => ? [N2: nat] :
% 7.75/5.72 ! [X5: list_o] :
% 7.75/5.72 ( ( member_list_o @ X5 @ M7 )
% 7.75/5.72 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_maxlen
% 7.75/5.72 thf(fact_6501_finite__maxlen,axiom,
% 7.75/5.72 ! [M7: set_list_nat] :
% 7.75/5.72 ( ( finite8100373058378681591st_nat @ M7 )
% 7.75/5.72 => ? [N2: nat] :
% 7.75/5.72 ! [X5: list_nat] :
% 7.75/5.72 ( ( member_list_nat @ X5 @ M7 )
% 7.75/5.72 => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_maxlen
% 7.75/5.72 thf(fact_6502_finite__maxlen,axiom,
% 7.75/5.72 ! [M7: set_list_int] :
% 7.75/5.72 ( ( finite3922522038869484883st_int @ M7 )
% 7.75/5.72 => ? [N2: nat] :
% 7.75/5.72 ! [X5: list_int] :
% 7.75/5.72 ( ( member_list_int @ X5 @ M7 )
% 7.75/5.72 => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % finite_maxlen
% 7.75/5.72 thf(fact_6503_nth__equalityI,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 7.75/5.72 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.75/5.72 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 7.75/5.72 => ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.72 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 7.75/5.72 = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 7.75/5.72 => ( Xs2 = Ys ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_equalityI
% 7.75/5.72 thf(fact_6504_nth__equalityI,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi] :
% 7.75/5.72 ( ( ( size_s7982070591426661849_VEBTi @ Xs2 )
% 7.75/5.72 = ( size_s7982070591426661849_VEBTi @ Ys ) )
% 7.75/5.72 => ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.72 => ( ( nth_VEBT_VEBTi @ Xs2 @ I3 )
% 7.75/5.72 = ( nth_VEBT_VEBTi @ Ys @ I3 ) ) )
% 7.75/5.72 => ( Xs2 = Ys ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_equalityI
% 7.75/5.72 thf(fact_6505_nth__equalityI,axiom,
% 7.75/5.72 ! [Xs2: list_real,Ys: list_real] :
% 7.75/5.72 ( ( ( size_size_list_real @ Xs2 )
% 7.75/5.72 = ( size_size_list_real @ Ys ) )
% 7.75/5.72 => ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.72 => ( ( nth_real @ Xs2 @ I3 )
% 7.75/5.72 = ( nth_real @ Ys @ I3 ) ) )
% 7.75/5.72 => ( Xs2 = Ys ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_equalityI
% 7.75/5.72 thf(fact_6506_nth__equalityI,axiom,
% 7.75/5.72 ! [Xs2: list_o,Ys: list_o] :
% 7.75/5.72 ( ( ( size_size_list_o @ Xs2 )
% 7.75/5.72 = ( size_size_list_o @ Ys ) )
% 7.75/5.72 => ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.72 => ( ( nth_o @ Xs2 @ I3 )
% 7.75/5.72 = ( nth_o @ Ys @ I3 ) ) )
% 7.75/5.72 => ( Xs2 = Ys ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_equalityI
% 7.75/5.72 thf(fact_6507_nth__equalityI,axiom,
% 7.75/5.72 ! [Xs2: list_nat,Ys: list_nat] :
% 7.75/5.72 ( ( ( size_size_list_nat @ Xs2 )
% 7.75/5.72 = ( size_size_list_nat @ Ys ) )
% 7.75/5.72 => ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.72 => ( ( nth_nat @ Xs2 @ I3 )
% 7.75/5.72 = ( nth_nat @ Ys @ I3 ) ) )
% 7.75/5.72 => ( Xs2 = Ys ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_equalityI
% 7.75/5.72 thf(fact_6508_nth__equalityI,axiom,
% 7.75/5.72 ! [Xs2: list_int,Ys: list_int] :
% 7.75/5.72 ( ( ( size_size_list_int @ Xs2 )
% 7.75/5.72 = ( size_size_list_int @ Ys ) )
% 7.75/5.72 => ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.72 => ( ( nth_int @ Xs2 @ I3 )
% 7.75/5.72 = ( nth_int @ Ys @ I3 ) ) )
% 7.75/5.72 => ( Xs2 = Ys ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_equalityI
% 7.75/5.72 thf(fact_6509_Skolem__list__nth,axiom,
% 7.75/5.72 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 7.75/5.72 ( ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ? [X7: vEBT_VEBT] : ( P @ I2 @ X7 ) ) )
% 7.75/5.72 = ( ? [Xs: list_VEBT_VEBT] :
% 7.75/5.72 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 7.75/5.72 = K )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ( P @ I2 @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Skolem_list_nth
% 7.75/5.72 thf(fact_6510_Skolem__list__nth,axiom,
% 7.75/5.72 ! [K: nat,P: nat > vEBT_VEBTi > $o] :
% 7.75/5.72 ( ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ? [X7: vEBT_VEBTi] : ( P @ I2 @ X7 ) ) )
% 7.75/5.72 = ( ? [Xs: list_VEBT_VEBTi] :
% 7.75/5.72 ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 7.75/5.72 = K )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ( P @ I2 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Skolem_list_nth
% 7.75/5.72 thf(fact_6511_Skolem__list__nth,axiom,
% 7.75/5.72 ! [K: nat,P: nat > real > $o] :
% 7.75/5.72 ( ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ? [X7: real] : ( P @ I2 @ X7 ) ) )
% 7.75/5.72 = ( ? [Xs: list_real] :
% 7.75/5.72 ( ( ( size_size_list_real @ Xs )
% 7.75/5.72 = K )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ( P @ I2 @ ( nth_real @ Xs @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Skolem_list_nth
% 7.75/5.72 thf(fact_6512_Skolem__list__nth,axiom,
% 7.75/5.72 ! [K: nat,P: nat > $o > $o] :
% 7.75/5.72 ( ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ? [X7: $o] : ( P @ I2 @ X7 ) ) )
% 7.75/5.72 = ( ? [Xs: list_o] :
% 7.75/5.72 ( ( ( size_size_list_o @ Xs )
% 7.75/5.72 = K )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ( P @ I2 @ ( nth_o @ Xs @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Skolem_list_nth
% 7.75/5.72 thf(fact_6513_Skolem__list__nth,axiom,
% 7.75/5.72 ! [K: nat,P: nat > nat > $o] :
% 7.75/5.72 ( ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ? [X7: nat] : ( P @ I2 @ X7 ) ) )
% 7.75/5.72 = ( ? [Xs: list_nat] :
% 7.75/5.72 ( ( ( size_size_list_nat @ Xs )
% 7.75/5.72 = K )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ( P @ I2 @ ( nth_nat @ Xs @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Skolem_list_nth
% 7.75/5.72 thf(fact_6514_Skolem__list__nth,axiom,
% 7.75/5.72 ! [K: nat,P: nat > int > $o] :
% 7.75/5.72 ( ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ? [X7: int] : ( P @ I2 @ X7 ) ) )
% 7.75/5.72 = ( ? [Xs: list_int] :
% 7.75/5.72 ( ( ( size_size_list_int @ Xs )
% 7.75/5.72 = K )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ K )
% 7.75/5.72 => ( P @ I2 @ ( nth_int @ Xs @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % Skolem_list_nth
% 7.75/5.72 thf(fact_6515_list__eq__iff__nth__eq,axiom,
% 7.75/5.72 ( ( ^ [Y2: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y2 = Z2 ) )
% 7.75/5.72 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 7.75/5.72 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 7.75/5.72 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 7.75/5.72 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 7.75/5.72 = ( nth_VEBT_VEBT @ Ys3 @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_eq_iff_nth_eq
% 7.75/5.72 thf(fact_6516_list__eq__iff__nth__eq,axiom,
% 7.75/5.72 ( ( ^ [Y2: list_VEBT_VEBTi,Z2: list_VEBT_VEBTi] : ( Y2 = Z2 ) )
% 7.75/5.72 = ( ^ [Xs: list_VEBT_VEBTi,Ys3: list_VEBT_VEBTi] :
% 7.75/5.72 ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 7.75/5.72 = ( size_s7982070591426661849_VEBTi @ Ys3 ) )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 7.75/5.72 => ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 7.75/5.72 = ( nth_VEBT_VEBTi @ Ys3 @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_eq_iff_nth_eq
% 7.75/5.72 thf(fact_6517_list__eq__iff__nth__eq,axiom,
% 7.75/5.72 ( ( ^ [Y2: list_real,Z2: list_real] : ( Y2 = Z2 ) )
% 7.75/5.72 = ( ^ [Xs: list_real,Ys3: list_real] :
% 7.75/5.72 ( ( ( size_size_list_real @ Xs )
% 7.75/5.72 = ( size_size_list_real @ Ys3 ) )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 7.75/5.72 => ( ( nth_real @ Xs @ I2 )
% 7.75/5.72 = ( nth_real @ Ys3 @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_eq_iff_nth_eq
% 7.75/5.72 thf(fact_6518_list__eq__iff__nth__eq,axiom,
% 7.75/5.72 ( ( ^ [Y2: list_o,Z2: list_o] : ( Y2 = Z2 ) )
% 7.75/5.72 = ( ^ [Xs: list_o,Ys3: list_o] :
% 7.75/5.72 ( ( ( size_size_list_o @ Xs )
% 7.75/5.72 = ( size_size_list_o @ Ys3 ) )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 7.75/5.72 => ( ( nth_o @ Xs @ I2 )
% 7.75/5.72 = ( nth_o @ Ys3 @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_eq_iff_nth_eq
% 7.75/5.72 thf(fact_6519_list__eq__iff__nth__eq,axiom,
% 7.75/5.72 ( ( ^ [Y2: list_nat,Z2: list_nat] : ( Y2 = Z2 ) )
% 7.75/5.72 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 7.75/5.72 ( ( ( size_size_list_nat @ Xs )
% 7.75/5.72 = ( size_size_list_nat @ Ys3 ) )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 7.75/5.72 => ( ( nth_nat @ Xs @ I2 )
% 7.75/5.72 = ( nth_nat @ Ys3 @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_eq_iff_nth_eq
% 7.75/5.72 thf(fact_6520_list__eq__iff__nth__eq,axiom,
% 7.75/5.72 ( ( ^ [Y2: list_int,Z2: list_int] : ( Y2 = Z2 ) )
% 7.75/5.72 = ( ^ [Xs: list_int,Ys3: list_int] :
% 7.75/5.72 ( ( ( size_size_list_int @ Xs )
% 7.75/5.72 = ( size_size_list_int @ Ys3 ) )
% 7.75/5.72 & ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 7.75/5.72 => ( ( nth_int @ Xs @ I2 )
% 7.75/5.72 = ( nth_int @ Ys3 @ I2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_eq_iff_nth_eq
% 7.75/5.72 thf(fact_6521_obtain__list__from__elements,axiom,
% 7.75/5.72 ! [N: nat,P: vEBT_VEBT > nat > $o] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ N )
% 7.75/5.72 => ? [Li: vEBT_VEBT] : ( P @ Li @ I3 ) )
% 7.75/5.72 => ~ ! [L4: list_VEBT_VEBT] :
% 7.75/5.72 ( ( ( size_s6755466524823107622T_VEBT @ L4 )
% 7.75/5.72 = N )
% 7.75/5.72 => ~ ! [I4: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I4 @ N )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBT @ L4 @ I4 ) @ I4 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % obtain_list_from_elements
% 7.75/5.72 thf(fact_6522_obtain__list__from__elements,axiom,
% 7.75/5.72 ! [N: nat,P: vEBT_VEBTi > nat > $o] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ N )
% 7.75/5.72 => ? [Li: vEBT_VEBTi] : ( P @ Li @ I3 ) )
% 7.75/5.72 => ~ ! [L4: list_VEBT_VEBTi] :
% 7.75/5.72 ( ( ( size_s7982070591426661849_VEBTi @ L4 )
% 7.75/5.72 = N )
% 7.75/5.72 => ~ ! [I4: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I4 @ N )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBTi @ L4 @ I4 ) @ I4 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % obtain_list_from_elements
% 7.75/5.72 thf(fact_6523_obtain__list__from__elements,axiom,
% 7.75/5.72 ! [N: nat,P: real > nat > $o] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ N )
% 7.75/5.72 => ? [Li: real] : ( P @ Li @ I3 ) )
% 7.75/5.72 => ~ ! [L4: list_real] :
% 7.75/5.72 ( ( ( size_size_list_real @ L4 )
% 7.75/5.72 = N )
% 7.75/5.72 => ~ ! [I4: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I4 @ N )
% 7.75/5.72 => ( P @ ( nth_real @ L4 @ I4 ) @ I4 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % obtain_list_from_elements
% 7.75/5.72 thf(fact_6524_obtain__list__from__elements,axiom,
% 7.75/5.72 ! [N: nat,P: $o > nat > $o] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ N )
% 7.75/5.72 => ? [Li: $o] : ( P @ Li @ I3 ) )
% 7.75/5.72 => ~ ! [L4: list_o] :
% 7.75/5.72 ( ( ( size_size_list_o @ L4 )
% 7.75/5.72 = N )
% 7.75/5.72 => ~ ! [I4: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I4 @ N )
% 7.75/5.72 => ( P @ ( nth_o @ L4 @ I4 ) @ I4 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % obtain_list_from_elements
% 7.75/5.72 thf(fact_6525_obtain__list__from__elements,axiom,
% 7.75/5.72 ! [N: nat,P: nat > nat > $o] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ N )
% 7.75/5.72 => ? [Li: nat] : ( P @ Li @ I3 ) )
% 7.75/5.72 => ~ ! [L4: list_nat] :
% 7.75/5.72 ( ( ( size_size_list_nat @ L4 )
% 7.75/5.72 = N )
% 7.75/5.72 => ~ ! [I4: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I4 @ N )
% 7.75/5.72 => ( P @ ( nth_nat @ L4 @ I4 ) @ I4 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % obtain_list_from_elements
% 7.75/5.72 thf(fact_6526_obtain__list__from__elements,axiom,
% 7.75/5.72 ! [N: nat,P: int > nat > $o] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ N )
% 7.75/5.72 => ? [Li: int] : ( P @ Li @ I3 ) )
% 7.75/5.72 => ~ ! [L4: list_int] :
% 7.75/5.72 ( ( ( size_size_list_int @ L4 )
% 7.75/5.72 = N )
% 7.75/5.72 => ~ ! [I4: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I4 @ N )
% 7.75/5.72 => ( P @ ( nth_int @ L4 @ I4 ) @ I4 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % obtain_list_from_elements
% 7.75/5.72 thf(fact_6527_replicate__eqI,axiom,
% 7.75/5.72 ! [Xs2: list_complex,N: nat,X: complex] :
% 7.75/5.72 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 7.75/5.72 = N )
% 7.75/5.72 => ( ! [Y3: complex] :
% 7.75/5.72 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 7.75/5.72 => ( Y3 = X ) )
% 7.75/5.72 => ( Xs2
% 7.75/5.72 = ( replicate_complex @ N @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_eqI
% 7.75/5.72 thf(fact_6528_replicate__eqI,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 7.75/5.72 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.75/5.72 = N )
% 7.75/5.72 => ( ! [Y3: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.75/5.72 => ( Y3 = X ) )
% 7.75/5.72 => ( Xs2
% 7.75/5.72 = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_eqI
% 7.75/5.72 thf(fact_6529_replicate__eqI,axiom,
% 7.75/5.72 ! [Xs2: list_real,N: nat,X: real] :
% 7.75/5.72 ( ( ( size_size_list_real @ Xs2 )
% 7.75/5.72 = N )
% 7.75/5.72 => ( ! [Y3: real] :
% 7.75/5.72 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 7.75/5.72 => ( Y3 = X ) )
% 7.75/5.72 => ( Xs2
% 7.75/5.72 = ( replicate_real @ N @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_eqI
% 7.75/5.72 thf(fact_6530_replicate__eqI,axiom,
% 7.75/5.72 ! [Xs2: list_o,N: nat,X: $o] :
% 7.75/5.72 ( ( ( size_size_list_o @ Xs2 )
% 7.75/5.72 = N )
% 7.75/5.72 => ( ! [Y3: $o] :
% 7.75/5.72 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 7.75/5.72 => ( Y3 = X ) )
% 7.75/5.72 => ( Xs2
% 7.75/5.72 = ( replicate_o @ N @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_eqI
% 7.75/5.72 thf(fact_6531_replicate__eqI,axiom,
% 7.75/5.72 ! [Xs2: list_nat,N: nat,X: nat] :
% 7.75/5.72 ( ( ( size_size_list_nat @ Xs2 )
% 7.75/5.72 = N )
% 7.75/5.72 => ( ! [Y3: nat] :
% 7.75/5.72 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 7.75/5.72 => ( Y3 = X ) )
% 7.75/5.72 => ( Xs2
% 7.75/5.72 = ( replicate_nat @ N @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_eqI
% 7.75/5.72 thf(fact_6532_replicate__eqI,axiom,
% 7.75/5.72 ! [Xs2: list_int,N: nat,X: int] :
% 7.75/5.72 ( ( ( size_size_list_int @ Xs2 )
% 7.75/5.72 = N )
% 7.75/5.72 => ( ! [Y3: int] :
% 7.75/5.72 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 7.75/5.72 => ( Y3 = X ) )
% 7.75/5.72 => ( Xs2
% 7.75/5.72 = ( replicate_int @ N @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_eqI
% 7.75/5.72 thf(fact_6533_replicate__length__same,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 7.75/5.72 ( ! [X3: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.75/5.72 => ( X3 = X ) )
% 7.75/5.72 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 7.75/5.72 = Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_length_same
% 7.75/5.72 thf(fact_6534_replicate__length__same,axiom,
% 7.75/5.72 ! [Xs2: list_real,X: real] :
% 7.75/5.72 ( ! [X3: real] :
% 7.75/5.72 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.75/5.72 => ( X3 = X ) )
% 7.75/5.72 => ( ( replicate_real @ ( size_size_list_real @ Xs2 ) @ X )
% 7.75/5.72 = Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_length_same
% 7.75/5.72 thf(fact_6535_replicate__length__same,axiom,
% 7.75/5.72 ! [Xs2: list_o,X: $o] :
% 7.75/5.72 ( ! [X3: $o] :
% 7.75/5.72 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 7.75/5.72 => ( X3 = X ) )
% 7.75/5.72 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 7.75/5.72 = Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_length_same
% 7.75/5.72 thf(fact_6536_replicate__length__same,axiom,
% 7.75/5.72 ! [Xs2: list_nat,X: nat] :
% 7.75/5.72 ( ! [X3: nat] :
% 7.75/5.72 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.75/5.72 => ( X3 = X ) )
% 7.75/5.72 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X )
% 7.75/5.72 = Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_length_same
% 7.75/5.72 thf(fact_6537_replicate__length__same,axiom,
% 7.75/5.72 ! [Xs2: list_int,X: int] :
% 7.75/5.72 ( ! [X3: int] :
% 7.75/5.72 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 7.75/5.72 => ( X3 = X ) )
% 7.75/5.72 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 7.75/5.72 = Xs2 ) ) ).
% 7.75/5.72
% 7.75/5.72 % replicate_length_same
% 7.75/5.72 thf(fact_6538_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: real > real > assn,Xs2: list_real,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L1930518968523514909l_real @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_real @ Xsi )
% 7.75/5.72 = ( size_size_list_real @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6539_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: $o > real > assn,Xs2: list_o,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L4725278957065240257o_real @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_real @ Xsi )
% 7.75/5.72 = ( size_size_list_o @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6540_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: nat > real > assn,Xs2: list_nat,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L6102073776069194049t_real @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_real @ Xsi )
% 7.75/5.72 = ( size_size_list_nat @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6541_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: int > real > assn,Xs2: list_int,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L8288995350762215837t_real @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_real @ Xsi )
% 7.75/5.72 = ( size_size_list_int @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6542_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: real > $o > assn,Xs2: list_real,Xsi: list_o,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L6234343332106409831real_o @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_o @ Xsi )
% 7.75/5.72 = ( size_size_list_real @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6543_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: $o > $o > assn,Xs2: list_o,Xsi: list_o,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L7363604446928714179sn_o_o @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_o @ Xsi )
% 7.75/5.72 = ( size_size_list_o @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6544_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: nat > $o > assn,Xs2: list_nat,Xsi: list_o,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L7887682484454631235_nat_o @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_o @ Xsi )
% 7.75/5.72 = ( size_size_list_nat @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6545_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: int > $o > assn,Xs2: list_int,Xsi: list_o,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L6066640139021943271_int_o @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_o @ Xsi )
% 7.75/5.72 = ( size_size_list_int @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6546_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: real > nat > assn,Xs2: list_real,Xsi: list_nat,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L1446010312343316929al_nat @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_nat @ Xsi )
% 7.75/5.72 = ( size_size_list_real @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6547_extract__pre__list__assn__lengthD,axiom,
% 7.75/5.72 ! [A2: $o > nat > assn,Xs2: list_o,Xsi: list_nat,H2: produc3658429121746597890et_nat] :
% 7.75/5.72 ( ( rep_assn @ ( vEBT_L4785011123346445925_o_nat @ A2 @ Xs2 @ Xsi ) @ H2 )
% 7.75/5.72 => ( ( size_size_list_nat @ Xsi )
% 7.75/5.72 = ( size_size_list_o @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % extract_pre_list_assn_lengthD
% 7.75/5.72 thf(fact_6548_frac__ge__0,axiom,
% 7.75/5.72 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % frac_ge_0
% 7.75/5.72 thf(fact_6549_frac__ge__0,axiom,
% 7.75/5.72 ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % frac_ge_0
% 7.75/5.72 thf(fact_6550_frac__lt__1,axiom,
% 7.75/5.72 ! [X: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X ) @ one_one_real ) ).
% 7.75/5.72
% 7.75/5.72 % frac_lt_1
% 7.75/5.72 thf(fact_6551_frac__lt__1,axiom,
% 7.75/5.72 ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 7.75/5.72
% 7.75/5.72 % frac_lt_1
% 7.75/5.72 thf(fact_6552_frac__1__eq,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ one_one_real ) )
% 7.75/5.72 = ( archim2898591450579166408c_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % frac_1_eq
% 7.75/5.72 thf(fact_6553_frac__1__eq,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 7.75/5.72 = ( archimedean_frac_rat @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % frac_1_eq
% 7.75/5.72 thf(fact_6554_nonzero__of__real__divide,axiom,
% 7.75/5.72 ! [Y: real,X: real] :
% 7.75/5.72 ( ( Y != zero_zero_real )
% 7.75/5.72 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y ) )
% 7.75/5.72 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nonzero_of_real_divide
% 7.75/5.72 thf(fact_6555_nonzero__of__real__divide,axiom,
% 7.75/5.72 ! [Y: real,X: real] :
% 7.75/5.72 ( ( Y != zero_zero_real )
% 7.75/5.72 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y ) )
% 7.75/5.72 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nonzero_of_real_divide
% 7.75/5.72 thf(fact_6556_length__pos__if__in__set,axiom,
% 7.75/5.72 ! [X: complex,Xs2: list_complex] :
% 7.75/5.72 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 7.75/5.72 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_pos_if_in_set
% 7.75/5.72 thf(fact_6557_length__pos__if__in__set,axiom,
% 7.75/5.72 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.75/5.72 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_pos_if_in_set
% 7.75/5.72 thf(fact_6558_length__pos__if__in__set,axiom,
% 7.75/5.72 ! [X: real,Xs2: list_real] :
% 7.75/5.72 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 7.75/5.72 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_pos_if_in_set
% 7.75/5.72 thf(fact_6559_length__pos__if__in__set,axiom,
% 7.75/5.72 ! [X: $o,Xs2: list_o] :
% 7.75/5.72 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 7.75/5.72 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_pos_if_in_set
% 7.75/5.72 thf(fact_6560_length__pos__if__in__set,axiom,
% 7.75/5.72 ! [X: nat,Xs2: list_nat] :
% 7.75/5.72 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 7.75/5.72 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_pos_if_in_set
% 7.75/5.72 thf(fact_6561_length__pos__if__in__set,axiom,
% 7.75/5.72 ! [X: int,Xs2: list_int] :
% 7.75/5.72 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 7.75/5.72 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % length_pos_if_in_set
% 7.75/5.72 thf(fact_6562_all__set__conv__all__nth,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBTi,P: vEBT_VEBTi > $o] :
% 7.75/5.72 ( ( ! [X2: vEBT_VEBTi] :
% 7.75/5.72 ( ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBTi @ Xs2 @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_all_nth
% 7.75/5.72 thf(fact_6563_all__set__conv__all__nth,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 7.75/5.72 ( ( ! [X2: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_all_nth
% 7.75/5.72 thf(fact_6564_all__set__conv__all__nth,axiom,
% 7.75/5.72 ! [Xs2: list_real,P: real > $o] :
% 7.75/5.72 ( ( ! [X2: real] :
% 7.75/5.72 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_real @ Xs2 @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_all_nth
% 7.75/5.72 thf(fact_6565_all__set__conv__all__nth,axiom,
% 7.75/5.72 ! [Xs2: list_o,P: $o > $o] :
% 7.75/5.72 ( ( ! [X2: $o] :
% 7.75/5.72 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_o @ Xs2 @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_all_nth
% 7.75/5.72 thf(fact_6566_all__set__conv__all__nth,axiom,
% 7.75/5.72 ! [Xs2: list_nat,P: nat > $o] :
% 7.75/5.72 ( ( ! [X2: nat] :
% 7.75/5.72 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_all_nth
% 7.75/5.72 thf(fact_6567_all__set__conv__all__nth,axiom,
% 7.75/5.72 ! [Xs2: list_int,P: int > $o] :
% 7.75/5.72 ( ( ! [X2: int] :
% 7.75/5.72 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_int @ Xs2 @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_all_nth
% 7.75/5.72 thf(fact_6568_all__nth__imp__all__set,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBTi,P: vEBT_VEBTi > $o,X: vEBT_VEBTi] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBTi @ Xs2 @ I3 ) ) )
% 7.75/5.72 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_nth_imp_all_set
% 7.75/5.72 thf(fact_6569_all__nth__imp__all__set,axiom,
% 7.75/5.72 ! [Xs2: list_complex,P: complex > $o,X: complex] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_complex @ Xs2 @ I3 ) ) )
% 7.75/5.72 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_nth_imp_all_set
% 7.75/5.72 thf(fact_6570_all__nth__imp__all__set,axiom,
% 7.75/5.72 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 7.75/5.72 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_nth_imp_all_set
% 7.75/5.72 thf(fact_6571_all__nth__imp__all__set,axiom,
% 7.75/5.72 ! [Xs2: list_real,P: real > $o,X: real] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_real @ Xs2 @ I3 ) ) )
% 7.75/5.72 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_nth_imp_all_set
% 7.75/5.72 thf(fact_6572_all__nth__imp__all__set,axiom,
% 7.75/5.72 ! [Xs2: list_o,P: $o > $o,X: $o] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_o @ Xs2 @ I3 ) ) )
% 7.75/5.72 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_nth_imp_all_set
% 7.75/5.72 thf(fact_6573_all__nth__imp__all__set,axiom,
% 7.75/5.72 ! [Xs2: list_nat,P: nat > $o,X: nat] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_nat @ Xs2 @ I3 ) ) )
% 7.75/5.72 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_nth_imp_all_set
% 7.75/5.72 thf(fact_6574_all__nth__imp__all__set,axiom,
% 7.75/5.72 ! [Xs2: list_int,P: int > $o,X: int] :
% 7.75/5.72 ( ! [I3: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.72 => ( P @ ( nth_int @ Xs2 @ I3 ) ) )
% 7.75/5.72 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_nth_imp_all_set
% 7.75/5.72 thf(fact_6575_all__set__conv__nth,axiom,
% 7.75/5.72 ! [L: list_VEBT_VEBTi,P: vEBT_VEBTi > $o] :
% 7.75/5.72 ( ( ! [X2: vEBT_VEBTi] :
% 7.75/5.72 ( ( member_VEBT_VEBTi @ X2 @ ( set_VEBT_VEBTi2 @ L ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBTi @ L @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_nth
% 7.75/5.72 thf(fact_6576_all__set__conv__nth,axiom,
% 7.75/5.72 ! [L: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 7.75/5.72 ( ( ! [X2: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ L ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ L ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBT @ L @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_nth
% 7.75/5.72 thf(fact_6577_all__set__conv__nth,axiom,
% 7.75/5.72 ! [L: list_real,P: real > $o] :
% 7.75/5.72 ( ( ! [X2: real] :
% 7.75/5.72 ( ( member_real @ X2 @ ( set_real2 @ L ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ L ) )
% 7.75/5.72 => ( P @ ( nth_real @ L @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_nth
% 7.75/5.72 thf(fact_6578_all__set__conv__nth,axiom,
% 7.75/5.72 ! [L: list_o,P: $o > $o] :
% 7.75/5.72 ( ( ! [X2: $o] :
% 7.75/5.72 ( ( member_o @ X2 @ ( set_o2 @ L ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ L ) )
% 7.75/5.72 => ( P @ ( nth_o @ L @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_nth
% 7.75/5.72 thf(fact_6579_all__set__conv__nth,axiom,
% 7.75/5.72 ! [L: list_nat,P: nat > $o] :
% 7.75/5.72 ( ( ! [X2: nat] :
% 7.75/5.72 ( ( member_nat @ X2 @ ( set_nat2 @ L ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ L ) )
% 7.75/5.72 => ( P @ ( nth_nat @ L @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_nth
% 7.75/5.72 thf(fact_6580_all__set__conv__nth,axiom,
% 7.75/5.72 ! [L: list_int,P: int > $o] :
% 7.75/5.72 ( ( ! [X2: int] :
% 7.75/5.72 ( ( member_int @ X2 @ ( set_int2 @ L ) )
% 7.75/5.72 => ( P @ X2 ) ) )
% 7.75/5.72 = ( ! [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ L ) )
% 7.75/5.72 => ( P @ ( nth_int @ L @ I2 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % all_set_conv_nth
% 7.75/5.72 thf(fact_6581_in__set__conv__nth,axiom,
% 7.75/5.72 ! [X: vEBT_VEBTi,Xs2: list_VEBT_VEBTi] :
% 7.75/5.72 ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs2 ) )
% 7.75/5.72 = ( ? [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.72 & ( ( nth_VEBT_VEBTi @ Xs2 @ I2 )
% 7.75/5.72 = X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_conv_nth
% 7.75/5.72 thf(fact_6582_in__set__conv__nth,axiom,
% 7.75/5.72 ! [X: complex,Xs2: list_complex] :
% 7.75/5.72 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 7.75/5.72 = ( ? [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 7.75/5.72 & ( ( nth_complex @ Xs2 @ I2 )
% 7.75/5.72 = X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_conv_nth
% 7.75/5.72 thf(fact_6583_in__set__conv__nth,axiom,
% 7.75/5.72 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.75/5.72 = ( ? [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.72 & ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 7.75/5.72 = X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_conv_nth
% 7.75/5.72 thf(fact_6584_in__set__conv__nth,axiom,
% 7.75/5.72 ! [X: real,Xs2: list_real] :
% 7.75/5.72 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 7.75/5.72 = ( ? [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.72 & ( ( nth_real @ Xs2 @ I2 )
% 7.75/5.72 = X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_conv_nth
% 7.75/5.72 thf(fact_6585_in__set__conv__nth,axiom,
% 7.75/5.72 ! [X: $o,Xs2: list_o] :
% 7.75/5.72 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 7.75/5.72 = ( ? [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.72 & ( ( nth_o @ Xs2 @ I2 )
% 7.75/5.72 = X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_conv_nth
% 7.75/5.72 thf(fact_6586_in__set__conv__nth,axiom,
% 7.75/5.72 ! [X: nat,Xs2: list_nat] :
% 7.75/5.72 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 7.75/5.72 = ( ? [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.72 & ( ( nth_nat @ Xs2 @ I2 )
% 7.75/5.72 = X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_conv_nth
% 7.75/5.72 thf(fact_6587_in__set__conv__nth,axiom,
% 7.75/5.72 ! [X: int,Xs2: list_int] :
% 7.75/5.72 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 7.75/5.72 = ( ? [I2: nat] :
% 7.75/5.72 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.72 & ( ( nth_int @ Xs2 @ I2 )
% 7.75/5.72 = X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % in_set_conv_nth
% 7.75/5.72 thf(fact_6588_list__ball__nth,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_VEBT_VEBTi,P: vEBT_VEBTi > $o] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.72 => ( ! [X3: vEBT_VEBTi] :
% 7.75/5.72 ( ( member_VEBT_VEBTi @ X3 @ ( set_VEBT_VEBTi2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBTi @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_ball_nth
% 7.75/5.72 thf(fact_6589_list__ball__nth,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.72 => ( ! [X3: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_ball_nth
% 7.75/5.72 thf(fact_6590_list__ball__nth,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_real,P: real > $o] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.72 => ( ! [X3: real] :
% 7.75/5.72 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_ball_nth
% 7.75/5.72 thf(fact_6591_list__ball__nth,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_o,P: $o > $o] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.72 => ( ! [X3: $o] :
% 7.75/5.72 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_ball_nth
% 7.75/5.72 thf(fact_6592_list__ball__nth,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.72 => ( ! [X3: nat] :
% 7.75/5.72 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_ball_nth
% 7.75/5.72 thf(fact_6593_list__ball__nth,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_int,P: int > $o] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.72 => ( ! [X3: int] :
% 7.75/5.72 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 7.75/5.72 => ( P @ X3 ) )
% 7.75/5.72 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % list_ball_nth
% 7.75/5.72 thf(fact_6594_nth__mem,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_VEBT_VEBTi] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.72 => ( member_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs2 @ N ) @ ( set_VEBT_VEBTi2 @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_mem
% 7.75/5.72 thf(fact_6595_nth__mem,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_complex] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 7.75/5.72 => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_mem
% 7.75/5.72 thf(fact_6596_nth__mem,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.72 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_mem
% 7.75/5.72 thf(fact_6597_nth__mem,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_real] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.72 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_mem
% 7.75/5.72 thf(fact_6598_nth__mem,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_o] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.72 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_mem
% 7.75/5.72 thf(fact_6599_nth__mem,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_nat] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.72 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_mem
% 7.75/5.72 thf(fact_6600_nth__mem,axiom,
% 7.75/5.72 ! [N: nat,Xs2: list_int] :
% 7.75/5.72 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.72 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % nth_mem
% 7.75/5.72 thf(fact_6601_norm__less__p1,axiom,
% 7.75/5.72 ! [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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % norm_less_p1
% 7.75/5.72 thf(fact_6602_norm__less__p1,axiom,
% 7.75/5.72 ! [X: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X ) ) @ one_one_complex ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % norm_less_p1
% 7.75/5.72 thf(fact_6603_frac__eq,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( archim2898591450579166408c_real @ X )
% 7.75/5.72 = X )
% 7.75/5.72 = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % frac_eq
% 7.75/5.72 thf(fact_6604_frac__eq,axiom,
% 7.75/5.72 ! [X: rat] :
% 7.75/5.72 ( ( ( archimedean_frac_rat @ X )
% 7.75/5.72 = X )
% 7.75/5.72 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 7.75/5.72 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % frac_eq
% 7.75/5.72 thf(fact_6605_frac__add,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 7.75/5.72 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 7.75/5.72 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 7.75/5.72 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 7.75/5.72 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 7.75/5.72 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % frac_add
% 7.75/5.72 thf(fact_6606_frac__add,axiom,
% 7.75/5.72 ! [X: rat,Y: rat] :
% 7.75/5.72 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 7.75/5.72 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 7.75/5.72 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 7.75/5.72 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 7.75/5.72 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 7.75/5.72 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % frac_add
% 7.75/5.72 thf(fact_6607_floor__add,axiom,
% 7.75/5.72 ! [X: rat,Y: rat] :
% 7.75/5.72 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 7.75/5.72 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 7.75/5.72 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 7.75/5.72 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 7.75/5.72 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 7.75/5.72 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_add
% 7.75/5.72 thf(fact_6608_floor__add,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 7.75/5.72 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 7.75/5.72 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) ) )
% 7.75/5.72 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 7.75/5.72 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y ) )
% 7.75/5.72 = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y ) ) @ one_one_int ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % floor_add
% 7.75/5.72 thf(fact_6609_invar__vebt_Ointros_I2_J,axiom,
% 7.75/5.72 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 7.75/5.72 ( ! [X3: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.72 => ( vEBT_invar_vebt @ X3 @ N ) )
% 7.75/5.72 => ( ( vEBT_invar_vebt @ Summary @ M )
% 7.75/5.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 7.75/5.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.72 => ( ( M = N )
% 7.75/5.72 => ( ( Deg
% 7.75/5.72 = ( plus_plus_nat @ N @ M ) )
% 7.75/5.72 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 7.75/5.72 => ( ! [X3: vEBT_VEBT] :
% 7.75/5.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.72 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 7.75/5.72 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % invar_vebt.intros(2)
% 7.75/5.72 thf(fact_6610_mod__frame__fwd,axiom,
% 7.75/5.72 ! [Ps: assn,H2: produc3658429121746597890et_nat,P: assn,R: assn,F2: assn] :
% 7.75/5.72 ( ( rep_assn @ Ps @ H2 )
% 7.75/5.72 => ( ( entails @ P @ R )
% 7.75/5.72 => ( ( entails @ Ps @ ( times_times_assn @ P @ F2 ) )
% 7.75/5.72 => ( rep_assn @ ( times_times_assn @ R @ F2 ) @ H2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % mod_frame_fwd
% 7.75/5.72 thf(fact_6611_log__base__10__eq1,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 7.75/5.72 = ( 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 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_base_10_eq1
% 7.75/5.72 thf(fact_6612_Leaf__0__not,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 7.75/5.72
% 7.75/5.72 % Leaf_0_not
% 7.75/5.72 thf(fact_6613_deg1Leaf,axiom,
% 7.75/5.72 ! [T: vEBT_VEBT] :
% 7.75/5.72 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 7.75/5.72 = ( ? [A3: $o,B4: $o] :
% 7.75/5.72 ( T
% 7.75/5.72 = ( vEBT_Leaf @ A3 @ B4 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % deg1Leaf
% 7.75/5.72 thf(fact_6614_deg__1__Leaf,axiom,
% 7.75/5.72 ! [T: vEBT_VEBT] :
% 7.75/5.72 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 7.75/5.72 => ? [A5: $o,B2: $o] :
% 7.75/5.72 ( T
% 7.75/5.72 = ( vEBT_Leaf @ A5 @ B2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % deg_1_Leaf
% 7.75/5.72 thf(fact_6615_deg__1__Leafy,axiom,
% 7.75/5.72 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.72 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.72 => ( ( N = one_one_nat )
% 7.75/5.72 => ? [A5: $o,B2: $o] :
% 7.75/5.72 ( T
% 7.75/5.72 = ( vEBT_Leaf @ A5 @ B2 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % deg_1_Leafy
% 7.75/5.72 thf(fact_6616_VEBT_Oinject_I2_J,axiom,
% 7.75/5.72 ! [X21: $o,X222: $o,Y21: $o,Y222: $o] :
% 7.75/5.72 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 7.75/5.72 = ( vEBT_Leaf @ Y21 @ Y222 ) )
% 7.75/5.72 = ( ( X21 = Y21 )
% 7.75/5.72 & ( X222 = Y222 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT.inject(2)
% 7.75/5.72 thf(fact_6617_take__bit__of__0,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 7.75/5.72 = zero_zero_nat ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_0
% 7.75/5.72 thf(fact_6618_take__bit__of__0,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 7.75/5.72 = zero_zero_int ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_0
% 7.75/5.72 thf(fact_6619_exp__less__cancel__iff,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 7.75/5.72 = ( ord_less_real @ X @ Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_less_cancel_iff
% 7.75/5.72 thf(fact_6620_exp__less__mono,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ X @ Y )
% 7.75/5.72 => ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_less_mono
% 7.75/5.72 thf(fact_6621_take__bit__0,axiom,
% 7.75/5.72 ! [A: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 7.75/5.72 = zero_zero_nat ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_0
% 7.75/5.72 thf(fact_6622_take__bit__0,axiom,
% 7.75/5.72 ! [A: int] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 7.75/5.72 = zero_zero_int ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_0
% 7.75/5.72 thf(fact_6623_take__bit__Suc__1,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_1
% 7.75/5.72 thf(fact_6624_take__bit__Suc__1,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 7.75/5.72 = one_one_int ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_1
% 7.75/5.72 thf(fact_6625_take__bit__numeral__1,axiom,
% 7.75/5.72 ! [L: num] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_1
% 7.75/5.72 thf(fact_6626_take__bit__numeral__1,axiom,
% 7.75/5.72 ! [L: num] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 7.75/5.72 = one_one_int ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_1
% 7.75/5.72 thf(fact_6627_exp__zero,axiom,
% 7.75/5.72 ( ( exp_complex @ zero_zero_complex )
% 7.75/5.72 = one_one_complex ) ).
% 7.75/5.72
% 7.75/5.72 % exp_zero
% 7.75/5.72 thf(fact_6628_exp__zero,axiom,
% 7.75/5.72 ( ( exp_real @ zero_zero_real )
% 7.75/5.72 = one_one_real ) ).
% 7.75/5.72
% 7.75/5.72 % exp_zero
% 7.75/5.72 thf(fact_6629_exp__eq__one__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( exp_real @ X )
% 7.75/5.72 = one_one_real )
% 7.75/5.72 = ( X = zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_eq_one_iff
% 7.75/5.72 thf(fact_6630_take__bit__of__1__eq__0__iff,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 7.75/5.72 = zero_zero_nat )
% 7.75/5.72 = ( N = zero_zero_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_1_eq_0_iff
% 7.75/5.72 thf(fact_6631_take__bit__of__1__eq__0__iff,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 7.75/5.72 = zero_zero_int )
% 7.75/5.72 = ( N = zero_zero_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_1_eq_0_iff
% 7.75/5.72 thf(fact_6632_exp__less__one__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 7.75/5.72 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_less_one_iff
% 7.75/5.72 thf(fact_6633_one__less__exp__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 7.75/5.72 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % one_less_exp_iff
% 7.75/5.72 thf(fact_6634_exp__le__one__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 7.75/5.72 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_le_one_iff
% 7.75/5.72 thf(fact_6635_one__le__exp__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % one_le_exp_iff
% 7.75/5.72 thf(fact_6636_exp__ln__iff,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 7.75/5.72 = X )
% 7.75/5.72 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_ln_iff
% 7.75/5.72 thf(fact_6637_exp__ln,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( exp_real @ ( ln_ln_real @ X ) )
% 7.75/5.72 = X ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_ln
% 7.75/5.72 thf(fact_6638_take__bit__of__1,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 7.75/5.72 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_1
% 7.75/5.72 thf(fact_6639_take__bit__of__1,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 7.75/5.72 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_1
% 7.75/5.72 thf(fact_6640_take__bit__of__1,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 7.75/5.72 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_1
% 7.75/5.72 thf(fact_6641_even__take__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,A: nat] :
% 7.75/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 7.75/5.72 = ( ( N = zero_zero_nat )
% 7.75/5.72 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % even_take_bit_eq
% 7.75/5.72 thf(fact_6642_even__take__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,A: int] :
% 7.75/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 7.75/5.72 = ( ( N = zero_zero_nat )
% 7.75/5.72 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % even_take_bit_eq
% 7.75/5.72 thf(fact_6643_take__bit__Suc__0,axiom,
% 7.75/5.72 ! [A: code_integer] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 7.75/5.72 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_0
% 7.75/5.72 thf(fact_6644_take__bit__Suc__0,axiom,
% 7.75/5.72 ! [A: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 7.75/5.72 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_0
% 7.75/5.72 thf(fact_6645_take__bit__Suc__0,axiom,
% 7.75/5.72 ! [A: int] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 7.75/5.72 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_0
% 7.75/5.72 thf(fact_6646_take__bit__of__exp,axiom,
% 7.75/5.72 ! [M: nat,N: nat] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.72 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_exp
% 7.75/5.72 thf(fact_6647_take__bit__of__exp,axiom,
% 7.75/5.72 ! [M: nat,N: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.72 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_exp
% 7.75/5.72 thf(fact_6648_take__bit__of__exp,axiom,
% 7.75/5.72 ! [M: nat,N: nat] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.72 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_exp
% 7.75/5.72 thf(fact_6649_take__bit__of__2,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.72 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_2
% 7.75/5.72 thf(fact_6650_take__bit__of__2,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.72 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_2
% 7.75/5.72 thf(fact_6651_take__bit__of__2,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.72 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_2
% 7.75/5.72 thf(fact_6652_VEBT_Osize_I4_J,axiom,
% 7.75/5.72 ! [X21: $o,X222: $o] :
% 7.75/5.72 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 7.75/5.72 = zero_zero_nat ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT.size(4)
% 7.75/5.72 thf(fact_6653_exp__less__cancel,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 7.75/5.72 => ( ord_less_real @ X @ Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_less_cancel
% 7.75/5.72 thf(fact_6654_take__bit__add,axiom,
% 7.75/5.72 ! [N: nat,A: nat,B: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 7.75/5.72 = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_add
% 7.75/5.72 thf(fact_6655_take__bit__add,axiom,
% 7.75/5.72 ! [N: nat,A: int,B: int] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 7.75/5.72 = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_add
% 7.75/5.72 thf(fact_6656_take__bit__tightened,axiom,
% 7.75/5.72 ! [N: nat,A: nat,B: nat,M: nat] :
% 7.75/5.72 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 7.75/5.72 = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 7.75/5.72 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.72 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 7.75/5.72 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_tightened
% 7.75/5.72 thf(fact_6657_take__bit__tightened,axiom,
% 7.75/5.72 ! [N: nat,A: int,B: int,M: nat] :
% 7.75/5.72 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 7.75/5.72 = ( bit_se2923211474154528505it_int @ N @ B ) )
% 7.75/5.72 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 7.75/5.72 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_tightened
% 7.75/5.72 thf(fact_6658_take__bit__of__int,axiom,
% 7.75/5.72 ! [N: nat,K: int] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 7.75/5.72 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_int
% 7.75/5.72 thf(fact_6659_take__bit__of__nat,axiom,
% 7.75/5.72 ! [N: nat,M: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 7.75/5.72 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_nat
% 7.75/5.72 thf(fact_6660_take__bit__of__nat,axiom,
% 7.75/5.72 ! [N: nat,M: nat] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 7.75/5.72 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_nat
% 7.75/5.72 thf(fact_6661_exp__not__eq__zero,axiom,
% 7.75/5.72 ! [X: complex] :
% 7.75/5.72 ( ( exp_complex @ X )
% 7.75/5.72 != zero_zero_complex ) ).
% 7.75/5.72
% 7.75/5.72 % exp_not_eq_zero
% 7.75/5.72 thf(fact_6662_exp__not__eq__zero,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( exp_real @ X )
% 7.75/5.72 != zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % exp_not_eq_zero
% 7.75/5.72 thf(fact_6663_exp__times__arg__commute,axiom,
% 7.75/5.72 ! [A2: real] :
% 7.75/5.72 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 7.75/5.72 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_times_arg_commute
% 7.75/5.72 thf(fact_6664_exp__times__arg__commute,axiom,
% 7.75/5.72 ! [A2: complex] :
% 7.75/5.72 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 7.75/5.72 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_times_arg_commute
% 7.75/5.72 thf(fact_6665_VEBT_Oexhaust,axiom,
% 7.75/5.72 ! [Y: vEBT_VEBT] :
% 7.75/5.72 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 7.75/5.72 ( Y
% 7.75/5.72 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 7.75/5.72 => ~ ! [X212: $o,X223: $o] :
% 7.75/5.72 ( Y
% 7.75/5.72 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT.exhaust
% 7.75/5.72 thf(fact_6666_VEBT_Odistinct_I1_J,axiom,
% 7.75/5.72 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 7.75/5.72 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 7.75/5.72 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT.distinct(1)
% 7.75/5.72 thf(fact_6667_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 7.75/5.72 ! [Uu: $o,Uv: $o,Uw: nat] :
% 7.75/5.72 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.membermima.simps(1)
% 7.75/5.72 thf(fact_6668_exp__total,axiom,
% 7.75/5.72 ! [Y: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ Y )
% 7.75/5.72 => ? [X3: real] :
% 7.75/5.72 ( ( exp_real @ X3 )
% 7.75/5.72 = Y ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_total
% 7.75/5.72 thf(fact_6669_exp__gt__zero,axiom,
% 7.75/5.72 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_gt_zero
% 7.75/5.72 thf(fact_6670_not__exp__less__zero,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % not_exp_less_zero
% 7.75/5.72 thf(fact_6671_not__exp__le__zero,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 7.75/5.72
% 7.75/5.72 % not_exp_le_zero
% 7.75/5.72 thf(fact_6672_exp__ge__zero,axiom,
% 7.75/5.72 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_ge_zero
% 7.75/5.72 thf(fact_6673_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,A: int,B: int] :
% 7.75/5.72 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 7.75/5.72 = ( bit_ri631733984087533419it_int @ N @ B ) )
% 7.75/5.72 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 7.75/5.72 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % signed_take_bit_eq_iff_take_bit_eq
% 7.75/5.72 thf(fact_6674_signed__take__bit__take__bit,axiom,
% 7.75/5.72 ! [M: nat,N: nat,A: int] :
% 7.75/5.72 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 7.75/5.72 = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 7.75/5.72
% 7.75/5.72 % signed_take_bit_take_bit
% 7.75/5.72 thf(fact_6675_exp__add__commuting,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ( times_times_real @ X @ Y )
% 7.75/5.72 = ( times_times_real @ Y @ X ) )
% 7.75/5.72 => ( ( exp_real @ ( plus_plus_real @ X @ Y ) )
% 7.75/5.72 = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_add_commuting
% 7.75/5.72 thf(fact_6676_exp__add__commuting,axiom,
% 7.75/5.72 ! [X: complex,Y: complex] :
% 7.75/5.72 ( ( ( times_times_complex @ X @ Y )
% 7.75/5.72 = ( times_times_complex @ Y @ X ) )
% 7.75/5.72 => ( ( exp_complex @ ( plus_plus_complex @ X @ Y ) )
% 7.75/5.72 = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_add_commuting
% 7.75/5.72 thf(fact_6677_mult__exp__exp,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 7.75/5.72 = ( exp_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % mult_exp_exp
% 7.75/5.72 thf(fact_6678_mult__exp__exp,axiom,
% 7.75/5.72 ! [X: complex,Y: complex] :
% 7.75/5.72 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) )
% 7.75/5.72 = ( exp_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % mult_exp_exp
% 7.75/5.72 thf(fact_6679_take__bit__unset__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,M: nat,A: int] :
% 7.75/5.72 ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 7.75/5.72 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 7.75/5.72 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 7.75/5.72 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_unset_bit_eq
% 7.75/5.72 thf(fact_6680_take__bit__unset__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,M: nat,A: nat] :
% 7.75/5.72 ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 7.75/5.72 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 7.75/5.72 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 7.75/5.72 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_unset_bit_eq
% 7.75/5.72 thf(fact_6681_take__bit__set__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,M: nat,A: code_integer] :
% 7.75/5.72 ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se1745604003318907178nteger @ N @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 7.75/5.72 = ( bit_se1745604003318907178nteger @ N @ A ) ) )
% 7.75/5.72 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se1745604003318907178nteger @ N @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 7.75/5.72 = ( bit_se2793503036327961859nteger @ M @ ( bit_se1745604003318907178nteger @ N @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_set_bit_eq
% 7.75/5.72 thf(fact_6682_take__bit__set__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,M: nat,A: nat] :
% 7.75/5.72 ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 7.75/5.72 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 7.75/5.72 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 7.75/5.72 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_set_bit_eq
% 7.75/5.72 thf(fact_6683_take__bit__set__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,M: nat,A: int] :
% 7.75/5.72 ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 7.75/5.72 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 7.75/5.72 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 7.75/5.72 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_set_bit_eq
% 7.75/5.72 thf(fact_6684_exp__diff,axiom,
% 7.75/5.72 ! [X: complex,Y: complex] :
% 7.75/5.72 ( ( exp_complex @ ( minus_minus_complex @ X @ Y ) )
% 7.75/5.72 = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_diff
% 7.75/5.72 thf(fact_6685_exp__diff,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( exp_real @ ( minus_minus_real @ X @ Y ) )
% 7.75/5.72 = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_diff
% 7.75/5.72 thf(fact_6686_take__bit__flip__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,M: nat,A: nat] :
% 7.75/5.72 ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 7.75/5.72 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 7.75/5.72 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 7.75/5.72 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_flip_bit_eq
% 7.75/5.72 thf(fact_6687_take__bit__flip__bit__eq,axiom,
% 7.75/5.72 ! [N: nat,M: nat,A: int] :
% 7.75/5.72 ( ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 7.75/5.72 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 7.75/5.72 & ( ~ ( ord_less_eq_nat @ N @ M )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 7.75/5.72 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_flip_bit_eq
% 7.75/5.72 thf(fact_6688_vebt__buildup_Osimps_I1_J,axiom,
% 7.75/5.72 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 7.75/5.72 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 7.75/5.72
% 7.75/5.72 % vebt_buildup.simps(1)
% 7.75/5.72 thf(fact_6689_VEBT__internal_Ocnt_Osimps_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_VEBT_cnt @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.72 = one_one_real ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.cnt.simps(1)
% 7.75/5.72 thf(fact_6690_VEBT__internal_Ocnt_H_Osimps_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_VEBT_cnt2 @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.cnt'.simps(1)
% 7.75/5.72 thf(fact_6691_take__bit__signed__take__bit,axiom,
% 7.75/5.72 ! [M: nat,N: nat,A: int] :
% 7.75/5.72 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 7.75/5.72 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_signed_take_bit
% 7.75/5.72 thf(fact_6692_exp__gt__one,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_gt_one
% 7.75/5.72 thf(fact_6693_exp__ge__add__one__self,axiom,
% 7.75/5.72 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_ge_add_one_self
% 7.75/5.72 thf(fact_6694_exp__minus__inverse,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 7.75/5.72 = one_one_real ) ).
% 7.75/5.72
% 7.75/5.72 % exp_minus_inverse
% 7.75/5.72 thf(fact_6695_exp__minus__inverse,axiom,
% 7.75/5.72 ! [X: complex] :
% 7.75/5.72 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 7.75/5.72 = one_one_complex ) ).
% 7.75/5.72
% 7.75/5.72 % exp_minus_inverse
% 7.75/5.72 thf(fact_6696_exp__of__nat2__mult,axiom,
% 7.75/5.72 ! [X: real,N: nat] :
% 7.75/5.72 ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 7.75/5.72 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_of_nat2_mult
% 7.75/5.72 thf(fact_6697_exp__of__nat2__mult,axiom,
% 7.75/5.72 ! [X: complex,N: nat] :
% 7.75/5.72 ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 7.75/5.72 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_of_nat2_mult
% 7.75/5.72 thf(fact_6698_exp__of__nat__mult,axiom,
% 7.75/5.72 ! [N: nat,X: real] :
% 7.75/5.72 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 7.75/5.72 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_of_nat_mult
% 7.75/5.72 thf(fact_6699_exp__of__nat__mult,axiom,
% 7.75/5.72 ! [N: nat,X: complex] :
% 7.75/5.72 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 7.75/5.72 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_of_nat_mult
% 7.75/5.72 thf(fact_6700_invar__vebt_Ointros_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % invar_vebt.intros(1)
% 7.75/5.72 thf(fact_6701_log__ln,axiom,
% 7.75/5.72 ( ln_ln_real
% 7.75/5.72 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_ln
% 7.75/5.72 thf(fact_6702_vebt__member_Osimps_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o,X: nat] :
% 7.75/5.72 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 7.75/5.72 = ( ( ( X = zero_zero_nat )
% 7.75/5.72 => A )
% 7.75/5.72 & ( ( X != zero_zero_nat )
% 7.75/5.72 => ( ( ( X = one_one_nat )
% 7.75/5.72 => B )
% 7.75/5.72 & ( X = one_one_nat ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % vebt_member.simps(1)
% 7.75/5.72 thf(fact_6703_vebt__buildup_Osimps_I2_J,axiom,
% 7.75/5.72 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 7.75/5.72 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 7.75/5.72
% 7.75/5.72 % vebt_buildup.simps(2)
% 7.75/5.72 thf(fact_6704_vebt__insert_Osimps_I1_J,axiom,
% 7.75/5.72 ! [X: nat,A: $o,B: $o] :
% 7.75/5.72 ( ( ( X = zero_zero_nat )
% 7.75/5.72 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 7.75/5.72 = ( vEBT_Leaf @ $true @ B ) ) )
% 7.75/5.72 & ( ( X != zero_zero_nat )
% 7.75/5.72 => ( ( ( X = one_one_nat )
% 7.75/5.72 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 7.75/5.72 = ( vEBT_Leaf @ A @ $true ) ) )
% 7.75/5.72 & ( ( X != one_one_nat )
% 7.75/5.72 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 7.75/5.72 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % vebt_insert.simps(1)
% 7.75/5.72 thf(fact_6705_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I3_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o,N: nat] :
% 7.75/5.72 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(3)
% 7.75/5.72 thf(fact_6706_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I3_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o,N: nat] :
% 7.75/5.72 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(3)
% 7.75/5.72 thf(fact_6707_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(1)
% 7.75/5.72 thf(fact_6708_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(1)
% 7.75/5.72 thf(fact_6709_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o,X: nat] :
% 7.75/5.72 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 7.75/5.72 = ( ( ( X = zero_zero_nat )
% 7.75/5.72 => A )
% 7.75/5.72 & ( ( X != zero_zero_nat )
% 7.75/5.72 => ( ( ( X = one_one_nat )
% 7.75/5.72 => B )
% 7.75/5.72 & ( X = one_one_nat ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.naive_member.simps(1)
% 7.75/5.72 thf(fact_6710_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I3_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o,Va2: nat] :
% 7.75/5.72 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(3)
% 7.75/5.72 thf(fact_6711_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I1_J,axiom,
% 7.75/5.72 ! [Uu: $o,Uv: $o] :
% 7.75/5.72 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(1)
% 7.75/5.72 thf(fact_6712_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I1_J,axiom,
% 7.75/5.72 ! [Uu: $o,Uv: $o] :
% 7.75/5.72 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(1)
% 7.75/5.72 thf(fact_6713_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I2_J,axiom,
% 7.75/5.72 ! [Uv: $o,Uw: $o,N: nat] :
% 7.75/5.72 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(2)
% 7.75/5.72 thf(fact_6714_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I2_J,axiom,
% 7.75/5.72 ! [Uv: $o,Uw: $o,N: nat] :
% 7.75/5.72 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(2)
% 7.75/5.72 thf(fact_6715_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J,axiom,
% 7.75/5.72 ! [Uu: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(1)
% 7.75/5.72 thf(fact_6716_num_Osize_I4_J,axiom,
% 7.75/5.72 ( ( size_size_num @ one )
% 7.75/5.72 = zero_zero_nat ) ).
% 7.75/5.72
% 7.75/5.72 % num.size(4)
% 7.75/5.72 thf(fact_6717_star__assoc,axiom,
% 7.75/5.72 ! [A: assn,B: assn,C: assn] :
% 7.75/5.72 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 7.75/5.72 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % star_assoc
% 7.75/5.72 thf(fact_6718_star__aci_I2_J,axiom,
% 7.75/5.72 ( times_times_assn
% 7.75/5.72 = ( ^ [A3: assn,B4: assn] : ( times_times_assn @ B4 @ A3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % star_aci(2)
% 7.75/5.72 thf(fact_6719_star__aci_I3_J,axiom,
% 7.75/5.72 ! [A: assn,B: assn,C: assn] :
% 7.75/5.72 ( ( times_times_assn @ A @ ( times_times_assn @ B @ C ) )
% 7.75/5.72 = ( times_times_assn @ B @ ( times_times_assn @ A @ C ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % star_aci(3)
% 7.75/5.72 thf(fact_6720_assn__aci_I10_J,axiom,
% 7.75/5.72 ! [A: assn,B: assn,C: assn] :
% 7.75/5.72 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 7.75/5.72 = ( times_times_assn @ ( times_times_assn @ A @ C ) @ B ) ) ).
% 7.75/5.72
% 7.75/5.72 % assn_aci(10)
% 7.75/5.72 thf(fact_6721_is__entails,axiom,
% 7.75/5.72 ! [P: assn,Q: assn] :
% 7.75/5.72 ( ( entails @ P @ Q )
% 7.75/5.72 => ( entails @ P @ Q ) ) ).
% 7.75/5.72
% 7.75/5.72 % is_entails
% 7.75/5.72 thf(fact_6722_exp__ge__add__one__self__aux,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_ge_add_one_self_aux
% 7.75/5.72 thf(fact_6723_lemma__exp__total,axiom,
% 7.75/5.72 ! [Y: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ one_one_real @ Y )
% 7.75/5.72 => ? [X3: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 7.75/5.72 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y @ one_one_real ) )
% 7.75/5.72 & ( ( exp_real @ X3 )
% 7.75/5.72 = Y ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % lemma_exp_total
% 7.75/5.72 thf(fact_6724_ln__ge__iff,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 7.75/5.72 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ln_ge_iff
% 7.75/5.72 thf(fact_6725_ln__x__over__x__mono,axiom,
% 7.75/5.72 ! [X: real,Y: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ X @ Y )
% 7.75/5.72 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ln_x_over_x_mono
% 7.75/5.72 thf(fact_6726_powr__def,axiom,
% 7.75/5.72 ( powr_real
% 7.75/5.72 = ( ^ [X2: real,A3: real] : ( if_real @ ( X2 = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A3 @ ( ln_ln_real @ X2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % powr_def
% 7.75/5.72 thf(fact_6727_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I2_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(2)
% 7.75/5.72 thf(fact_6728_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I2_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(2)
% 7.75/5.72 thf(fact_6729_VEBT__internal_Ospace_H_Osimps_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_VEBT_space2 @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.72 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.space'.simps(1)
% 7.75/5.72 thf(fact_6730_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I2_J,axiom,
% 7.75/5.72 ! [A: $o,Uw: $o] :
% 7.75/5.72 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 7.75/5.72 = one_one_nat ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(2)
% 7.75/5.72 thf(fact_6731_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I3_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o,Va2: nat] :
% 7.75/5.72 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.72 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(3)
% 7.75/5.72 thf(fact_6732_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,
% 7.75/5.72 ! [A: $o,B: $o,X: nat] :
% 7.75/5.72 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X )
% 7.75/5.72 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(1)
% 7.75/5.72 thf(fact_6733_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J,axiom,
% 7.75/5.72 ! [Uu: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 7.75/5.72 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(1)
% 7.75/5.72 thf(fact_6734_VEBT__internal_Ospace_Osimps_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_VEBT_space @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.72 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.space.simps(1)
% 7.75/5.72 thf(fact_6735_take__bit__Suc__bit0,axiom,
% 7.75/5.72 ! [N: nat,K: num] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 7.75/5.72 = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_bit0
% 7.75/5.72 thf(fact_6736_take__bit__Suc__bit0,axiom,
% 7.75/5.72 ! [N: nat,K: num] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 7.75/5.72 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_bit0
% 7.75/5.72 thf(fact_6737_take__bit__Suc__bit0,axiom,
% 7.75/5.72 ! [N: nat,K: num] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 7.75/5.72 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_bit0
% 7.75/5.72 thf(fact_6738_take__bit__eq__mod,axiom,
% 7.75/5.72 ( bit_se1745604003318907178nteger
% 7.75/5.72 = ( ^ [N3: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_eq_mod
% 7.75/5.72 thf(fact_6739_take__bit__eq__mod,axiom,
% 7.75/5.72 ( bit_se2925701944663578781it_nat
% 7.75/5.72 = ( ^ [N3: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_eq_mod
% 7.75/5.72 thf(fact_6740_take__bit__eq__mod,axiom,
% 7.75/5.72 ( bit_se2923211474154528505it_int
% 7.75/5.72 = ( ^ [N3: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_eq_mod
% 7.75/5.72 thf(fact_6741_exp__le,axiom,
% 7.75/5.72 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_le
% 7.75/5.72 thf(fact_6742_exp__divide__power__eq,axiom,
% 7.75/5.72 ! [N: nat,X: real] :
% 7.75/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.72 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 7.75/5.72 = ( exp_real @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_divide_power_eq
% 7.75/5.72 thf(fact_6743_exp__divide__power__eq,axiom,
% 7.75/5.72 ! [N: nat,X: complex] :
% 7.75/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.72 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 7.75/5.72 = ( exp_complex @ X ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_divide_power_eq
% 7.75/5.72 thf(fact_6744_tanh__altdef,axiom,
% 7.75/5.72 ( tanh_real
% 7.75/5.72 = ( ^ [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 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % tanh_altdef
% 7.75/5.72 thf(fact_6745_tanh__altdef,axiom,
% 7.75/5.72 ( tanh_complex
% 7.75/5.72 = ( ^ [X2: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % tanh_altdef
% 7.75/5.72 thf(fact_6746_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J,axiom,
% 7.75/5.72 ! [A: $o,Uw: $o] :
% 7.75/5.72 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 7.75/5.72 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(2)
% 7.75/5.72 thf(fact_6747_take__bit__eq__0__iff,axiom,
% 7.75/5.72 ! [N: nat,A: code_integer] :
% 7.75/5.72 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 7.75/5.72 = zero_z3403309356797280102nteger )
% 7.75/5.72 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_eq_0_iff
% 7.75/5.72 thf(fact_6748_take__bit__eq__0__iff,axiom,
% 7.75/5.72 ! [N: nat,A: nat] :
% 7.75/5.72 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 7.75/5.72 = zero_zero_nat )
% 7.75/5.72 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_eq_0_iff
% 7.75/5.72 thf(fact_6749_take__bit__eq__0__iff,axiom,
% 7.75/5.72 ! [N: nat,A: int] :
% 7.75/5.72 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 7.75/5.72 = zero_zero_int )
% 7.75/5.72 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_eq_0_iff
% 7.75/5.72 thf(fact_6750_bin__last__bintrunc,axiom,
% 7.75/5.72 ! [L: nat,N: nat] :
% 7.75/5.72 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ L @ N ) ) )
% 7.75/5.72 = ( ( ord_less_nat @ zero_zero_nat @ L )
% 7.75/5.72 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % bin_last_bintrunc
% 7.75/5.72 thf(fact_6751_bin__last__bintrunc,axiom,
% 7.75/5.72 ! [L: nat,N: int] :
% 7.75/5.72 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ L @ N ) ) )
% 7.75/5.72 = ( ( ord_less_nat @ zero_zero_nat @ L )
% 7.75/5.72 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % bin_last_bintrunc
% 7.75/5.72 thf(fact_6752_take__bit__numeral__bit0,axiom,
% 7.75/5.72 ! [L: num,K: num] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 7.75/5.72 = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_bit0
% 7.75/5.72 thf(fact_6753_take__bit__numeral__bit0,axiom,
% 7.75/5.72 ! [L: num,K: num] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 7.75/5.72 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_bit0
% 7.75/5.72 thf(fact_6754_take__bit__numeral__bit0,axiom,
% 7.75/5.72 ! [L: num,K: num] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 7.75/5.72 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_bit0
% 7.75/5.72 thf(fact_6755_exp__half__le2,axiom,
% 7.75/5.72 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_half_le2
% 7.75/5.72 thf(fact_6756_exp__double,axiom,
% 7.75/5.72 ! [Z: complex] :
% 7.75/5.72 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 7.75/5.72 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_double
% 7.75/5.72 thf(fact_6757_exp__double,axiom,
% 7.75/5.72 ! [Z: real] :
% 7.75/5.72 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 7.75/5.72 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_double
% 7.75/5.72 thf(fact_6758_num_Osize_I5_J,axiom,
% 7.75/5.72 ! [X22: num] :
% 7.75/5.72 ( ( size_size_num @ ( bit0 @ X22 ) )
% 7.75/5.72 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % num.size(5)
% 7.75/5.72 thf(fact_6759_num_Osize_I6_J,axiom,
% 7.75/5.72 ! [X32: num] :
% 7.75/5.72 ( ( size_size_num @ ( bit1 @ X32 ) )
% 7.75/5.72 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % num.size(6)
% 7.75/5.72 thf(fact_6760_exp__bound__half,axiom,
% 7.75/5.72 ! [Z: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.72 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_bound_half
% 7.75/5.72 thf(fact_6761_exp__bound__half,axiom,
% 7.75/5.72 ! [Z: complex] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.72 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_bound_half
% 7.75/5.72 thf(fact_6762_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,
% 7.75/5.72 ! [A: $o,B: $o,X: nat] :
% 7.75/5.72 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X )
% 7.75/5.72 = ( 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 ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(1)
% 7.75/5.72 thf(fact_6763_take__bit__Suc__bit1,axiom,
% 7.75/5.72 ! [N: nat,K: num] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 7.75/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_bit1
% 7.75/5.72 thf(fact_6764_take__bit__Suc__bit1,axiom,
% 7.75/5.72 ! [N: nat,K: num] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 7.75/5.72 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_bit1
% 7.75/5.72 thf(fact_6765_take__bit__Suc__bit1,axiom,
% 7.75/5.72 ! [N: nat,K: num] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 7.75/5.72 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_bit1
% 7.75/5.72 thf(fact_6766_take__bit__Suc__minus__1__eq,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.72 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_minus_1_eq
% 7.75/5.72 thf(fact_6767_take__bit__Suc__minus__1__eq,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.72 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc_minus_1_eq
% 7.75/5.72 thf(fact_6768_take__bit__numeral__minus__1__eq,axiom,
% 7.75/5.72 ! [K: num] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.72 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_minus_1_eq
% 7.75/5.72 thf(fact_6769_take__bit__numeral__minus__1__eq,axiom,
% 7.75/5.72 ! [K: num] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.72 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_minus_1_eq
% 7.75/5.72 thf(fact_6770_take__bit__Suc,axiom,
% 7.75/5.72 ! [N: nat,A: code_integer] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 7.75/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc
% 7.75/5.72 thf(fact_6771_take__bit__Suc,axiom,
% 7.75/5.72 ! [N: nat,A: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 7.75/5.72 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc
% 7.75/5.72 thf(fact_6772_take__bit__Suc,axiom,
% 7.75/5.72 ! [N: nat,A: int] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 7.75/5.72 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_Suc
% 7.75/5.72 thf(fact_6773_ent__frame__fwd,axiom,
% 7.75/5.72 ! [P: assn,R: assn,Ps: assn,F2: assn,Q: assn] :
% 7.75/5.72 ( ( entails @ P @ R )
% 7.75/5.72 => ( ( entails @ Ps @ ( times_times_assn @ P @ F2 ) )
% 7.75/5.72 => ( ( entails @ ( times_times_assn @ R @ F2 ) @ Q )
% 7.75/5.72 => ( entails @ Ps @ Q ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % ent_frame_fwd
% 7.75/5.72 thf(fact_6774_fr__rot__rhs,axiom,
% 7.75/5.72 ! [A2: assn,B3: assn,C5: assn] :
% 7.75/5.72 ( ( entails @ A2 @ ( times_times_assn @ B3 @ C5 ) )
% 7.75/5.72 => ( entails @ A2 @ ( times_times_assn @ C5 @ B3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % fr_rot_rhs
% 7.75/5.72 thf(fact_6775_fr__refl,axiom,
% 7.75/5.72 ! [A2: assn,B3: assn,C5: assn] :
% 7.75/5.72 ( ( entails @ A2 @ B3 )
% 7.75/5.72 => ( entails @ ( times_times_assn @ A2 @ C5 ) @ ( times_times_assn @ B3 @ C5 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % fr_refl
% 7.75/5.72 thf(fact_6776_fr__rot,axiom,
% 7.75/5.72 ! [A2: assn,B3: assn,C5: assn] :
% 7.75/5.72 ( ( entails @ ( times_times_assn @ A2 @ B3 ) @ C5 )
% 7.75/5.72 => ( entails @ ( times_times_assn @ B3 @ A2 ) @ C5 ) ) ).
% 7.75/5.72
% 7.75/5.72 % fr_rot
% 7.75/5.72 thf(fact_6777_exp__bound,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.75/5.72 => ( 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 ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_bound
% 7.75/5.72 thf(fact_6778_norm__assertion__simps_I1_J,axiom,
% 7.75/5.72 ! [A: assn] :
% 7.75/5.72 ( ( times_times_assn @ one_one_assn @ A )
% 7.75/5.72 = A ) ).
% 7.75/5.72
% 7.75/5.72 % norm_assertion_simps(1)
% 7.75/5.72 thf(fact_6779_norm__assertion__simps_I2_J,axiom,
% 7.75/5.72 ! [A: assn] :
% 7.75/5.72 ( ( times_times_assn @ A @ one_one_assn )
% 7.75/5.72 = A ) ).
% 7.75/5.72
% 7.75/5.72 % norm_assertion_simps(2)
% 7.75/5.72 thf(fact_6780_stable__imp__take__bit__eq,axiom,
% 7.75/5.72 ! [A: code_integer,N: nat] :
% 7.75/5.72 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.75/5.72 = A )
% 7.75/5.72 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.72 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 7.75/5.72 = zero_z3403309356797280102nteger ) )
% 7.75/5.72 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.72 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 7.75/5.72 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % stable_imp_take_bit_eq
% 7.75/5.72 thf(fact_6781_stable__imp__take__bit__eq,axiom,
% 7.75/5.72 ! [A: nat,N: nat] :
% 7.75/5.72 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.72 = A )
% 7.75/5.72 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.72 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 7.75/5.72 = zero_zero_nat ) )
% 7.75/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.72 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 7.75/5.72 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % stable_imp_take_bit_eq
% 7.75/5.72 thf(fact_6782_stable__imp__take__bit__eq,axiom,
% 7.75/5.72 ! [A: int,N: nat] :
% 7.75/5.72 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.72 = A )
% 7.75/5.72 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 7.75/5.72 = zero_zero_int ) )
% 7.75/5.72 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.72 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 7.75/5.72 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % stable_imp_take_bit_eq
% 7.75/5.72 thf(fact_6783_take__bit__numeral__bit1,axiom,
% 7.75/5.72 ! [L: num,K: num] :
% 7.75/5.72 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 7.75/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_bit1
% 7.75/5.72 thf(fact_6784_take__bit__numeral__bit1,axiom,
% 7.75/5.72 ! [L: num,K: num] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 7.75/5.72 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_bit1
% 7.75/5.72 thf(fact_6785_take__bit__numeral__bit1,axiom,
% 7.75/5.72 ! [L: num,K: num] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 7.75/5.72 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_numeral_bit1
% 7.75/5.72 thf(fact_6786_real__exp__bound__lemma,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.72 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % real_exp_bound_lemma
% 7.75/5.72 thf(fact_6787_exp__ge__one__plus__x__over__n__power__n,axiom,
% 7.75/5.72 ! [N: nat,X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 7.75/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.72 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_ge_one_plus_x_over_n_power_n
% 7.75/5.72 thf(fact_6788_exp__ge__one__minus__x__over__n__power__n,axiom,
% 7.75/5.72 ! [X: real,N: nat] :
% 7.75/5.72 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.72 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_ge_one_minus_x_over_n_power_n
% 7.75/5.72 thf(fact_6789_exp__bound__lemma,axiom,
% 7.75/5.72 ! [Z: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.72 => ( 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 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_bound_lemma
% 7.75/5.72 thf(fact_6790_exp__bound__lemma,axiom,
% 7.75/5.72 ! [Z: complex] :
% 7.75/5.72 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.72 => ( 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 ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_bound_lemma
% 7.75/5.72 thf(fact_6791_exp__lower__Taylor__quadratic,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.72 => ( 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 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % exp_lower_Taylor_quadratic
% 7.75/5.72 thf(fact_6792_log__base__10__eq2,axiom,
% 7.75/5.72 ! [X: real] :
% 7.75/5.72 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.72 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 7.75/5.72 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % log_base_10_eq2
% 7.75/5.72 thf(fact_6793_tanh__real__altdef,axiom,
% 7.75/5.72 ( tanh_real
% 7.75/5.72 = ( ^ [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 ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % tanh_real_altdef
% 7.75/5.72 thf(fact_6794_take__bit__rec,axiom,
% 7.75/5.72 ( bit_se1745604003318907178nteger
% 7.75/5.72 = ( ^ [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 ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_rec
% 7.75/5.72 thf(fact_6795_take__bit__rec,axiom,
% 7.75/5.72 ( bit_se2925701944663578781it_nat
% 7.75/5.72 = ( ^ [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 ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_rec
% 7.75/5.72 thf(fact_6796_take__bit__rec,axiom,
% 7.75/5.72 ( bit_se2923211474154528505it_int
% 7.75/5.72 = ( ^ [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 ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_rec
% 7.75/5.72 thf(fact_6797_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 7.75/5.72 ! [A: $o,B: $o] :
% 7.75/5.72 ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.72 = zero_zero_nat ) ).
% 7.75/5.72
% 7.75/5.72 % VEBT_internal.height.simps(1)
% 7.75/5.72 thf(fact_6798_option_Osize_I3_J,axiom,
% 7.75/5.72 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 7.75/5.72 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % option.size(3)
% 7.75/5.72 thf(fact_6799_option_Osize_I3_J,axiom,
% 7.75/5.72 ( ( size_size_option_nat @ none_nat )
% 7.75/5.72 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % option.size(3)
% 7.75/5.72 thf(fact_6800_option_Osize_I3_J,axiom,
% 7.75/5.72 ( ( size_size_option_num @ none_num )
% 7.75/5.72 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.72
% 7.75/5.72 % option.size(3)
% 7.75/5.72 thf(fact_6801_uint32_Osize__eq,axiom,
% 7.75/5.72 ( size_size_uint32
% 7.75/5.72 = ( ^ [P5: uint32] : ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % uint32.size_eq
% 7.75/5.72 thf(fact_6802_slice__nth,axiom,
% 7.75/5.72 ! [From: nat,To: nat,Xs2: list_VEBT_VEBT,I: nat] :
% 7.75/5.72 ( ( ord_less_nat @ From @ To )
% 7.75/5.72 => ( ( ord_less_eq_nat @ To @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.72 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 7.75/5.72 => ( ( nth_VEBT_VEBT @ ( slice_VEBT_VEBT @ From @ To @ Xs2 ) @ I )
% 7.75/5.72 = ( nth_VEBT_VEBT @ Xs2 @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % slice_nth
% 7.75/5.72 thf(fact_6803_slice__nth,axiom,
% 7.75/5.72 ! [From: nat,To: nat,Xs2: list_VEBT_VEBTi,I: nat] :
% 7.75/5.72 ( ( ord_less_nat @ From @ To )
% 7.75/5.72 => ( ( ord_less_eq_nat @ To @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.72 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 7.75/5.72 => ( ( nth_VEBT_VEBTi @ ( slice_VEBT_VEBTi @ From @ To @ Xs2 ) @ I )
% 7.75/5.72 = ( nth_VEBT_VEBTi @ Xs2 @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % slice_nth
% 7.75/5.72 thf(fact_6804_slice__nth,axiom,
% 7.75/5.72 ! [From: nat,To: nat,Xs2: list_real,I: nat] :
% 7.75/5.72 ( ( ord_less_nat @ From @ To )
% 7.75/5.72 => ( ( ord_less_eq_nat @ To @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.72 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 7.75/5.72 => ( ( nth_real @ ( slice_real @ From @ To @ Xs2 ) @ I )
% 7.75/5.72 = ( nth_real @ Xs2 @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % slice_nth
% 7.75/5.72 thf(fact_6805_slice__nth,axiom,
% 7.75/5.72 ! [From: nat,To: nat,Xs2: list_o,I: nat] :
% 7.75/5.72 ( ( ord_less_nat @ From @ To )
% 7.75/5.72 => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.72 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 7.75/5.72 => ( ( nth_o @ ( slice_o @ From @ To @ Xs2 ) @ I )
% 7.75/5.72 = ( nth_o @ Xs2 @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % slice_nth
% 7.75/5.72 thf(fact_6806_slice__nth,axiom,
% 7.75/5.72 ! [From: nat,To: nat,Xs2: list_nat,I: nat] :
% 7.75/5.72 ( ( ord_less_nat @ From @ To )
% 7.75/5.72 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.72 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 7.75/5.72 => ( ( nth_nat @ ( slice_nat @ From @ To @ Xs2 ) @ I )
% 7.75/5.72 = ( nth_nat @ Xs2 @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % slice_nth
% 7.75/5.72 thf(fact_6807_slice__nth,axiom,
% 7.75/5.72 ! [From: nat,To: nat,Xs2: list_int,I: nat] :
% 7.75/5.72 ( ( ord_less_nat @ From @ To )
% 7.75/5.72 => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.72 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 7.75/5.72 => ( ( nth_int @ ( slice_int @ From @ To @ Xs2 ) @ I )
% 7.75/5.72 = ( nth_int @ Xs2 @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % slice_nth
% 7.75/5.72 thf(fact_6808_pred__numeral__inc,axiom,
% 7.75/5.72 ! [K: num] :
% 7.75/5.72 ( ( pred_numeral @ ( inc @ K ) )
% 7.75/5.72 = ( numeral_numeral_nat @ K ) ) ).
% 7.75/5.72
% 7.75/5.72 % pred_numeral_inc
% 7.75/5.72 thf(fact_6809_slice__complete,axiom,
% 7.75/5.72 ! [Xs2: list_real] :
% 7.75/5.72 ( ( slice_real @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) @ Xs2 )
% 7.75/5.72 = Xs2 ) ).
% 7.75/5.72
% 7.75/5.72 % slice_complete
% 7.75/5.72 thf(fact_6810_slice__complete,axiom,
% 7.75/5.72 ! [Xs2: list_o] :
% 7.75/5.72 ( ( slice_o @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) @ Xs2 )
% 7.75/5.72 = Xs2 ) ).
% 7.75/5.72
% 7.75/5.72 % slice_complete
% 7.75/5.72 thf(fact_6811_slice__complete,axiom,
% 7.75/5.72 ! [Xs2: list_nat] :
% 7.75/5.72 ( ( slice_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) @ Xs2 )
% 7.75/5.72 = Xs2 ) ).
% 7.75/5.72
% 7.75/5.72 % slice_complete
% 7.75/5.72 thf(fact_6812_slice__complete,axiom,
% 7.75/5.72 ! [Xs2: list_int] :
% 7.75/5.72 ( ( slice_int @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) @ Xs2 )
% 7.75/5.72 = Xs2 ) ).
% 7.75/5.72
% 7.75/5.72 % slice_complete
% 7.75/5.72 thf(fact_6813_add__neg__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.75/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(5)
% 7.75/5.72 thf(fact_6814_add__neg__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 7.75/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(5)
% 7.75/5.72 thf(fact_6815_add__neg__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 7.75/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(5)
% 7.75/5.72 thf(fact_6816_add__neg__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 7.75/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(5)
% 7.75/5.72 thf(fact_6817_add__neg__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 7.75/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(5)
% 7.75/5.72 thf(fact_6818_add__neg__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(6)
% 7.75/5.72 thf(fact_6819_add__neg__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(6)
% 7.75/5.72 thf(fact_6820_add__neg__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(6)
% 7.75/5.72 thf(fact_6821_add__neg__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(6)
% 7.75/5.72 thf(fact_6822_add__neg__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % add_neg_numeral_special(6)
% 7.75/5.72 thf(fact_6823_diff__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 7.75/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(5)
% 7.75/5.72 thf(fact_6824_diff__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 7.75/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(5)
% 7.75/5.72 thf(fact_6825_diff__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 7.75/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(5)
% 7.75/5.72 thf(fact_6826_diff__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 7.75/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(5)
% 7.75/5.72 thf(fact_6827_diff__numeral__special_I5_J,axiom,
% 7.75/5.72 ! [N: num] :
% 7.75/5.72 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 7.75/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(5)
% 7.75/5.72 thf(fact_6828_diff__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.72 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(6)
% 7.75/5.72 thf(fact_6829_diff__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.72 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(6)
% 7.75/5.72 thf(fact_6830_diff__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.72 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(6)
% 7.75/5.72 thf(fact_6831_diff__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.72 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(6)
% 7.75/5.72 thf(fact_6832_diff__numeral__special_I6_J,axiom,
% 7.75/5.72 ! [M: num] :
% 7.75/5.72 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.72 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % diff_numeral_special(6)
% 7.75/5.72 thf(fact_6833_take__bit__of__Suc__0,axiom,
% 7.75/5.72 ! [N: nat] :
% 7.75/5.72 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 7.75/5.72 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_of_Suc_0
% 7.75/5.72 thf(fact_6834_take__bit__tightened__less__eq__nat,axiom,
% 7.75/5.72 ! [M: nat,N: nat,Q3: nat] :
% 7.75/5.72 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.72 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N @ Q3 ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_tightened_less_eq_nat
% 7.75/5.72 thf(fact_6835_take__bit__nat__less__eq__self,axiom,
% 7.75/5.72 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_nat_less_eq_self
% 7.75/5.72 thf(fact_6836_take__bit__minus,axiom,
% 7.75/5.72 ! [N: nat,K: int] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 7.75/5.72 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 7.75/5.72
% 7.75/5.72 % take_bit_minus
% 7.75/5.72 thf(fact_6837_take__bit__mult,axiom,
% 7.75/5.72 ! [N: nat,K: int,L: int] :
% 7.75/5.72 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 7.75/5.73 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_mult
% 7.75/5.73 thf(fact_6838_take__bit__diff,axiom,
% 7.75/5.73 ! [N: nat,K: int,L: int] :
% 7.75/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 7.75/5.73 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_diff
% 7.75/5.73 thf(fact_6839_num__induct,axiom,
% 7.75/5.73 ! [P: num > $o,X: num] :
% 7.75/5.73 ( ( P @ one )
% 7.75/5.73 => ( ! [X3: num] :
% 7.75/5.73 ( ( P @ X3 )
% 7.75/5.73 => ( P @ ( inc @ X3 ) ) )
% 7.75/5.73 => ( P @ X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % num_induct
% 7.75/5.73 thf(fact_6840_add__inc,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 7.75/5.73 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % add_inc
% 7.75/5.73 thf(fact_6841_take__bit__tightened__less__eq__int,axiom,
% 7.75/5.73 ! [M: nat,N: nat,K: int] :
% 7.75/5.73 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.73 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_tightened_less_eq_int
% 7.75/5.73 thf(fact_6842_take__bit__nonnegative,axiom,
% 7.75/5.73 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_nonnegative
% 7.75/5.73 thf(fact_6843_take__bit__int__less__eq__self__iff,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 7.75/5.73 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_less_eq_self_iff
% 7.75/5.73 thf(fact_6844_not__take__bit__negative,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % not_take_bit_negative
% 7.75/5.73 thf(fact_6845_take__bit__int__greater__self__iff,axiom,
% 7.75/5.73 ! [K: int,N: nat] :
% 7.75/5.73 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 7.75/5.73 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_greater_self_iff
% 7.75/5.73 thf(fact_6846_inc_Osimps_I1_J,axiom,
% 7.75/5.73 ( ( inc @ one )
% 7.75/5.73 = ( bit0 @ one ) ) ).
% 7.75/5.73
% 7.75/5.73 % inc.simps(1)
% 7.75/5.73 thf(fact_6847_inc_Osimps_I3_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( inc @ ( bit1 @ X ) )
% 7.75/5.73 = ( bit0 @ ( inc @ X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % inc.simps(3)
% 7.75/5.73 thf(fact_6848_inc_Osimps_I2_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( inc @ ( bit0 @ X ) )
% 7.75/5.73 = ( bit1 @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % inc.simps(2)
% 7.75/5.73 thf(fact_6849_add__One,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( plus_plus_num @ X @ one )
% 7.75/5.73 = ( inc @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % add_One
% 7.75/5.73 thf(fact_6850_mult__inc,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( times_times_num @ X @ ( inc @ Y ) )
% 7.75/5.73 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % mult_inc
% 7.75/5.73 thf(fact_6851_take__bit__decr__eq,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 7.75/5.73 != zero_zero_int )
% 7.75/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 7.75/5.73 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_decr_eq
% 7.75/5.73 thf(fact_6852_numeral__inc,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 7.75/5.73 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 7.75/5.73
% 7.75/5.73 % numeral_inc
% 7.75/5.73 thf(fact_6853_numeral__inc,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( numeral_numeral_real @ ( inc @ X ) )
% 7.75/5.73 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % numeral_inc
% 7.75/5.73 thf(fact_6854_numeral__inc,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( numeral_numeral_rat @ ( inc @ X ) )
% 7.75/5.73 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 7.75/5.73
% 7.75/5.73 % numeral_inc
% 7.75/5.73 thf(fact_6855_numeral__inc,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 7.75/5.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % numeral_inc
% 7.75/5.73 thf(fact_6856_numeral__inc,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( numeral_numeral_int @ ( inc @ X ) )
% 7.75/5.73 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % numeral_inc
% 7.75/5.73 thf(fact_6857_take__bit__nat__eq__self,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 7.75/5.73 = M ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_nat_eq_self
% 7.75/5.73 thf(fact_6858_take__bit__nat__less__exp,axiom,
% 7.75/5.73 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_nat_less_exp
% 7.75/5.73 thf(fact_6859_take__bit__nat__eq__self__iff,axiom,
% 7.75/5.73 ! [N: nat,M: nat] :
% 7.75/5.73 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 7.75/5.73 = M )
% 7.75/5.73 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_nat_eq_self_iff
% 7.75/5.73 thf(fact_6860_take__bit__nat__def,axiom,
% 7.75/5.73 ( bit_se2925701944663578781it_nat
% 7.75/5.73 = ( ^ [N3: nat,M4: nat] : ( modulo_modulo_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_nat_def
% 7.75/5.73 thf(fact_6861_take__bit__Suc__minus__bit1,axiom,
% 7.75/5.73 ! [N: nat,K: num] :
% 7.75/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 7.75/5.73 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_Suc_minus_bit1
% 7.75/5.73 thf(fact_6862_take__bit__int__less__exp,axiom,
% 7.75/5.73 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_less_exp
% 7.75/5.73 thf(fact_6863_take__bit__int__def,axiom,
% 7.75/5.73 ( bit_se2923211474154528505it_int
% 7.75/5.73 = ( ^ [N3: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_def
% 7.75/5.73 thf(fact_6864_take__bit__numeral__minus__bit1,axiom,
% 7.75/5.73 ! [L: num,K: num] :
% 7.75/5.73 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 7.75/5.73 = ( 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 ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_numeral_minus_bit1
% 7.75/5.73 thf(fact_6865_take__bit__nat__less__self__iff,axiom,
% 7.75/5.73 ! [N: nat,M: nat] :
% 7.75/5.73 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 7.75/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_nat_less_self_iff
% 7.75/5.73 thf(fact_6866_take__bit__Suc__minus__bit0,axiom,
% 7.75/5.73 ! [N: nat,K: num] :
% 7.75/5.73 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 7.75/5.73 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_Suc_minus_bit0
% 7.75/5.73 thf(fact_6867_take__bit__int__less__self__iff,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 7.75/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_less_self_iff
% 7.75/5.73 thf(fact_6868_take__bit__int__greater__eq__self__iff,axiom,
% 7.75/5.73 ! [K: int,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 7.75/5.73 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_greater_eq_self_iff
% 7.75/5.73 thf(fact_6869_take__bit__int__eq__self__iff,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 7.75/5.73 = K )
% 7.75/5.73 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.73 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_eq_self_iff
% 7.75/5.73 thf(fact_6870_take__bit__int__eq__self,axiom,
% 7.75/5.73 ! [K: int,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.73 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.73 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 7.75/5.73 = K ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_eq_self
% 7.75/5.73 thf(fact_6871_take__bit__incr__eq,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 7.75/5.73 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 7.75/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 7.75/5.73 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_incr_eq
% 7.75/5.73 thf(fact_6872_take__bit__numeral__minus__bit0,axiom,
% 7.75/5.73 ! [L: num,K: num] :
% 7.75/5.73 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 7.75/5.73 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_numeral_minus_bit0
% 7.75/5.73 thf(fact_6873_take__bit__int__less__eq,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 7.75/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.73 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_less_eq
% 7.75/5.73 thf(fact_6874_take__bit__int__greater__eq,axiom,
% 7.75/5.73 ! [K: int,N: nat] :
% 7.75/5.73 ( ( ord_less_int @ K @ zero_zero_int )
% 7.75/5.73 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_int_greater_eq
% 7.75/5.73 thf(fact_6875_signed__take__bit__eq__take__bit__shift,axiom,
% 7.75/5.73 ( bit_ri631733984087533419it_int
% 7.75/5.73 = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % signed_take_bit_eq_take_bit_shift
% 7.75/5.73 thf(fact_6876_take__bit__minus__small__eq,axiom,
% 7.75/5.73 ! [K: int,N: nat] :
% 7.75/5.73 ( ( ord_less_int @ zero_zero_int @ K )
% 7.75/5.73 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.73 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 7.75/5.73 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_minus_small_eq
% 7.75/5.73 thf(fact_6877_powr__int,axiom,
% 7.75/5.73 ! [X: real,I: int] :
% 7.75/5.73 ( ( ord_less_real @ zero_zero_real @ X )
% 7.75/5.73 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 7.75/5.73 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 7.75/5.73 = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 7.75/5.73 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 7.75/5.73 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 7.75/5.73 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % powr_int
% 7.75/5.73 thf(fact_6878_fact__double,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.73 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_double
% 7.75/5.73 thf(fact_6879_fact__double,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.73 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_double
% 7.75/5.73 thf(fact_6880_fact__double,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 7.75/5.73 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_double
% 7.75/5.73 thf(fact_6881_even__set__encode__iff,axiom,
% 7.75/5.73 ! [A2: set_nat] :
% 7.75/5.73 ( ( finite_finite_nat @ A2 )
% 7.75/5.73 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 7.75/5.73 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % even_set_encode_iff
% 7.75/5.73 thf(fact_6882_set__decode__inverse,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 7.75/5.73 = N ) ).
% 7.75/5.73
% 7.75/5.73 % set_decode_inverse
% 7.75/5.73 thf(fact_6883_fact__0,axiom,
% 7.75/5.73 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 7.75/5.73 = one_one_rat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_0
% 7.75/5.73 thf(fact_6884_fact__0,axiom,
% 7.75/5.73 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 7.75/5.73 = one_one_int ) ).
% 7.75/5.73
% 7.75/5.73 % fact_0
% 7.75/5.73 thf(fact_6885_fact__0,axiom,
% 7.75/5.73 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_0
% 7.75/5.73 thf(fact_6886_fact__0,axiom,
% 7.75/5.73 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 7.75/5.73 = one_one_real ) ).
% 7.75/5.73
% 7.75/5.73 % fact_0
% 7.75/5.73 thf(fact_6887_fact__0,axiom,
% 7.75/5.73 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 7.75/5.73 = one_one_complex ) ).
% 7.75/5.73
% 7.75/5.73 % fact_0
% 7.75/5.73 thf(fact_6888_nat__numeral,axiom,
% 7.75/5.73 ! [K: num] :
% 7.75/5.73 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 7.75/5.73 = ( numeral_numeral_nat @ K ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_numeral
% 7.75/5.73 thf(fact_6889_fact__1,axiom,
% 7.75/5.73 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 7.75/5.73 = one_one_rat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_1
% 7.75/5.73 thf(fact_6890_fact__1,axiom,
% 7.75/5.73 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 7.75/5.73 = one_one_int ) ).
% 7.75/5.73
% 7.75/5.73 % fact_1
% 7.75/5.73 thf(fact_6891_fact__1,axiom,
% 7.75/5.73 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_1
% 7.75/5.73 thf(fact_6892_fact__1,axiom,
% 7.75/5.73 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 7.75/5.73 = one_one_real ) ).
% 7.75/5.73
% 7.75/5.73 % fact_1
% 7.75/5.73 thf(fact_6893_fact__1,axiom,
% 7.75/5.73 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 7.75/5.73 = one_one_complex ) ).
% 7.75/5.73
% 7.75/5.73 % fact_1
% 7.75/5.73 thf(fact_6894_set__encode__inverse,axiom,
% 7.75/5.73 ! [A2: set_nat] :
% 7.75/5.73 ( ( finite_finite_nat @ A2 )
% 7.75/5.73 => ( ( nat_set_decode @ ( nat_set_encode @ A2 ) )
% 7.75/5.73 = A2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_encode_inverse
% 7.75/5.73 thf(fact_6895_fact__Suc__0,axiom,
% 7.75/5.73 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = one_one_rat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc_0
% 7.75/5.73 thf(fact_6896_fact__Suc__0,axiom,
% 7.75/5.73 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = one_one_int ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc_0
% 7.75/5.73 thf(fact_6897_fact__Suc__0,axiom,
% 7.75/5.73 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc_0
% 7.75/5.73 thf(fact_6898_fact__Suc__0,axiom,
% 7.75/5.73 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = one_one_real ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc_0
% 7.75/5.73 thf(fact_6899_fact__Suc__0,axiom,
% 7.75/5.73 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = one_one_complex ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc_0
% 7.75/5.73 thf(fact_6900_fact__Suc,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri3624122377584611663nteger @ ( suc @ N ) )
% 7.75/5.73 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc
% 7.75/5.73 thf(fact_6901_fact__Suc,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 7.75/5.73 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc
% 7.75/5.73 thf(fact_6902_fact__Suc,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 7.75/5.73 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc
% 7.75/5.73 thf(fact_6903_fact__Suc,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 7.75/5.73 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc
% 7.75/5.73 thf(fact_6904_fact__Suc,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri5044797733671781792omplex @ ( suc @ N ) )
% 7.75/5.73 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_Suc
% 7.75/5.73 thf(fact_6905_nat__1,axiom,
% 7.75/5.73 ( ( nat2 @ one_one_int )
% 7.75/5.73 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_1
% 7.75/5.73 thf(fact_6906_nat__le__0,axiom,
% 7.75/5.73 ! [Z: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 7.75/5.73 => ( ( nat2 @ Z )
% 7.75/5.73 = zero_zero_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_le_0
% 7.75/5.73 thf(fact_6907_nat__0__iff,axiom,
% 7.75/5.73 ! [I: int] :
% 7.75/5.73 ( ( ( nat2 @ I )
% 7.75/5.73 = zero_zero_nat )
% 7.75/5.73 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_0_iff
% 7.75/5.73 thf(fact_6908_nat__neg__numeral,axiom,
% 7.75/5.73 ! [K: num] :
% 7.75/5.73 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 7.75/5.73 = zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % nat_neg_numeral
% 7.75/5.73 thf(fact_6909_zless__nat__conj,axiom,
% 7.75/5.73 ! [W: int,Z: int] :
% 7.75/5.73 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ( ord_less_int @ zero_zero_int @ Z )
% 7.75/5.73 & ( ord_less_int @ W @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % zless_nat_conj
% 7.75/5.73 thf(fact_6910_of__nat__nat__take__bit__eq,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 7.75/5.73 = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_nat_take_bit_eq
% 7.75/5.73 thf(fact_6911_of__nat__nat__take__bit__eq,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 7.75/5.73 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_nat_take_bit_eq
% 7.75/5.73 thf(fact_6912_of__nat__nat__take__bit__eq,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( semiri8010041392384452111omplex @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 7.75/5.73 = ( ring_17405671764205052669omplex @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_nat_take_bit_eq
% 7.75/5.73 thf(fact_6913_nat__zminus__int,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 7.75/5.73 = zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % nat_zminus_int
% 7.75/5.73 thf(fact_6914_int__nat__eq,axiom,
% 7.75/5.73 ! [Z: int] :
% 7.75/5.73 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 7.75/5.73 = Z ) )
% 7.75/5.73 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 7.75/5.73 = zero_zero_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % int_nat_eq
% 7.75/5.73 thf(fact_6915_fact__2,axiom,
% 7.75/5.73 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.73 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_2
% 7.75/5.73 thf(fact_6916_fact__2,axiom,
% 7.75/5.73 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.73 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_2
% 7.75/5.73 thf(fact_6917_fact__2,axiom,
% 7.75/5.73 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_2
% 7.75/5.73 thf(fact_6918_fact__2,axiom,
% 7.75/5.73 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.73 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_2
% 7.75/5.73 thf(fact_6919_fact__2,axiom,
% 7.75/5.73 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.73 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_2
% 7.75/5.73 thf(fact_6920_zero__less__nat__eq,axiom,
% 7.75/5.73 ! [Z: int] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 7.75/5.73
% 7.75/5.73 % zero_less_nat_eq
% 7.75/5.73 thf(fact_6921_of__nat__nat,axiom,
% 7.75/5.73 ! [Z: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ring_1_of_int_real @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_nat
% 7.75/5.73 thf(fact_6922_of__nat__nat,axiom,
% 7.75/5.73 ! [Z: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ring_1_of_int_int @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_nat
% 7.75/5.73 thf(fact_6923_of__nat__nat,axiom,
% 7.75/5.73 ! [Z: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( semiri8010041392384452111omplex @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_nat
% 7.75/5.73 thf(fact_6924_diff__nat__numeral,axiom,
% 7.75/5.73 ! [V: num,V2: num] :
% 7.75/5.73 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V2 ) )
% 7.75/5.73 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % diff_nat_numeral
% 7.75/5.73 thf(fact_6925_numeral__power__eq__nat__cancel__iff,axiom,
% 7.75/5.73 ! [X: num,N: nat,Y: int] :
% 7.75/5.73 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 7.75/5.73 = ( nat2 @ Y ) )
% 7.75/5.73 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 7.75/5.73 = Y ) ) ).
% 7.75/5.73
% 7.75/5.73 % numeral_power_eq_nat_cancel_iff
% 7.75/5.73 thf(fact_6926_nat__eq__numeral__power__cancel__iff,axiom,
% 7.75/5.73 ! [Y: int,X: num,N: nat] :
% 7.75/5.73 ( ( ( nat2 @ Y )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 7.75/5.73 = ( Y
% 7.75/5.73 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_eq_numeral_power_cancel_iff
% 7.75/5.73 thf(fact_6927_dvd__nat__abs__iff,axiom,
% 7.75/5.73 ! [N: nat,K: int] :
% 7.75/5.73 ( ( dvd_dvd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 7.75/5.73 = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 7.75/5.73
% 7.75/5.73 % dvd_nat_abs_iff
% 7.75/5.73 thf(fact_6928_nat__abs__dvd__iff,axiom,
% 7.75/5.73 ! [K: int,N: nat] :
% 7.75/5.73 ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 7.75/5.73 = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_abs_dvd_iff
% 7.75/5.73 thf(fact_6929_nat__ceiling__le__eq,axiom,
% 7.75/5.73 ! [X: real,A: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 7.75/5.73 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_ceiling_le_eq
% 7.75/5.73 thf(fact_6930_one__less__nat__eq,axiom,
% 7.75/5.73 ! [Z: int] :
% 7.75/5.73 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 7.75/5.73
% 7.75/5.73 % one_less_nat_eq
% 7.75/5.73 thf(fact_6931_nat__numeral__diff__1,axiom,
% 7.75/5.73 ! [V: num] :
% 7.75/5.73 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 7.75/5.73 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_numeral_diff_1
% 7.75/5.73 thf(fact_6932_numeral__power__less__nat__cancel__iff,axiom,
% 7.75/5.73 ! [X: num,N: nat,A: int] :
% 7.75/5.73 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 7.75/5.73 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % numeral_power_less_nat_cancel_iff
% 7.75/5.73 thf(fact_6933_nat__less__numeral__power__cancel__iff,axiom,
% 7.75/5.73 ! [A: int,X: num,N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 7.75/5.73 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_less_numeral_power_cancel_iff
% 7.75/5.73 thf(fact_6934_numeral__power__le__nat__cancel__iff,axiom,
% 7.75/5.73 ! [X: num,N: nat,A: int] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 7.75/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % numeral_power_le_nat_cancel_iff
% 7.75/5.73 thf(fact_6935_nat__le__numeral__power__cancel__iff,axiom,
% 7.75/5.73 ! [A: int,X: num,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 7.75/5.73 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_le_numeral_power_cancel_iff
% 7.75/5.73 thf(fact_6936_fact__nonzero,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri773545260158071498ct_rat @ N )
% 7.75/5.73 != zero_zero_rat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_nonzero
% 7.75/5.73 thf(fact_6937_fact__nonzero,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri1406184849735516958ct_int @ N )
% 7.75/5.73 != zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % fact_nonzero
% 7.75/5.73 thf(fact_6938_fact__nonzero,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri1408675320244567234ct_nat @ N )
% 7.75/5.73 != zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_nonzero
% 7.75/5.73 thf(fact_6939_fact__nonzero,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri2265585572941072030t_real @ N )
% 7.75/5.73 != zero_zero_real ) ).
% 7.75/5.73
% 7.75/5.73 % fact_nonzero
% 7.75/5.73 thf(fact_6940_fact__nonzero,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( semiri5044797733671781792omplex @ N )
% 7.75/5.73 != zero_zero_complex ) ).
% 7.75/5.73
% 7.75/5.73 % fact_nonzero
% 7.75/5.73 thf(fact_6941_fact__less__mono__nat,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.73 => ( ( ord_less_nat @ M @ N )
% 7.75/5.73 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_less_mono_nat
% 7.75/5.73 thf(fact_6942_nat__numeral__as__int,axiom,
% 7.75/5.73 ( numeral_numeral_nat
% 7.75/5.73 = ( ^ [I2: num] : ( nat2 @ ( numeral_numeral_int @ I2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_numeral_as_int
% 7.75/5.73 thf(fact_6943_nat__zero__as__int,axiom,
% 7.75/5.73 ( zero_zero_nat
% 7.75/5.73 = ( nat2 @ zero_zero_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_zero_as_int
% 7.75/5.73 thf(fact_6944_fact__ge__zero,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_ge_zero
% 7.75/5.73 thf(fact_6945_fact__ge__zero,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_ge_zero
% 7.75/5.73 thf(fact_6946_fact__ge__zero,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_ge_zero
% 7.75/5.73 thf(fact_6947_fact__ge__zero,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_ge_zero
% 7.75/5.73 thf(fact_6948_fact__gt__zero,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_gt_zero
% 7.75/5.73 thf(fact_6949_fact__gt__zero,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_gt_zero
% 7.75/5.73 thf(fact_6950_fact__gt__zero,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_gt_zero
% 7.75/5.73 thf(fact_6951_fact__gt__zero,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_gt_zero
% 7.75/5.73 thf(fact_6952_fact__not__neg,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_not_neg
% 7.75/5.73 thf(fact_6953_fact__not__neg,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % fact_not_neg
% 7.75/5.73 thf(fact_6954_fact__not__neg,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % fact_not_neg
% 7.75/5.73 thf(fact_6955_fact__not__neg,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 7.75/5.73
% 7.75/5.73 % fact_not_neg
% 7.75/5.73 thf(fact_6956_fact__ge__1,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_ge_1
% 7.75/5.73 thf(fact_6957_fact__ge__1,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_ge_1
% 7.75/5.73 thf(fact_6958_fact__ge__1,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_ge_1
% 7.75/5.73 thf(fact_6959_fact__ge__1,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_ge_1
% 7.75/5.73 thf(fact_6960_nat__one__as__int,axiom,
% 7.75/5.73 ( one_one_nat
% 7.75/5.73 = ( nat2 @ one_one_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_one_as_int
% 7.75/5.73 thf(fact_6961_ex__nat,axiom,
% 7.75/5.73 ( ( ^ [P6: nat > $o] :
% 7.75/5.73 ? [X8: nat] : ( P6 @ X8 ) )
% 7.75/5.73 = ( ^ [P2: nat > $o] :
% 7.75/5.73 ? [X2: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 7.75/5.73 & ( P2 @ ( nat2 @ X2 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % ex_nat
% 7.75/5.73 thf(fact_6962_all__nat,axiom,
% 7.75/5.73 ( ( ^ [P6: nat > $o] :
% 7.75/5.73 ! [X8: nat] : ( P6 @ X8 ) )
% 7.75/5.73 = ( ^ [P2: nat > $o] :
% 7.75/5.73 ! [X2: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 7.75/5.73 => ( P2 @ ( nat2 @ X2 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % all_nat
% 7.75/5.73 thf(fact_6963_eq__nat__nat__iff,axiom,
% 7.75/5.73 ! [Z: int,Z5: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
% 7.75/5.73 => ( ( ( nat2 @ Z )
% 7.75/5.73 = ( nat2 @ Z5 ) )
% 7.75/5.73 = ( Z = Z5 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % eq_nat_nat_iff
% 7.75/5.73 thf(fact_6964_fact__dvd,axiom,
% 7.75/5.73 ! [N: nat,M: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.73 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_dvd
% 7.75/5.73 thf(fact_6965_fact__dvd,axiom,
% 7.75/5.73 ! [N: nat,M: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.73 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_dvd
% 7.75/5.73 thf(fact_6966_fact__dvd,axiom,
% 7.75/5.73 ! [N: nat,M: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.73 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_dvd
% 7.75/5.73 thf(fact_6967_set__encode__eq,axiom,
% 7.75/5.73 ! [A2: set_nat,B3: set_nat] :
% 7.75/5.73 ( ( finite_finite_nat @ A2 )
% 7.75/5.73 => ( ( finite_finite_nat @ B3 )
% 7.75/5.73 => ( ( ( nat_set_encode @ A2 )
% 7.75/5.73 = ( nat_set_encode @ B3 ) )
% 7.75/5.73 = ( A2 = B3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_encode_eq
% 7.75/5.73 thf(fact_6968_pochhammer__fact,axiom,
% 7.75/5.73 ( semiri773545260158071498ct_rat
% 7.75/5.73 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_fact
% 7.75/5.73 thf(fact_6969_pochhammer__fact,axiom,
% 7.75/5.73 ( semiri1406184849735516958ct_int
% 7.75/5.73 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_fact
% 7.75/5.73 thf(fact_6970_pochhammer__fact,axiom,
% 7.75/5.73 ( semiri1408675320244567234ct_nat
% 7.75/5.73 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_fact
% 7.75/5.73 thf(fact_6971_pochhammer__fact,axiom,
% 7.75/5.73 ( semiri2265585572941072030t_real
% 7.75/5.73 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_fact
% 7.75/5.73 thf(fact_6972_pochhammer__fact,axiom,
% 7.75/5.73 ( semiri5044797733671781792omplex
% 7.75/5.73 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_fact
% 7.75/5.73 thf(fact_6973_unset__bit__nat__def,axiom,
% 7.75/5.73 ( bit_se4205575877204974255it_nat
% 7.75/5.73 = ( ^ [M4: nat,N3: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M4 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % unset_bit_nat_def
% 7.75/5.73 thf(fact_6974_fact__ge__Suc__0__nat,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_ge_Suc_0_nat
% 7.75/5.73 thf(fact_6975_dvd__fact,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 7.75/5.73 => ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.73 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % dvd_fact
% 7.75/5.73 thf(fact_6976_nat__mono__iff,axiom,
% 7.75/5.73 ! [Z: int,W: int] :
% 7.75/5.73 ( ( ord_less_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ord_less_int @ W @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_mono_iff
% 7.75/5.73 thf(fact_6977_zless__nat__eq__int__zless,axiom,
% 7.75/5.73 ! [M: nat,Z: int] :
% 7.75/5.73 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 7.75/5.73
% 7.75/5.73 % zless_nat_eq_int_zless
% 7.75/5.73 thf(fact_6978_fact__less__mono,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.73 => ( ( ord_less_nat @ M @ N )
% 7.75/5.73 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_less_mono
% 7.75/5.73 thf(fact_6979_fact__less__mono,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.73 => ( ( ord_less_nat @ M @ N )
% 7.75/5.73 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_less_mono
% 7.75/5.73 thf(fact_6980_fact__less__mono,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.73 => ( ( ord_less_nat @ M @ N )
% 7.75/5.73 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_less_mono
% 7.75/5.73 thf(fact_6981_fact__less__mono,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.73 => ( ( ord_less_nat @ M @ N )
% 7.75/5.73 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_less_mono
% 7.75/5.73 thf(fact_6982_nat__0__le,axiom,
% 7.75/5.73 ! [Z: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 7.75/5.73 = Z ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_0_le
% 7.75/5.73 thf(fact_6983_int__eq__iff,axiom,
% 7.75/5.73 ! [M: nat,Z: int] :
% 7.75/5.73 ( ( ( semiri1314217659103216013at_int @ M )
% 7.75/5.73 = Z )
% 7.75/5.73 = ( ( M
% 7.75/5.73 = ( nat2 @ Z ) )
% 7.75/5.73 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % int_eq_iff
% 7.75/5.73 thf(fact_6984_nat__int__add,axiom,
% 7.75/5.73 ! [A: nat,B: nat] :
% 7.75/5.73 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 7.75/5.73 = ( plus_plus_nat @ A @ B ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_int_add
% 7.75/5.73 thf(fact_6985_int__minus,axiom,
% 7.75/5.73 ! [N: nat,M: nat] :
% 7.75/5.73 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 7.75/5.73 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % int_minus
% 7.75/5.73 thf(fact_6986_fact__mod,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.73 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 7.75/5.73 = zero_zero_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_mod
% 7.75/5.73 thf(fact_6987_fact__mod,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.73 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 7.75/5.73 = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_mod
% 7.75/5.73 thf(fact_6988_fact__mod,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.73 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 7.75/5.73 = zero_zero_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_mod
% 7.75/5.73 thf(fact_6989_fact__fact__dvd__fact,axiom,
% 7.75/5.73 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_fact_dvd_fact
% 7.75/5.73 thf(fact_6990_fact__fact__dvd__fact,axiom,
% 7.75/5.73 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_fact_dvd_fact
% 7.75/5.73 thf(fact_6991_fact__fact__dvd__fact,axiom,
% 7.75/5.73 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_fact_dvd_fact
% 7.75/5.73 thf(fact_6992_fact__fact__dvd__fact,axiom,
% 7.75/5.73 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_fact_dvd_fact
% 7.75/5.73 thf(fact_6993_fact__le__power,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_le_power
% 7.75/5.73 thf(fact_6994_fact__le__power,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_le_power
% 7.75/5.73 thf(fact_6995_fact__le__power,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_le_power
% 7.75/5.73 thf(fact_6996_fact__le__power,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_le_power
% 7.75/5.73 thf(fact_6997_nat__abs__mult__distrib,axiom,
% 7.75/5.73 ! [W: int,Z: int] :
% 7.75/5.73 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 7.75/5.73 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_abs_mult_distrib
% 7.75/5.73 thf(fact_6998_real__nat__ceiling__ge,axiom,
% 7.75/5.73 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % real_nat_ceiling_ge
% 7.75/5.73 thf(fact_6999_set__encode__inf,axiom,
% 7.75/5.73 ! [A2: set_nat] :
% 7.75/5.73 ( ~ ( finite_finite_nat @ A2 )
% 7.75/5.73 => ( ( nat_set_encode @ A2 )
% 7.75/5.73 = zero_zero_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_encode_inf
% 7.75/5.73 thf(fact_7000_fact__diff__Suc,axiom,
% 7.75/5.73 ! [N: nat,M: nat] :
% 7.75/5.73 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 7.75/5.73 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 7.75/5.73 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_diff_Suc
% 7.75/5.73 thf(fact_7001_fact__div__fact__le__pow,axiom,
% 7.75/5.73 ! [R2: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ R2 @ N )
% 7.75/5.73 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_div_fact_le_pow
% 7.75/5.73 thf(fact_7002_of__nat__floor,axiom,
% 7.75/5.73 ! [R2: rat] :
% 7.75/5.73 ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 7.75/5.73 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R2 ) ) ) @ R2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_floor
% 7.75/5.73 thf(fact_7003_of__nat__floor,axiom,
% 7.75/5.73 ! [R2: real] :
% 7.75/5.73 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 7.75/5.73 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R2 ) ) ) @ R2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_floor
% 7.75/5.73 thf(fact_7004_binomial__fact__lemma,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 7.75/5.73 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % binomial_fact_lemma
% 7.75/5.73 thf(fact_7005_nat__less__eq__zless,axiom,
% 7.75/5.73 ! [W: int,Z: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 7.75/5.73 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ord_less_int @ W @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_less_eq_zless
% 7.75/5.73 thf(fact_7006_nat__eq__iff,axiom,
% 7.75/5.73 ! [W: int,M: nat] :
% 7.75/5.73 ( ( ( nat2 @ W )
% 7.75/5.73 = M )
% 7.75/5.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 7.75/5.73 => ( W
% 7.75/5.73 = ( semiri1314217659103216013at_int @ M ) ) )
% 7.75/5.73 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 7.75/5.73 => ( M = zero_zero_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_eq_iff
% 7.75/5.73 thf(fact_7007_nat__eq__iff2,axiom,
% 7.75/5.73 ! [M: nat,W: int] :
% 7.75/5.73 ( ( M
% 7.75/5.73 = ( nat2 @ W ) )
% 7.75/5.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 7.75/5.73 => ( W
% 7.75/5.73 = ( semiri1314217659103216013at_int @ M ) ) )
% 7.75/5.73 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 7.75/5.73 => ( M = zero_zero_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_eq_iff2
% 7.75/5.73 thf(fact_7008_split__nat,axiom,
% 7.75/5.73 ! [P: nat > $o,I: int] :
% 7.75/5.73 ( ( P @ ( nat2 @ I ) )
% 7.75/5.73 = ( ! [N3: nat] :
% 7.75/5.73 ( ( I
% 7.75/5.73 = ( semiri1314217659103216013at_int @ N3 ) )
% 7.75/5.73 => ( P @ N3 ) )
% 7.75/5.73 & ( ( ord_less_int @ I @ zero_zero_int )
% 7.75/5.73 => ( P @ zero_zero_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % split_nat
% 7.75/5.73 thf(fact_7009_nat__le__eq__zle,axiom,
% 7.75/5.73 ! [W: int,Z: int] :
% 7.75/5.73 ( ( ( ord_less_int @ zero_zero_int @ W )
% 7.75/5.73 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 7.75/5.73 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 7.75/5.73 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_le_eq_zle
% 7.75/5.73 thf(fact_7010_nat__add__distrib,axiom,
% 7.75/5.73 ! [Z: int,Z5: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
% 7.75/5.73 => ( ( nat2 @ ( plus_plus_int @ Z @ Z5 ) )
% 7.75/5.73 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_add_distrib
% 7.75/5.73 thf(fact_7011_le__nat__iff,axiom,
% 7.75/5.73 ! [K: int,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.73 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 7.75/5.73 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % le_nat_iff
% 7.75/5.73 thf(fact_7012_Suc__as__int,axiom,
% 7.75/5.73 ( suc
% 7.75/5.73 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % Suc_as_int
% 7.75/5.73 thf(fact_7013_le__mult__nat__floor,axiom,
% 7.75/5.73 ! [A: real,B: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % le_mult_nat_floor
% 7.75/5.73 thf(fact_7014_nat__mult__distrib,axiom,
% 7.75/5.73 ! [Z: int,Z5: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( nat2 @ ( times_times_int @ Z @ Z5 ) )
% 7.75/5.73 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_mult_distrib
% 7.75/5.73 thf(fact_7015_nat__diff__distrib,axiom,
% 7.75/5.73 ! [Z5: int,Z: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
% 7.75/5.73 => ( ( ord_less_eq_int @ Z5 @ Z )
% 7.75/5.73 => ( ( nat2 @ ( minus_minus_int @ Z @ Z5 ) )
% 7.75/5.73 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_diff_distrib
% 7.75/5.73 thf(fact_7016_nat__diff__distrib_H,axiom,
% 7.75/5.73 ! [X: int,Y: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.73 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 7.75/5.73 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_diff_distrib'
% 7.75/5.73 thf(fact_7017_nat__abs__triangle__ineq,axiom,
% 7.75/5.73 ! [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 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_abs_triangle_ineq
% 7.75/5.73 thf(fact_7018_nat__div__distrib_H,axiom,
% 7.75/5.73 ! [Y: int,X: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.73 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 7.75/5.73 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_div_distrib'
% 7.75/5.73 thf(fact_7019_nat__div__distrib,axiom,
% 7.75/5.73 ! [X: int,Y: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.73 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 7.75/5.73 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_div_distrib
% 7.75/5.73 thf(fact_7020_nat__power__eq,axiom,
% 7.75/5.73 ! [Z: int,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 7.75/5.73 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_power_eq
% 7.75/5.73 thf(fact_7021_nat__mod__distrib,axiom,
% 7.75/5.73 ! [X: int,Y: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.73 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 7.75/5.73 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_mod_distrib
% 7.75/5.73 thf(fact_7022_choose__dvd,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % choose_dvd
% 7.75/5.73 thf(fact_7023_choose__dvd,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % choose_dvd
% 7.75/5.73 thf(fact_7024_choose__dvd,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % choose_dvd
% 7.75/5.73 thf(fact_7025_choose__dvd,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % choose_dvd
% 7.75/5.73 thf(fact_7026_div__abs__eq__div__nat,axiom,
% 7.75/5.73 ! [K: int,L: int] :
% 7.75/5.73 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 7.75/5.73 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % div_abs_eq_div_nat
% 7.75/5.73 thf(fact_7027_nat__floor__neg,axiom,
% 7.75/5.73 ! [X: real] :
% 7.75/5.73 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.75/5.73 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.73 = zero_zero_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_floor_neg
% 7.75/5.73 thf(fact_7028_mod__abs__eq__div__nat,axiom,
% 7.75/5.73 ! [K: int,L: int] :
% 7.75/5.73 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 7.75/5.73 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mod_abs_eq_div_nat
% 7.75/5.73 thf(fact_7029_fact__numeral,axiom,
% 7.75/5.73 ! [K: num] :
% 7.75/5.73 ( ( semiri3624122377584611663nteger @ ( numeral_numeral_nat @ K ) )
% 7.75/5.73 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ K ) @ ( semiri3624122377584611663nteger @ ( pred_numeral @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_numeral
% 7.75/5.73 thf(fact_7030_fact__numeral,axiom,
% 7.75/5.73 ! [K: num] :
% 7.75/5.73 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 7.75/5.73 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_numeral
% 7.75/5.73 thf(fact_7031_fact__numeral,axiom,
% 7.75/5.73 ! [K: num] :
% 7.75/5.73 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 7.75/5.73 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_numeral
% 7.75/5.73 thf(fact_7032_fact__numeral,axiom,
% 7.75/5.73 ! [K: num] :
% 7.75/5.73 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 7.75/5.73 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_numeral
% 7.75/5.73 thf(fact_7033_fact__numeral,axiom,
% 7.75/5.73 ! [K: num] :
% 7.75/5.73 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 7.75/5.73 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_numeral
% 7.75/5.73 thf(fact_7034_fact__numeral,axiom,
% 7.75/5.73 ! [K: num] :
% 7.75/5.73 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 7.75/5.73 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_numeral
% 7.75/5.73 thf(fact_7035_take__bit__nat__eq,axiom,
% 7.75/5.73 ! [K: int,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.73 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 7.75/5.73 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_nat_eq
% 7.75/5.73 thf(fact_7036_nat__take__bit__eq,axiom,
% 7.75/5.73 ! [K: int,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.73 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 7.75/5.73 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_take_bit_eq
% 7.75/5.73 thf(fact_7037_floor__eq3,axiom,
% 7.75/5.73 ! [N: nat,X: real] :
% 7.75/5.73 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 7.75/5.73 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 7.75/5.73 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.73 = N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % floor_eq3
% 7.75/5.73 thf(fact_7038_le__nat__floor,axiom,
% 7.75/5.73 ! [X: nat,A: real] :
% 7.75/5.73 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 7.75/5.73 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % le_nat_floor
% 7.75/5.73 thf(fact_7039_nat__2,axiom,
% 7.75/5.73 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.73 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_2
% 7.75/5.73 thf(fact_7040_binomial__altdef__nat,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( ( binomial @ N @ K )
% 7.75/5.73 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % binomial_altdef_nat
% 7.75/5.73 thf(fact_7041_Suc__nat__eq__nat__zadd1,axiom,
% 7.75/5.73 ! [Z: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( ( suc @ ( nat2 @ Z ) )
% 7.75/5.73 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % Suc_nat_eq_nat_zadd1
% 7.75/5.73 thf(fact_7042_nat__less__iff,axiom,
% 7.75/5.73 ! [W: int,M: nat] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 7.75/5.73 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 7.75/5.73 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_less_iff
% 7.75/5.73 thf(fact_7043_nat__mult__distrib__neg,axiom,
% 7.75/5.73 ! [Z: int,Z5: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 7.75/5.73 => ( ( nat2 @ ( times_times_int @ Z @ Z5 ) )
% 7.75/5.73 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z5 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_mult_distrib_neg
% 7.75/5.73 thf(fact_7044_floor__eq4,axiom,
% 7.75/5.73 ! [N: nat,X: real] :
% 7.75/5.73 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 7.75/5.73 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 7.75/5.73 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 7.75/5.73 = N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % floor_eq4
% 7.75/5.73 thf(fact_7045_square__fact__le__2__fact,axiom,
% 7.75/5.73 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % square_fact_le_2_fact
% 7.75/5.73 thf(fact_7046_of__int__of__nat,axiom,
% 7.75/5.73 ( ring_18347121197199848620nteger
% 7.75/5.73 = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_int_of_nat
% 7.75/5.73 thf(fact_7047_of__int__of__nat,axiom,
% 7.75/5.73 ( ring_1_of_int_rat
% 7.75/5.73 = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_int_of_nat
% 7.75/5.73 thf(fact_7048_of__int__of__nat,axiom,
% 7.75/5.73 ( ring_1_of_int_real
% 7.75/5.73 = ( ^ [K3: int] : ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K3 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_int_of_nat
% 7.75/5.73 thf(fact_7049_of__int__of__nat,axiom,
% 7.75/5.73 ( ring_1_of_int_int
% 7.75/5.73 = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_int_of_nat
% 7.75/5.73 thf(fact_7050_of__int__of__nat,axiom,
% 7.75/5.73 ( ring_17405671764205052669omplex
% 7.75/5.73 = ( ^ [K3: int] : ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K3 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_int_of_nat
% 7.75/5.73 thf(fact_7051_nat__dvd__iff,axiom,
% 7.75/5.73 ! [Z: int,M: nat] :
% 7.75/5.73 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 7.75/5.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 7.75/5.73 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 7.75/5.73 => ( M = zero_zero_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nat_dvd_iff
% 7.75/5.73 thf(fact_7052_fact__num__eq__if,axiom,
% 7.75/5.73 ( semiri773545260158071498ct_rat
% 7.75/5.73 = ( ^ [M4: nat] : ( if_rat @ ( M4 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M4 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_num_eq_if
% 7.75/5.73 thf(fact_7053_fact__num__eq__if,axiom,
% 7.75/5.73 ( semiri3624122377584611663nteger
% 7.75/5.73 = ( ^ [M4: nat] : ( if_Code_integer @ ( M4 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M4 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_num_eq_if
% 7.75/5.73 thf(fact_7054_fact__num__eq__if,axiom,
% 7.75/5.73 ( semiri1406184849735516958ct_int
% 7.75/5.73 = ( ^ [M4: nat] : ( if_int @ ( M4 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_num_eq_if
% 7.75/5.73 thf(fact_7055_fact__num__eq__if,axiom,
% 7.75/5.73 ( semiri1408675320244567234ct_nat
% 7.75/5.73 = ( ^ [M4: nat] : ( if_nat @ ( M4 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M4 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_num_eq_if
% 7.75/5.73 thf(fact_7056_fact__num__eq__if,axiom,
% 7.75/5.73 ( semiri2265585572941072030t_real
% 7.75/5.73 = ( ^ [M4: nat] : ( if_real @ ( M4 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_num_eq_if
% 7.75/5.73 thf(fact_7057_fact__num__eq__if,axiom,
% 7.75/5.73 ( semiri5044797733671781792omplex
% 7.75/5.73 = ( ^ [M4: nat] : ( if_complex @ ( M4 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M4 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_num_eq_if
% 7.75/5.73 thf(fact_7058_fact__reduce,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.73 => ( ( semiri3624122377584611663nteger @ N )
% 7.75/5.73 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_reduce
% 7.75/5.73 thf(fact_7059_fact__reduce,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.73 => ( ( semiri1406184849735516958ct_int @ N )
% 7.75/5.73 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_reduce
% 7.75/5.73 thf(fact_7060_fact__reduce,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.73 => ( ( semiri1408675320244567234ct_nat @ N )
% 7.75/5.73 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_reduce
% 7.75/5.73 thf(fact_7061_fact__reduce,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.73 => ( ( semiri2265585572941072030t_real @ N )
% 7.75/5.73 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_reduce
% 7.75/5.73 thf(fact_7062_fact__reduce,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.73 => ( ( semiri5044797733671781792omplex @ N )
% 7.75/5.73 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_reduce
% 7.75/5.73 thf(fact_7063_pochhammer__same,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 7.75/5.73 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_same
% 7.75/5.73 thf(fact_7064_pochhammer__same,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 7.75/5.73 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_same
% 7.75/5.73 thf(fact_7065_pochhammer__same,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 7.75/5.73 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_same
% 7.75/5.73 thf(fact_7066_pochhammer__same,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 7.75/5.73 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_same
% 7.75/5.73 thf(fact_7067_pochhammer__same,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 7.75/5.73 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % pochhammer_same
% 7.75/5.73 thf(fact_7068_fact__binomial,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 7.75/5.73 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_binomial
% 7.75/5.73 thf(fact_7069_fact__binomial,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 7.75/5.73 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_binomial
% 7.75/5.73 thf(fact_7070_fact__binomial,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 7.75/5.73 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_binomial
% 7.75/5.73 thf(fact_7071_binomial__fact,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 7.75/5.73 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % binomial_fact
% 7.75/5.73 thf(fact_7072_binomial__fact,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 7.75/5.73 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % binomial_fact
% 7.75/5.73 thf(fact_7073_binomial__fact,axiom,
% 7.75/5.73 ! [K: nat,N: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ K @ N )
% 7.75/5.73 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 7.75/5.73 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % binomial_fact
% 7.75/5.73 thf(fact_7074_even__nat__iff,axiom,
% 7.75/5.73 ! [K: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.73 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 7.75/5.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % even_nat_iff
% 7.75/5.73 thf(fact_7075_sin__coeff__def,axiom,
% 7.75/5.73 ( sin_coeff
% 7.75/5.73 = ( ^ [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 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sin_coeff_def
% 7.75/5.73 thf(fact_7076_binomial__code,axiom,
% 7.75/5.73 ( binomial
% 7.75/5.73 = ( ^ [N3: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N3 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N3 @ ( minus_minus_nat @ N3 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N3 @ K3 ) @ one_one_nat ) @ N3 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % binomial_code
% 7.75/5.73 thf(fact_7077_cos__coeff__def,axiom,
% 7.75/5.73 ( cos_coeff
% 7.75/5.73 = ( ^ [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 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % cos_coeff_def
% 7.75/5.73 thf(fact_7078_fact__code,axiom,
% 7.75/5.73 ( semiri1406184849735516958ct_int
% 7.75/5.73 = ( ^ [N3: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_code
% 7.75/5.73 thf(fact_7079_fact__code,axiom,
% 7.75/5.73 ( semiri1408675320244567234ct_nat
% 7.75/5.73 = ( ^ [N3: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_code
% 7.75/5.73 thf(fact_7080_fact__code,axiom,
% 7.75/5.73 ( semiri2265585572941072030t_real
% 7.75/5.73 = ( ^ [N3: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_code
% 7.75/5.73 thf(fact_7081_fact__code,axiom,
% 7.75/5.73 ( semiri5044797733671781792omplex
% 7.75/5.73 = ( ^ [N3: nat] : ( semiri8010041392384452111omplex @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fact_code
% 7.75/5.73 thf(fact_7082_divide__int__def,axiom,
% 7.75/5.73 ( divide_divide_int
% 7.75/5.73 = ( ^ [K3: int,L2: int] :
% 7.75/5.73 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 7.75/5.73 @ ( if_int
% 7.75/5.73 @ ( ( sgn_sgn_int @ K3 )
% 7.75/5.73 = ( sgn_sgn_int @ L2 ) )
% 7.75/5.73 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 7.75/5.73 @ ( uminus_uminus_int
% 7.75/5.73 @ ( semiri1314217659103216013at_int
% 7.75/5.73 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 7.75/5.73 @ ( zero_n2687167440665602831ol_nat
% 7.75/5.73 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % divide_int_def
% 7.75/5.73 thf(fact_7083_sgn__sgn,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 7.75/5.73 = ( sgn_sgn_int @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_sgn
% 7.75/5.73 thf(fact_7084_sgn__sgn,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 7.75/5.73 = ( sgn_sgn_real @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_sgn
% 7.75/5.73 thf(fact_7085_sgn__sgn,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 = ( sgn_sgn_Code_integer @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_sgn
% 7.75/5.73 thf(fact_7086_sgn__sgn,axiom,
% 7.75/5.73 ! [A: complex] :
% 7.75/5.73 ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 7.75/5.73 = ( sgn_sgn_complex @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_sgn
% 7.75/5.73 thf(fact_7087_sgn__sgn,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 7.75/5.73 = ( sgn_sgn_rat @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_sgn
% 7.75/5.73 thf(fact_7088_sgn__zero,axiom,
% 7.75/5.73 ( ( sgn_sgn_complex @ zero_zero_complex )
% 7.75/5.73 = zero_zero_complex ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_zero
% 7.75/5.73 thf(fact_7089_sgn__zero,axiom,
% 7.75/5.73 ( ( sgn_sgn_real @ zero_zero_real )
% 7.75/5.73 = zero_zero_real ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_zero
% 7.75/5.73 thf(fact_7090_sgn__0,axiom,
% 7.75/5.73 ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 7.75/5.73 = zero_z3403309356797280102nteger ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_0
% 7.75/5.73 thf(fact_7091_sgn__0,axiom,
% 7.75/5.73 ( ( sgn_sgn_complex @ zero_zero_complex )
% 7.75/5.73 = zero_zero_complex ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_0
% 7.75/5.73 thf(fact_7092_sgn__0,axiom,
% 7.75/5.73 ( ( sgn_sgn_real @ zero_zero_real )
% 7.75/5.73 = zero_zero_real ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_0
% 7.75/5.73 thf(fact_7093_sgn__0,axiom,
% 7.75/5.73 ( ( sgn_sgn_rat @ zero_zero_rat )
% 7.75/5.73 = zero_zero_rat ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_0
% 7.75/5.73 thf(fact_7094_sgn__0,axiom,
% 7.75/5.73 ( ( sgn_sgn_int @ zero_zero_int )
% 7.75/5.73 = zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_0
% 7.75/5.73 thf(fact_7095_sgn__one,axiom,
% 7.75/5.73 ( ( sgn_sgn_real @ one_one_real )
% 7.75/5.73 = one_one_real ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_one
% 7.75/5.73 thf(fact_7096_sgn__one,axiom,
% 7.75/5.73 ( ( sgn_sgn_complex @ one_one_complex )
% 7.75/5.73 = one_one_complex ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_one
% 7.75/5.73 thf(fact_7097_sgn__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_int @ one_one_int )
% 7.75/5.73 = one_one_int ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1
% 7.75/5.73 thf(fact_7098_sgn__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_real @ one_one_real )
% 7.75/5.73 = one_one_real ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1
% 7.75/5.73 thf(fact_7099_sgn__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 7.75/5.73 = one_one_Code_integer ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1
% 7.75/5.73 thf(fact_7100_sgn__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_complex @ one_one_complex )
% 7.75/5.73 = one_one_complex ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1
% 7.75/5.73 thf(fact_7101_sgn__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_rat @ one_one_rat )
% 7.75/5.73 = one_one_rat ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1
% 7.75/5.73 thf(fact_7102_sgn__divide,axiom,
% 7.75/5.73 ! [A: complex,B: complex] :
% 7.75/5.73 ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 7.75/5.73 = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_divide
% 7.75/5.73 thf(fact_7103_sgn__divide,axiom,
% 7.75/5.73 ! [A: real,B: real] :
% 7.75/5.73 ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B ) )
% 7.75/5.73 = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_divide
% 7.75/5.73 thf(fact_7104_sgn__divide,axiom,
% 7.75/5.73 ! [A: rat,B: rat] :
% 7.75/5.73 ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B ) )
% 7.75/5.73 = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_divide
% 7.75/5.73 thf(fact_7105_idom__abs__sgn__class_Osgn__minus,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 7.75/5.73 = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.sgn_minus
% 7.75/5.73 thf(fact_7106_idom__abs__sgn__class_Osgn__minus,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 7.75/5.73 = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.sgn_minus
% 7.75/5.73 thf(fact_7107_idom__abs__sgn__class_Osgn__minus,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 7.75/5.73 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.sgn_minus
% 7.75/5.73 thf(fact_7108_idom__abs__sgn__class_Osgn__minus,axiom,
% 7.75/5.73 ! [A: complex] :
% 7.75/5.73 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 7.75/5.73 = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.sgn_minus
% 7.75/5.73 thf(fact_7109_idom__abs__sgn__class_Osgn__minus,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 7.75/5.73 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.sgn_minus
% 7.75/5.73 thf(fact_7110_power__sgn,axiom,
% 7.75/5.73 ! [A: rat,N: nat] :
% 7.75/5.73 ( ( sgn_sgn_rat @ ( power_power_rat @ A @ N ) )
% 7.75/5.73 = ( power_power_rat @ ( sgn_sgn_rat @ A ) @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % power_sgn
% 7.75/5.73 thf(fact_7111_power__sgn,axiom,
% 7.75/5.73 ! [A: real,N: nat] :
% 7.75/5.73 ( ( sgn_sgn_real @ ( power_power_real @ A @ N ) )
% 7.75/5.73 = ( power_power_real @ ( sgn_sgn_real @ A ) @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % power_sgn
% 7.75/5.73 thf(fact_7112_power__sgn,axiom,
% 7.75/5.73 ! [A: int,N: nat] :
% 7.75/5.73 ( ( sgn_sgn_int @ ( power_power_int @ A @ N ) )
% 7.75/5.73 = ( power_power_int @ ( sgn_sgn_int @ A ) @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % power_sgn
% 7.75/5.73 thf(fact_7113_power__sgn,axiom,
% 7.75/5.73 ! [A: code_integer,N: nat] :
% 7.75/5.73 ( ( sgn_sgn_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 7.75/5.73 = ( power_8256067586552552935nteger @ ( sgn_sgn_Code_integer @ A ) @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % power_sgn
% 7.75/5.73 thf(fact_7114_sgn__less,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 7.75/5.73 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_less
% 7.75/5.73 thf(fact_7115_sgn__less,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 7.75/5.73 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_less
% 7.75/5.73 thf(fact_7116_sgn__less,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 7.75/5.73 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_less
% 7.75/5.73 thf(fact_7117_sgn__less,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 7.75/5.73 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_less
% 7.75/5.73 thf(fact_7118_sgn__greater,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_greater
% 7.75/5.73 thf(fact_7119_sgn__greater,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 7.75/5.73 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_greater
% 7.75/5.73 thf(fact_7120_sgn__greater,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 7.75/5.73 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_greater
% 7.75/5.73 thf(fact_7121_sgn__greater,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 7.75/5.73 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_greater
% 7.75/5.73 thf(fact_7122_divide__sgn,axiom,
% 7.75/5.73 ! [A: real,B: real] :
% 7.75/5.73 ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B ) )
% 7.75/5.73 = ( times_times_real @ A @ ( sgn_sgn_real @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % divide_sgn
% 7.75/5.73 thf(fact_7123_divide__sgn,axiom,
% 7.75/5.73 ! [A: rat,B: rat] :
% 7.75/5.73 ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 7.75/5.73 = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % divide_sgn
% 7.75/5.73 thf(fact_7124_sin__coeff__0,axiom,
% 7.75/5.73 ( ( sin_coeff @ zero_zero_nat )
% 7.75/5.73 = zero_zero_real ) ).
% 7.75/5.73
% 7.75/5.73 % sin_coeff_0
% 7.75/5.73 thf(fact_7125_cos__coeff__0,axiom,
% 7.75/5.73 ( ( cos_coeff @ zero_zero_nat )
% 7.75/5.73 = one_one_real ) ).
% 7.75/5.73
% 7.75/5.73 % cos_coeff_0
% 7.75/5.73 thf(fact_7126_sgn__pos,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.73 => ( ( sgn_sgn_Code_integer @ A )
% 7.75/5.73 = one_one_Code_integer ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_pos
% 7.75/5.73 thf(fact_7127_sgn__pos,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( ord_less_real @ zero_zero_real @ A )
% 7.75/5.73 => ( ( sgn_sgn_real @ A )
% 7.75/5.73 = one_one_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_pos
% 7.75/5.73 thf(fact_7128_sgn__pos,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( ord_less_rat @ zero_zero_rat @ A )
% 7.75/5.73 => ( ( sgn_sgn_rat @ A )
% 7.75/5.73 = one_one_rat ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_pos
% 7.75/5.73 thf(fact_7129_sgn__pos,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( ord_less_int @ zero_zero_int @ A )
% 7.75/5.73 => ( ( sgn_sgn_int @ A )
% 7.75/5.73 = one_one_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_pos
% 7.75/5.73 thf(fact_7130_abs__sgn__eq__1,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.73 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 = one_one_Code_integer ) ) ).
% 7.75/5.73
% 7.75/5.73 % abs_sgn_eq_1
% 7.75/5.73 thf(fact_7131_abs__sgn__eq__1,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( A != zero_zero_real )
% 7.75/5.73 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 7.75/5.73 = one_one_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % abs_sgn_eq_1
% 7.75/5.73 thf(fact_7132_abs__sgn__eq__1,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( A != zero_zero_rat )
% 7.75/5.73 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 7.75/5.73 = one_one_rat ) ) ).
% 7.75/5.73
% 7.75/5.73 % abs_sgn_eq_1
% 7.75/5.73 thf(fact_7133_abs__sgn__eq__1,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( A != zero_zero_int )
% 7.75/5.73 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 7.75/5.73 = one_one_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % abs_sgn_eq_1
% 7.75/5.73 thf(fact_7134_sgn__mult__self__eq,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 7.75/5.73 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_self_eq
% 7.75/5.73 thf(fact_7135_sgn__mult__self__eq,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 7.75/5.73 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_self_eq
% 7.75/5.73 thf(fact_7136_sgn__mult__self__eq,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 7.75/5.73 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_self_eq
% 7.75/5.73 thf(fact_7137_sgn__mult__self__eq,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_self_eq
% 7.75/5.73 thf(fact_7138_sgn__abs,axiom,
% 7.75/5.73 ! [A: complex] :
% 7.75/5.73 ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 7.75/5.73 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_abs
% 7.75/5.73 thf(fact_7139_sgn__abs,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 7.75/5.73 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_abs
% 7.75/5.73 thf(fact_7140_sgn__abs,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 7.75/5.73 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_abs
% 7.75/5.73 thf(fact_7141_sgn__abs,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 7.75/5.73 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_abs
% 7.75/5.73 thf(fact_7142_sgn__abs,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_abs
% 7.75/5.73 thf(fact_7143_idom__abs__sgn__class_Oabs__sgn,axiom,
% 7.75/5.73 ! [A: complex] :
% 7.75/5.73 ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 7.75/5.73 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.abs_sgn
% 7.75/5.73 thf(fact_7144_idom__abs__sgn__class_Oabs__sgn,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 7.75/5.73 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.abs_sgn
% 7.75/5.73 thf(fact_7145_idom__abs__sgn__class_Oabs__sgn,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 7.75/5.73 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.abs_sgn
% 7.75/5.73 thf(fact_7146_idom__abs__sgn__class_Oabs__sgn,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 7.75/5.73 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.abs_sgn
% 7.75/5.73 thf(fact_7147_idom__abs__sgn__class_Oabs__sgn,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 7.75/5.73 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % idom_abs_sgn_class.abs_sgn
% 7.75/5.73 thf(fact_7148_dvd__mult__sgn__iff,axiom,
% 7.75/5.73 ! [L: int,K: int,R2: int] :
% 7.75/5.73 ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 7.75/5.73 = ( ( dvd_dvd_int @ L @ K )
% 7.75/5.73 | ( R2 = zero_zero_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % dvd_mult_sgn_iff
% 7.75/5.73 thf(fact_7149_dvd__sgn__mult__iff,axiom,
% 7.75/5.73 ! [L: int,R2: int,K: int] :
% 7.75/5.73 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 7.75/5.73 = ( ( dvd_dvd_int @ L @ K )
% 7.75/5.73 | ( R2 = zero_zero_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % dvd_sgn_mult_iff
% 7.75/5.73 thf(fact_7150_mult__sgn__dvd__iff,axiom,
% 7.75/5.73 ! [L: int,R2: int,K: int] :
% 7.75/5.73 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 7.75/5.73 = ( ( dvd_dvd_int @ L @ K )
% 7.75/5.73 & ( ( R2 = zero_zero_int )
% 7.75/5.73 => ( K = zero_zero_int ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mult_sgn_dvd_iff
% 7.75/5.73 thf(fact_7151_sgn__mult__dvd__iff,axiom,
% 7.75/5.73 ! [R2: int,L: int,K: int] :
% 7.75/5.73 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 7.75/5.73 = ( ( dvd_dvd_int @ L @ K )
% 7.75/5.73 & ( ( R2 = zero_zero_int )
% 7.75/5.73 => ( K = zero_zero_int ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_dvd_iff
% 7.75/5.73 thf(fact_7152_sgn__neg,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( ord_less_int @ A @ zero_zero_int )
% 7.75/5.73 => ( ( sgn_sgn_int @ A )
% 7.75/5.73 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_neg
% 7.75/5.73 thf(fact_7153_sgn__neg,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( ord_less_real @ A @ zero_zero_real )
% 7.75/5.73 => ( ( sgn_sgn_real @ A )
% 7.75/5.73 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_neg
% 7.75/5.73 thf(fact_7154_sgn__neg,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.73 => ( ( sgn_sgn_Code_integer @ A )
% 7.75/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_neg
% 7.75/5.73 thf(fact_7155_sgn__neg,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( ord_less_rat @ A @ zero_zero_rat )
% 7.75/5.73 => ( ( sgn_sgn_rat @ A )
% 7.75/5.73 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_neg
% 7.75/5.73 thf(fact_7156_sgn__of__nat,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N ) )
% 7.75/5.73 = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_of_nat
% 7.75/5.73 thf(fact_7157_sgn__of__nat,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N ) )
% 7.75/5.73 = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_of_nat
% 7.75/5.73 thf(fact_7158_sgn__of__nat,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N ) )
% 7.75/5.73 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_of_nat
% 7.75/5.73 thf(fact_7159_sgn__of__nat,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 7.75/5.73 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_of_nat
% 7.75/5.73 thf(fact_7160_sgn__eq__0__iff,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( ( sgn_sgn_Code_integer @ A )
% 7.75/5.73 = zero_z3403309356797280102nteger )
% 7.75/5.73 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_eq_0_iff
% 7.75/5.73 thf(fact_7161_sgn__eq__0__iff,axiom,
% 7.75/5.73 ! [A: complex] :
% 7.75/5.73 ( ( ( sgn_sgn_complex @ A )
% 7.75/5.73 = zero_zero_complex )
% 7.75/5.73 = ( A = zero_zero_complex ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_eq_0_iff
% 7.75/5.73 thf(fact_7162_sgn__eq__0__iff,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( ( sgn_sgn_real @ A )
% 7.75/5.73 = zero_zero_real )
% 7.75/5.73 = ( A = zero_zero_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_eq_0_iff
% 7.75/5.73 thf(fact_7163_sgn__eq__0__iff,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( ( sgn_sgn_rat @ A )
% 7.75/5.73 = zero_zero_rat )
% 7.75/5.73 = ( A = zero_zero_rat ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_eq_0_iff
% 7.75/5.73 thf(fact_7164_sgn__eq__0__iff,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( ( sgn_sgn_int @ A )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 = ( A = zero_zero_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_eq_0_iff
% 7.75/5.73 thf(fact_7165_sgn__0__0,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( ( sgn_sgn_Code_integer @ A )
% 7.75/5.73 = zero_z3403309356797280102nteger )
% 7.75/5.73 = ( A = zero_z3403309356797280102nteger ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_0_0
% 7.75/5.73 thf(fact_7166_sgn__0__0,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( ( sgn_sgn_real @ A )
% 7.75/5.73 = zero_zero_real )
% 7.75/5.73 = ( A = zero_zero_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_0_0
% 7.75/5.73 thf(fact_7167_sgn__0__0,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( ( sgn_sgn_rat @ A )
% 7.75/5.73 = zero_zero_rat )
% 7.75/5.73 = ( A = zero_zero_rat ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_0_0
% 7.75/5.73 thf(fact_7168_sgn__0__0,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( ( sgn_sgn_int @ A )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 = ( A = zero_zero_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_0_0
% 7.75/5.73 thf(fact_7169_sgn__zero__iff,axiom,
% 7.75/5.73 ! [X: complex] :
% 7.75/5.73 ( ( ( sgn_sgn_complex @ X )
% 7.75/5.73 = zero_zero_complex )
% 7.75/5.73 = ( X = zero_zero_complex ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_zero_iff
% 7.75/5.73 thf(fact_7170_sgn__zero__iff,axiom,
% 7.75/5.73 ! [X: real] :
% 7.75/5.73 ( ( ( sgn_sgn_real @ X )
% 7.75/5.73 = zero_zero_real )
% 7.75/5.73 = ( X = zero_zero_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_zero_iff
% 7.75/5.73 thf(fact_7171_sgn__mult,axiom,
% 7.75/5.73 ! [A: rat,B: rat] :
% 7.75/5.73 ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 7.75/5.73 = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult
% 7.75/5.73 thf(fact_7172_sgn__mult,axiom,
% 7.75/5.73 ! [A: real,B: real] :
% 7.75/5.73 ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 7.75/5.73 = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult
% 7.75/5.73 thf(fact_7173_sgn__mult,axiom,
% 7.75/5.73 ! [A: int,B: int] :
% 7.75/5.73 ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 7.75/5.73 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult
% 7.75/5.73 thf(fact_7174_sgn__mult,axiom,
% 7.75/5.73 ! [A: code_integer,B: code_integer] :
% 7.75/5.73 ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 7.75/5.73 = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult
% 7.75/5.73 thf(fact_7175_sgn__mult,axiom,
% 7.75/5.73 ! [A: complex,B: complex] :
% 7.75/5.73 ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 7.75/5.73 = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult
% 7.75/5.73 thf(fact_7176_Real__Vector__Spaces_Osgn__mult,axiom,
% 7.75/5.73 ! [X: real,Y: real] :
% 7.75/5.73 ( ( sgn_sgn_real @ ( times_times_real @ X @ Y ) )
% 7.75/5.73 = ( times_times_real @ ( sgn_sgn_real @ X ) @ ( sgn_sgn_real @ Y ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % Real_Vector_Spaces.sgn_mult
% 7.75/5.73 thf(fact_7177_Real__Vector__Spaces_Osgn__mult,axiom,
% 7.75/5.73 ! [X: complex,Y: complex] :
% 7.75/5.73 ( ( sgn_sgn_complex @ ( times_times_complex @ X @ Y ) )
% 7.75/5.73 = ( times_times_complex @ ( sgn_sgn_complex @ X ) @ ( sgn_sgn_complex @ Y ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % Real_Vector_Spaces.sgn_mult
% 7.75/5.73 thf(fact_7178_same__sgn__sgn__add,axiom,
% 7.75/5.73 ! [B: code_integer,A: code_integer] :
% 7.75/5.73 ( ( ( sgn_sgn_Code_integer @ B )
% 7.75/5.73 = ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 7.75/5.73 = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % same_sgn_sgn_add
% 7.75/5.73 thf(fact_7179_same__sgn__sgn__add,axiom,
% 7.75/5.73 ! [B: real,A: real] :
% 7.75/5.73 ( ( ( sgn_sgn_real @ B )
% 7.75/5.73 = ( sgn_sgn_real @ A ) )
% 7.75/5.73 => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 7.75/5.73 = ( sgn_sgn_real @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % same_sgn_sgn_add
% 7.75/5.73 thf(fact_7180_same__sgn__sgn__add,axiom,
% 7.75/5.73 ! [B: rat,A: rat] :
% 7.75/5.73 ( ( ( sgn_sgn_rat @ B )
% 7.75/5.73 = ( sgn_sgn_rat @ A ) )
% 7.75/5.73 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.73 = ( sgn_sgn_rat @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % same_sgn_sgn_add
% 7.75/5.73 thf(fact_7181_same__sgn__sgn__add,axiom,
% 7.75/5.73 ! [B: int,A: int] :
% 7.75/5.73 ( ( ( sgn_sgn_int @ B )
% 7.75/5.73 = ( sgn_sgn_int @ A ) )
% 7.75/5.73 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 7.75/5.73 = ( sgn_sgn_int @ A ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % same_sgn_sgn_add
% 7.75/5.73 thf(fact_7182_sgn__not__eq__imp,axiom,
% 7.75/5.73 ! [B: int,A: int] :
% 7.75/5.73 ( ( ( sgn_sgn_int @ B )
% 7.75/5.73 != ( sgn_sgn_int @ A ) )
% 7.75/5.73 => ( ( ( sgn_sgn_int @ A )
% 7.75/5.73 != zero_zero_int )
% 7.75/5.73 => ( ( ( sgn_sgn_int @ B )
% 7.75/5.73 != zero_zero_int )
% 7.75/5.73 => ( ( sgn_sgn_int @ A )
% 7.75/5.73 = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_not_eq_imp
% 7.75/5.73 thf(fact_7183_sgn__not__eq__imp,axiom,
% 7.75/5.73 ! [B: real,A: real] :
% 7.75/5.73 ( ( ( sgn_sgn_real @ B )
% 7.75/5.73 != ( sgn_sgn_real @ A ) )
% 7.75/5.73 => ( ( ( sgn_sgn_real @ A )
% 7.75/5.73 != zero_zero_real )
% 7.75/5.73 => ( ( ( sgn_sgn_real @ B )
% 7.75/5.73 != zero_zero_real )
% 7.75/5.73 => ( ( sgn_sgn_real @ A )
% 7.75/5.73 = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_not_eq_imp
% 7.75/5.73 thf(fact_7184_sgn__not__eq__imp,axiom,
% 7.75/5.73 ! [B: code_integer,A: code_integer] :
% 7.75/5.73 ( ( ( sgn_sgn_Code_integer @ B )
% 7.75/5.73 != ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 => ( ( ( sgn_sgn_Code_integer @ A )
% 7.75/5.73 != zero_z3403309356797280102nteger )
% 7.75/5.73 => ( ( ( sgn_sgn_Code_integer @ B )
% 7.75/5.73 != zero_z3403309356797280102nteger )
% 7.75/5.73 => ( ( sgn_sgn_Code_integer @ A )
% 7.75/5.73 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_not_eq_imp
% 7.75/5.73 thf(fact_7185_sgn__not__eq__imp,axiom,
% 7.75/5.73 ! [B: rat,A: rat] :
% 7.75/5.73 ( ( ( sgn_sgn_rat @ B )
% 7.75/5.73 != ( sgn_sgn_rat @ A ) )
% 7.75/5.73 => ( ( ( sgn_sgn_rat @ A )
% 7.75/5.73 != zero_zero_rat )
% 7.75/5.73 => ( ( ( sgn_sgn_rat @ B )
% 7.75/5.73 != zero_zero_rat )
% 7.75/5.73 => ( ( sgn_sgn_rat @ A )
% 7.75/5.73 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_not_eq_imp
% 7.75/5.73 thf(fact_7186_sgn__minus__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.73 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_minus_1
% 7.75/5.73 thf(fact_7187_sgn__minus__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.73 = ( uminus_uminus_real @ one_one_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_minus_1
% 7.75/5.73 thf(fact_7188_sgn__minus__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_minus_1
% 7.75/5.73 thf(fact_7189_sgn__minus__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.75/5.73 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_minus_1
% 7.75/5.73 thf(fact_7190_sgn__minus__1,axiom,
% 7.75/5.73 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.73 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_minus_1
% 7.75/5.73 thf(fact_7191_same__sgn__abs__add,axiom,
% 7.75/5.73 ! [B: code_integer,A: code_integer] :
% 7.75/5.73 ( ( ( sgn_sgn_Code_integer @ B )
% 7.75/5.73 = ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 7.75/5.73 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % same_sgn_abs_add
% 7.75/5.73 thf(fact_7192_same__sgn__abs__add,axiom,
% 7.75/5.73 ! [B: real,A: real] :
% 7.75/5.73 ( ( ( sgn_sgn_real @ B )
% 7.75/5.73 = ( sgn_sgn_real @ A ) )
% 7.75/5.73 => ( ( abs_abs_real @ ( plus_plus_real @ A @ B ) )
% 7.75/5.73 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % same_sgn_abs_add
% 7.75/5.73 thf(fact_7193_same__sgn__abs__add,axiom,
% 7.75/5.73 ! [B: rat,A: rat] :
% 7.75/5.73 ( ( ( sgn_sgn_rat @ B )
% 7.75/5.73 = ( sgn_sgn_rat @ A ) )
% 7.75/5.73 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 7.75/5.73 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % same_sgn_abs_add
% 7.75/5.73 thf(fact_7194_same__sgn__abs__add,axiom,
% 7.75/5.73 ! [B: int,A: int] :
% 7.75/5.73 ( ( ( sgn_sgn_int @ B )
% 7.75/5.73 = ( sgn_sgn_int @ A ) )
% 7.75/5.73 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 7.75/5.73 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % same_sgn_abs_add
% 7.75/5.73 thf(fact_7195_linordered__idom__class_Oabs__sgn,axiom,
% 7.75/5.73 ( abs_abs_rat
% 7.75/5.73 = ( ^ [K3: rat] : ( times_times_rat @ K3 @ ( sgn_sgn_rat @ K3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % linordered_idom_class.abs_sgn
% 7.75/5.73 thf(fact_7196_linordered__idom__class_Oabs__sgn,axiom,
% 7.75/5.73 ( abs_abs_real
% 7.75/5.73 = ( ^ [K3: real] : ( times_times_real @ K3 @ ( sgn_sgn_real @ K3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % linordered_idom_class.abs_sgn
% 7.75/5.73 thf(fact_7197_linordered__idom__class_Oabs__sgn,axiom,
% 7.75/5.73 ( abs_abs_int
% 7.75/5.73 = ( ^ [K3: int] : ( times_times_int @ K3 @ ( sgn_sgn_int @ K3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % linordered_idom_class.abs_sgn
% 7.75/5.73 thf(fact_7198_linordered__idom__class_Oabs__sgn,axiom,
% 7.75/5.73 ( abs_abs_Code_integer
% 7.75/5.73 = ( ^ [K3: code_integer] : ( times_3573771949741848930nteger @ K3 @ ( sgn_sgn_Code_integer @ K3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % linordered_idom_class.abs_sgn
% 7.75/5.73 thf(fact_7199_abs__mult__sgn,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % abs_mult_sgn
% 7.75/5.73 thf(fact_7200_abs__mult__sgn,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % abs_mult_sgn
% 7.75/5.73 thf(fact_7201_abs__mult__sgn,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % abs_mult_sgn
% 7.75/5.73 thf(fact_7202_abs__mult__sgn,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % abs_mult_sgn
% 7.75/5.73 thf(fact_7203_abs__mult__sgn,axiom,
% 7.75/5.73 ! [A: complex] :
% 7.75/5.73 ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % abs_mult_sgn
% 7.75/5.73 thf(fact_7204_sgn__mult__abs,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_abs
% 7.75/5.73 thf(fact_7205_sgn__mult__abs,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_abs
% 7.75/5.73 thf(fact_7206_sgn__mult__abs,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_abs
% 7.75/5.73 thf(fact_7207_sgn__mult__abs,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_abs
% 7.75/5.73 thf(fact_7208_sgn__mult__abs,axiom,
% 7.75/5.73 ! [A: complex] :
% 7.75/5.73 ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mult_abs
% 7.75/5.73 thf(fact_7209_mult__sgn__abs,axiom,
% 7.75/5.73 ! [X: rat] :
% 7.75/5.73 ( ( times_times_rat @ ( sgn_sgn_rat @ X ) @ ( abs_abs_rat @ X ) )
% 7.75/5.73 = X ) ).
% 7.75/5.73
% 7.75/5.73 % mult_sgn_abs
% 7.75/5.73 thf(fact_7210_mult__sgn__abs,axiom,
% 7.75/5.73 ! [X: real] :
% 7.75/5.73 ( ( times_times_real @ ( sgn_sgn_real @ X ) @ ( abs_abs_real @ X ) )
% 7.75/5.73 = X ) ).
% 7.75/5.73
% 7.75/5.73 % mult_sgn_abs
% 7.75/5.73 thf(fact_7211_mult__sgn__abs,axiom,
% 7.75/5.73 ! [X: int] :
% 7.75/5.73 ( ( times_times_int @ ( sgn_sgn_int @ X ) @ ( abs_abs_int @ X ) )
% 7.75/5.73 = X ) ).
% 7.75/5.73
% 7.75/5.73 % mult_sgn_abs
% 7.75/5.73 thf(fact_7212_mult__sgn__abs,axiom,
% 7.75/5.73 ! [X: code_integer] :
% 7.75/5.73 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X ) @ ( abs_abs_Code_integer @ X ) )
% 7.75/5.73 = X ) ).
% 7.75/5.73
% 7.75/5.73 % mult_sgn_abs
% 7.75/5.73 thf(fact_7213_div__eq__sgn__abs,axiom,
% 7.75/5.73 ! [K: int,L: int] :
% 7.75/5.73 ( ( ( sgn_sgn_int @ K )
% 7.75/5.73 = ( sgn_sgn_int @ L ) )
% 7.75/5.73 => ( ( divide_divide_int @ K @ L )
% 7.75/5.73 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % div_eq_sgn_abs
% 7.75/5.73 thf(fact_7214_sin__coeff__Suc,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( sin_coeff @ ( suc @ N ) )
% 7.75/5.73 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sin_coeff_Suc
% 7.75/5.73 thf(fact_7215_sgn__1__pos,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( ( sgn_sgn_Code_integer @ A )
% 7.75/5.73 = one_one_Code_integer )
% 7.75/5.73 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1_pos
% 7.75/5.73 thf(fact_7216_sgn__1__pos,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( ( sgn_sgn_real @ A )
% 7.75/5.73 = one_one_real )
% 7.75/5.73 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1_pos
% 7.75/5.73 thf(fact_7217_sgn__1__pos,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( ( sgn_sgn_rat @ A )
% 7.75/5.73 = one_one_rat )
% 7.75/5.73 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1_pos
% 7.75/5.73 thf(fact_7218_sgn__1__pos,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( ( sgn_sgn_int @ A )
% 7.75/5.73 = one_one_int )
% 7.75/5.73 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1_pos
% 7.75/5.73 thf(fact_7219_abs__sgn__eq,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( ( A = zero_z3403309356797280102nteger )
% 7.75/5.73 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 = zero_z3403309356797280102nteger ) )
% 7.75/5.73 & ( ( A != zero_z3403309356797280102nteger )
% 7.75/5.73 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 7.75/5.73 = one_one_Code_integer ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % abs_sgn_eq
% 7.75/5.73 thf(fact_7220_abs__sgn__eq,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( ( A = zero_zero_real )
% 7.75/5.73 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 7.75/5.73 = zero_zero_real ) )
% 7.75/5.73 & ( ( A != zero_zero_real )
% 7.75/5.73 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 7.75/5.73 = one_one_real ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % abs_sgn_eq
% 7.75/5.73 thf(fact_7221_abs__sgn__eq,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( ( A = zero_zero_rat )
% 7.75/5.73 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 7.75/5.73 = zero_zero_rat ) )
% 7.75/5.73 & ( ( A != zero_zero_rat )
% 7.75/5.73 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 7.75/5.73 = one_one_rat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % abs_sgn_eq
% 7.75/5.73 thf(fact_7222_abs__sgn__eq,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( ( A = zero_zero_int )
% 7.75/5.73 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 7.75/5.73 = zero_zero_int ) )
% 7.75/5.73 & ( ( A != zero_zero_int )
% 7.75/5.73 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 7.75/5.73 = one_one_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % abs_sgn_eq
% 7.75/5.73 thf(fact_7223_sgn__mod,axiom,
% 7.75/5.73 ! [L: int,K: int] :
% 7.75/5.73 ( ( L != zero_zero_int )
% 7.75/5.73 => ( ~ ( dvd_dvd_int @ L @ K )
% 7.75/5.73 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 7.75/5.73 = ( sgn_sgn_int @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_mod
% 7.75/5.73 thf(fact_7224_cos__coeff__Suc,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( cos_coeff @ ( suc @ N ) )
% 7.75/5.73 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % cos_coeff_Suc
% 7.75/5.73 thf(fact_7225_sgn__if,axiom,
% 7.75/5.73 ( sgn_sgn_int
% 7.75/5.73 = ( ^ [X2: int] : ( if_int @ ( X2 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_if
% 7.75/5.73 thf(fact_7226_sgn__if,axiom,
% 7.75/5.73 ( sgn_sgn_real
% 7.75/5.73 = ( ^ [X2: real] : ( if_real @ ( X2 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X2 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_if
% 7.75/5.73 thf(fact_7227_sgn__if,axiom,
% 7.75/5.73 ( sgn_sgn_Code_integer
% 7.75/5.73 = ( ^ [X2: code_integer] : ( if_Code_integer @ ( X2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X2 ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_if
% 7.75/5.73 thf(fact_7228_sgn__if,axiom,
% 7.75/5.73 ( sgn_sgn_rat
% 7.75/5.73 = ( ^ [X2: rat] : ( if_rat @ ( X2 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X2 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_if
% 7.75/5.73 thf(fact_7229_sgn__1__neg,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( ( sgn_sgn_int @ A )
% 7.75/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.73 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1_neg
% 7.75/5.73 thf(fact_7230_sgn__1__neg,axiom,
% 7.75/5.73 ! [A: real] :
% 7.75/5.73 ( ( ( sgn_sgn_real @ A )
% 7.75/5.73 = ( uminus_uminus_real @ one_one_real ) )
% 7.75/5.73 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1_neg
% 7.75/5.73 thf(fact_7231_sgn__1__neg,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( ( sgn_sgn_Code_integer @ A )
% 7.75/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.73 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1_neg
% 7.75/5.73 thf(fact_7232_sgn__1__neg,axiom,
% 7.75/5.73 ! [A: rat] :
% 7.75/5.73 ( ( ( sgn_sgn_rat @ A )
% 7.75/5.73 = ( uminus_uminus_rat @ one_one_rat ) )
% 7.75/5.73 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_1_neg
% 7.75/5.73 thf(fact_7233_zsgn__def,axiom,
% 7.75/5.73 ( sgn_sgn_int
% 7.75/5.73 = ( ^ [I2: int] : ( if_int @ ( I2 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % zsgn_def
% 7.75/5.73 thf(fact_7234_norm__sgn,axiom,
% 7.75/5.73 ! [X: real] :
% 7.75/5.73 ( ( ( X = zero_zero_real )
% 7.75/5.73 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 7.75/5.73 = zero_zero_real ) )
% 7.75/5.73 & ( ( X != zero_zero_real )
% 7.75/5.73 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 7.75/5.73 = one_one_real ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % norm_sgn
% 7.75/5.73 thf(fact_7235_norm__sgn,axiom,
% 7.75/5.73 ! [X: complex] :
% 7.75/5.73 ( ( ( X = zero_zero_complex )
% 7.75/5.73 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 7.75/5.73 = zero_zero_real ) )
% 7.75/5.73 & ( ( X != zero_zero_complex )
% 7.75/5.73 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 7.75/5.73 = one_one_real ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % norm_sgn
% 7.75/5.73 thf(fact_7236_div__sgn__abs__cancel,axiom,
% 7.75/5.73 ! [V: int,K: int,L: int] :
% 7.75/5.73 ( ( V != zero_zero_int )
% 7.75/5.73 => ( ( 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 ) ) )
% 7.75/5.73 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % div_sgn_abs_cancel
% 7.75/5.73 thf(fact_7237_div__dvd__sgn__abs,axiom,
% 7.75/5.73 ! [L: int,K: int] :
% 7.75/5.73 ( ( dvd_dvd_int @ L @ K )
% 7.75/5.73 => ( ( divide_divide_int @ K @ L )
% 7.75/5.73 = ( 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 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % div_dvd_sgn_abs
% 7.75/5.73 thf(fact_7238_fold__atLeastAtMost__nat_Osimps,axiom,
% 7.75/5.73 ( set_fo2584398358068434914at_nat
% 7.75/5.73 = ( ^ [F3: nat > nat > nat,A3: nat,B4: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A3 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B4 @ ( F3 @ A3 @ Acc ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fold_atLeastAtMost_nat.simps
% 7.75/5.73 thf(fact_7239_fold__atLeastAtMost__nat_Oelims,axiom,
% 7.75/5.73 ! [X: nat > nat > nat,Xa3: nat,Xb3: nat,Xc: nat,Y: nat] :
% 7.75/5.73 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa3 @ Xb3 @ Xc )
% 7.75/5.73 = Y )
% 7.75/5.73 => ( ( ( ord_less_nat @ Xb3 @ Xa3 )
% 7.75/5.73 => ( Y = Xc ) )
% 7.75/5.73 & ( ~ ( ord_less_nat @ Xb3 @ Xa3 )
% 7.75/5.73 => ( Y
% 7.75/5.73 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa3 @ one_one_nat ) @ Xb3 @ ( X @ Xa3 @ Xc ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % fold_atLeastAtMost_nat.elims
% 7.75/5.73 thf(fact_7240_div__noneq__sgn__abs,axiom,
% 7.75/5.73 ! [L: int,K: int] :
% 7.75/5.73 ( ( L != zero_zero_int )
% 7.75/5.73 => ( ( ( sgn_sgn_int @ K )
% 7.75/5.73 != ( sgn_sgn_int @ L ) )
% 7.75/5.73 => ( ( divide_divide_int @ K @ L )
% 7.75/5.73 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 7.75/5.73 @ ( zero_n2684676970156552555ol_int
% 7.75/5.73 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % div_noneq_sgn_abs
% 7.75/5.73 thf(fact_7241_modulo__int__def,axiom,
% 7.75/5.73 ( modulo_modulo_int
% 7.75/5.73 = ( ^ [K3: int,L2: int] :
% 7.75/5.73 ( if_int @ ( L2 = zero_zero_int ) @ K3
% 7.75/5.73 @ ( if_int
% 7.75/5.73 @ ( ( sgn_sgn_int @ K3 )
% 7.75/5.73 = ( sgn_sgn_int @ L2 ) )
% 7.75/5.73 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 7.75/5.73 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 7.75/5.73 @ ( minus_minus_int
% 7.75/5.73 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 7.75/5.73 @ ( zero_n2684676970156552555ol_int
% 7.75/5.73 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 7.75/5.73 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % modulo_int_def
% 7.75/5.73 thf(fact_7242_divide__int__unfold,axiom,
% 7.75/5.73 ! [L: int,K: int,N: nat,M: nat] :
% 7.75/5.73 ( ( ( ( ( sgn_sgn_int @ L )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 | ( ( sgn_sgn_int @ K )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 | ( N = zero_zero_nat ) )
% 7.75/5.73 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 7.75/5.73 = zero_zero_int ) )
% 7.75/5.73 & ( ~ ( ( ( sgn_sgn_int @ L )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 | ( ( sgn_sgn_int @ K )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 | ( N = zero_zero_nat ) )
% 7.75/5.73 => ( ( ( ( sgn_sgn_int @ K )
% 7.75/5.73 = ( sgn_sgn_int @ L ) )
% 7.75/5.73 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 7.75/5.73 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 7.75/5.73 & ( ( ( sgn_sgn_int @ K )
% 7.75/5.73 != ( sgn_sgn_int @ L ) )
% 7.75/5.73 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 7.75/5.73 = ( uminus_uminus_int
% 7.75/5.73 @ ( semiri1314217659103216013at_int
% 7.75/5.73 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 7.75/5.73 @ ( zero_n2687167440665602831ol_nat
% 7.75/5.73 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % divide_int_unfold
% 7.75/5.73 thf(fact_7243_modulo__int__unfold,axiom,
% 7.75/5.73 ! [L: int,K: int,N: nat,M: nat] :
% 7.75/5.73 ( ( ( ( ( sgn_sgn_int @ L )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 | ( ( sgn_sgn_int @ K )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 | ( N = zero_zero_nat ) )
% 7.75/5.73 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 7.75/5.73 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 7.75/5.73 & ( ~ ( ( ( sgn_sgn_int @ L )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 | ( ( sgn_sgn_int @ K )
% 7.75/5.73 = zero_zero_int )
% 7.75/5.73 | ( N = zero_zero_nat ) )
% 7.75/5.73 => ( ( ( ( sgn_sgn_int @ K )
% 7.75/5.73 = ( sgn_sgn_int @ L ) )
% 7.75/5.73 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 7.75/5.73 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 7.75/5.73 & ( ( ( sgn_sgn_int @ K )
% 7.75/5.73 != ( sgn_sgn_int @ L ) )
% 7.75/5.73 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 7.75/5.73 = ( times_times_int @ ( sgn_sgn_int @ L )
% 7.75/5.73 @ ( minus_minus_int
% 7.75/5.73 @ ( semiri1314217659103216013at_int
% 7.75/5.73 @ ( times_times_nat @ N
% 7.75/5.73 @ ( zero_n2687167440665602831ol_nat
% 7.75/5.73 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 7.75/5.73 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % modulo_int_unfold
% 7.75/5.73 thf(fact_7244_sgn__div__eq__sgn__mult,axiom,
% 7.75/5.73 ! [A: int,B: int] :
% 7.75/5.73 ( ( ( divide_divide_int @ A @ B )
% 7.75/5.73 != zero_zero_int )
% 7.75/5.73 => ( ( sgn_sgn_int @ ( divide_divide_int @ A @ B ) )
% 7.75/5.73 = ( sgn_sgn_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_div_eq_sgn_mult
% 7.75/5.73 thf(fact_7245_invar__vebt_Ocases,axiom,
% 7.75/5.73 ! [A1: vEBT_VEBT,A22: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ A1 @ A22 )
% 7.75/5.73 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.73 ( A1
% 7.75/5.73 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.73 => ( A22
% 7.75/5.73 != ( suc @ zero_zero_nat ) ) )
% 7.75/5.73 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M2: nat,Deg2: nat] :
% 7.75/5.73 ( ( A1
% 7.75/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.73 => ( ( A22 = Deg2 )
% 7.75/5.73 => ( ! [X5: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 7.75/5.73 => ( ( vEBT_invar_vebt @ Summary2 @ M2 )
% 7.75/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 7.75/5.73 => ( ( M2 = N2 )
% 7.75/5.73 => ( ( Deg2
% 7.75/5.73 = ( plus_plus_nat @ N2 @ M2 ) )
% 7.75/5.73 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 7.75/5.73 => ~ ! [X5: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 7.75/5.73 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 7.75/5.73 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M2: nat,Deg2: nat] :
% 7.75/5.73 ( ( A1
% 7.75/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.73 => ( ( A22 = Deg2 )
% 7.75/5.73 => ( ! [X5: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 7.75/5.73 => ( ( vEBT_invar_vebt @ Summary2 @ M2 )
% 7.75/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 7.75/5.73 => ( ( M2
% 7.75/5.73 = ( suc @ N2 ) )
% 7.75/5.73 => ( ( Deg2
% 7.75/5.73 = ( plus_plus_nat @ N2 @ M2 ) )
% 7.75/5.73 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 7.75/5.73 => ~ ! [X5: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 7.75/5.73 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 7.75/5.73 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M2: nat,Deg2: nat,Mi: nat,Ma2: nat] :
% 7.75/5.73 ( ( A1
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.73 => ( ( A22 = Deg2 )
% 7.75/5.73 => ( ! [X5: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 7.75/5.73 => ( ( vEBT_invar_vebt @ Summary2 @ M2 )
% 7.75/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 7.75/5.73 => ( ( M2 = N2 )
% 7.75/5.73 => ( ( Deg2
% 7.75/5.73 = ( plus_plus_nat @ N2 @ M2 ) )
% 7.75/5.73 => ( ! [I4: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 7.75/5.73 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 7.75/5.73 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 7.75/5.73 => ( ( ( Mi = Ma2 )
% 7.75/5.73 => ! [X5: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 7.75/5.73 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 7.75/5.73 => ( ( ord_less_eq_nat @ Mi @ Ma2 )
% 7.75/5.73 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 7.75/5.73 => ~ ( ( Mi != Ma2 )
% 7.75/5.73 => ! [I4: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 7.75/5.73 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 7.75/5.73 = I4 )
% 7.75/5.73 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 7.75/5.73 & ! [X5: nat] :
% 7.75/5.73 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 7.75/5.73 = I4 )
% 7.75/5.73 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 7.75/5.73 => ( ( ord_less_nat @ Mi @ X5 )
% 7.75/5.73 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.73 => ~ ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M2: nat,Deg2: nat,Mi: nat,Ma2: nat] :
% 7.75/5.73 ( ( A1
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.73 => ( ( A22 = Deg2 )
% 7.75/5.73 => ( ! [X5: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 7.75/5.73 => ( ( vEBT_invar_vebt @ Summary2 @ M2 )
% 7.75/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 7.75/5.73 => ( ( M2
% 7.75/5.73 = ( suc @ N2 ) )
% 7.75/5.73 => ( ( Deg2
% 7.75/5.73 = ( plus_plus_nat @ N2 @ M2 ) )
% 7.75/5.73 => ( ! [I4: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 7.75/5.73 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X7 ) )
% 7.75/5.73 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 7.75/5.73 => ( ( ( Mi = Ma2 )
% 7.75/5.73 => ! [X5: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 7.75/5.73 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 7.75/5.73 => ( ( ord_less_eq_nat @ Mi @ Ma2 )
% 7.75/5.73 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 7.75/5.73 => ~ ( ( Mi != Ma2 )
% 7.75/5.73 => ! [I4: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 7.75/5.73 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 7.75/5.73 = I4 )
% 7.75/5.73 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 7.75/5.73 & ! [X5: nat] :
% 7.75/5.73 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 7.75/5.73 = I4 )
% 7.75/5.73 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 7.75/5.73 => ( ( ord_less_nat @ Mi @ X5 )
% 7.75/5.73 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % invar_vebt.cases
% 7.75/5.73 thf(fact_7246_invar__vebt_Osimps,axiom,
% 7.75/5.73 ( vEBT_invar_vebt
% 7.75/5.73 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 7.75/5.73 ( ( ? [A3: $o,B4: $o] :
% 7.75/5.73 ( A12
% 7.75/5.73 = ( vEBT_Leaf @ A3 @ B4 ) )
% 7.75/5.73 & ( A23
% 7.75/5.73 = ( suc @ zero_zero_nat ) ) )
% 7.75/5.73 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 7.75/5.73 ( ( A12
% 7.75/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 7.75/5.73 & ! [X2: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 7.75/5.73 & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 7.75/5.73 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 7.75/5.73 & ( A23
% 7.75/5.73 = ( plus_plus_nat @ N3 @ N3 ) )
% 7.75/5.73 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X7 )
% 7.75/5.73 & ! [X2: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 7.75/5.73 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 7.75/5.73 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 7.75/5.73 ( ( A12
% 7.75/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 7.75/5.73 & ! [X2: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 7.75/5.73 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 7.75/5.73 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 7.75/5.73 & ( A23
% 7.75/5.73 = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 7.75/5.73 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X7 )
% 7.75/5.73 & ! [X2: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 7.75/5.73 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 7.75/5.73 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi2: nat,Ma3: nat] :
% 7.75/5.73 ( ( A12
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 7.75/5.73 & ! [X2: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 7.75/5.73 & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 7.75/5.73 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 7.75/5.73 & ( A23
% 7.75/5.73 = ( plus_plus_nat @ N3 @ N3 ) )
% 7.75/5.73 & ! [I2: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 7.75/5.73 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X7 ) )
% 7.75/5.73 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 7.75/5.73 & ( ( Mi2 = Ma3 )
% 7.75/5.73 => ! [X2: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 7.75/5.73 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 7.75/5.73 & ( ord_less_eq_nat @ Mi2 @ Ma3 )
% 7.75/5.73 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 7.75/5.73 & ( ( Mi2 != Ma3 )
% 7.75/5.73 => ! [I2: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 7.75/5.73 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 7.75/5.73 = I2 )
% 7.75/5.73 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 7.75/5.73 & ! [X2: nat] :
% 7.75/5.73 ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 7.75/5.73 = I2 )
% 7.75/5.73 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 7.75/5.73 => ( ( ord_less_nat @ Mi2 @ X2 )
% 7.75/5.73 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) )
% 7.75/5.73 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi2: nat,Ma3: nat] :
% 7.75/5.73 ( ( A12
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 7.75/5.73 & ! [X2: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 7.75/5.73 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 7.75/5.73 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 7.75/5.73 & ( A23
% 7.75/5.73 = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 7.75/5.73 & ! [I2: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 7.75/5.73 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X7 ) )
% 7.75/5.73 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 7.75/5.73 & ( ( Mi2 = Ma3 )
% 7.75/5.73 => ! [X2: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 7.75/5.73 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 7.75/5.73 & ( ord_less_eq_nat @ Mi2 @ Ma3 )
% 7.75/5.73 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 7.75/5.73 & ( ( Mi2 != Ma3 )
% 7.75/5.73 => ! [I2: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 7.75/5.73 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 7.75/5.73 = I2 )
% 7.75/5.73 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 7.75/5.73 & ! [X2: nat] :
% 7.75/5.73 ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 7.75/5.73 = I2 )
% 7.75/5.73 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 7.75/5.73 => ( ( ord_less_nat @ Mi2 @ X2 )
% 7.75/5.73 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % invar_vebt.simps
% 7.75/5.73 thf(fact_7247_and__int__unfold,axiom,
% 7.75/5.73 ( bit_se725231765392027082nd_int
% 7.75/5.73 = ( ^ [K3: int,L2: int] :
% 7.75/5.73 ( if_int
% 7.75/5.73 @ ( ( K3 = zero_zero_int )
% 7.75/5.73 | ( L2 = zero_zero_int ) )
% 7.75/5.73 @ zero_zero_int
% 7.75/5.73 @ ( if_int
% 7.75/5.73 @ ( K3
% 7.75/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.73 @ L2
% 7.75/5.73 @ ( if_int
% 7.75/5.73 @ ( L2
% 7.75/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.73 @ K3
% 7.75/5.73 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_int_unfold
% 7.75/5.73 thf(fact_7248_and_Oright__idem,axiom,
% 7.75/5.73 ! [A: int,B: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 7.75/5.73 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.right_idem
% 7.75/5.73 thf(fact_7249_and_Oright__idem,axiom,
% 7.75/5.73 ! [A: nat,B: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 7.75/5.73 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.right_idem
% 7.75/5.73 thf(fact_7250_and_Oright__idem,axiom,
% 7.75/5.73 ! [A: code_integer,B: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ ( bit_se3949692690581998587nteger @ A @ B ) @ B )
% 7.75/5.73 = ( bit_se3949692690581998587nteger @ A @ B ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.right_idem
% 7.75/5.73 thf(fact_7251_and_Oleft__idem,axiom,
% 7.75/5.73 ! [A: int,B: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 7.75/5.73 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.left_idem
% 7.75/5.73 thf(fact_7252_and_Oleft__idem,axiom,
% 7.75/5.73 ! [A: nat,B: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 7.75/5.73 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.left_idem
% 7.75/5.73 thf(fact_7253_and_Oleft__idem,axiom,
% 7.75/5.73 ! [A: code_integer,B: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ A @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 7.75/5.73 = ( bit_se3949692690581998587nteger @ A @ B ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.left_idem
% 7.75/5.73 thf(fact_7254_and_Oidem,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ A @ A )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % and.idem
% 7.75/5.73 thf(fact_7255_and_Oidem,axiom,
% 7.75/5.73 ! [A: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % and.idem
% 7.75/5.73 thf(fact_7256_and_Oidem,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ A @ A )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % and.idem
% 7.75/5.73 thf(fact_7257_mi__eq__ma__no__ch,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 7.75/5.73 => ( ( Mi3 = Ma )
% 7.75/5.73 => ( ! [X5: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.73 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 7.75/5.73 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mi_eq_ma_no_ch
% 7.75/5.73 thf(fact_7258_insert__simp__mima,axiom,
% 7.75/5.73 ! [X: nat,Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( ( X = Mi3 )
% 7.75/5.73 | ( X = Ma ) )
% 7.75/5.73 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % insert_simp_mima
% 7.75/5.73 thf(fact_7259_bit_Oconj__zero__right,axiom,
% 7.75/5.73 ! [X: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 7.75/5.73 = zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % bit.conj_zero_right
% 7.75/5.73 thf(fact_7260_bit_Oconj__zero__right,axiom,
% 7.75/5.73 ! [X: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ X @ zero_z3403309356797280102nteger )
% 7.75/5.73 = zero_z3403309356797280102nteger ) ).
% 7.75/5.73
% 7.75/5.73 % bit.conj_zero_right
% 7.75/5.73 thf(fact_7261_bit_Oconj__zero__left,axiom,
% 7.75/5.73 ! [X: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 7.75/5.73 = zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % bit.conj_zero_left
% 7.75/5.73 thf(fact_7262_bit_Oconj__zero__left,axiom,
% 7.75/5.73 ! [X: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ zero_z3403309356797280102nteger @ X )
% 7.75/5.73 = zero_z3403309356797280102nteger ) ).
% 7.75/5.73
% 7.75/5.73 % bit.conj_zero_left
% 7.75/5.73 thf(fact_7263_zero__and__eq,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 7.75/5.73 = zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % zero_and_eq
% 7.75/5.73 thf(fact_7264_zero__and__eq,axiom,
% 7.75/5.73 ! [A: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 7.75/5.73 = zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % zero_and_eq
% 7.75/5.73 thf(fact_7265_zero__and__eq,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ zero_z3403309356797280102nteger @ A )
% 7.75/5.73 = zero_z3403309356797280102nteger ) ).
% 7.75/5.73
% 7.75/5.73 % zero_and_eq
% 7.75/5.73 thf(fact_7266_and__zero__eq,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 7.75/5.73 = zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % and_zero_eq
% 7.75/5.73 thf(fact_7267_and__zero__eq,axiom,
% 7.75/5.73 ! [A: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 7.75/5.73 = zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % and_zero_eq
% 7.75/5.73 thf(fact_7268_and__zero__eq,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ A @ zero_z3403309356797280102nteger )
% 7.75/5.73 = zero_z3403309356797280102nteger ) ).
% 7.75/5.73
% 7.75/5.73 % and_zero_eq
% 7.75/5.73 thf(fact_7269_sgn__le__0__iff,axiom,
% 7.75/5.73 ! [X: real] :
% 7.75/5.73 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 7.75/5.73 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_le_0_iff
% 7.75/5.73 thf(fact_7270_zero__le__sgn__iff,axiom,
% 7.75/5.73 ! [X: real] :
% 7.75/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 7.75/5.73 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % zero_le_sgn_iff
% 7.75/5.73 thf(fact_7271_not__None__eq,axiom,
% 7.75/5.73 ! [X: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( X != none_P5556105721700978146at_nat )
% 7.75/5.73 = ( ? [Y6: product_prod_nat_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ Y6 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_None_eq
% 7.75/5.73 thf(fact_7272_not__None__eq,axiom,
% 7.75/5.73 ! [X: option_nat] :
% 7.75/5.73 ( ( X != none_nat )
% 7.75/5.73 = ( ? [Y6: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( some_nat @ Y6 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_None_eq
% 7.75/5.73 thf(fact_7273_not__None__eq,axiom,
% 7.75/5.73 ! [X: option_num] :
% 7.75/5.73 ( ( X != none_num )
% 7.75/5.73 = ( ? [Y6: num] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( some_num @ Y6 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_None_eq
% 7.75/5.73 thf(fact_7274_not__Some__eq,axiom,
% 7.75/5.73 ! [X: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( ! [Y6: product_prod_nat_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( some_P7363390416028606310at_nat @ Y6 ) ) )
% 7.75/5.73 = ( X = none_P5556105721700978146at_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_Some_eq
% 7.75/5.73 thf(fact_7275_not__Some__eq,axiom,
% 7.75/5.73 ! [X: option_nat] :
% 7.75/5.73 ( ( ! [Y6: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( some_nat @ Y6 ) ) )
% 7.75/5.73 = ( X = none_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_Some_eq
% 7.75/5.73 thf(fact_7276_not__Some__eq,axiom,
% 7.75/5.73 ! [X: option_num] :
% 7.75/5.73 ( ( ! [Y6: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( some_num @ Y6 ) ) )
% 7.75/5.73 = ( X = none_num ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_Some_eq
% 7.75/5.73 thf(fact_7277_take__bit__and,axiom,
% 7.75/5.73 ! [N: nat,A: code_integer,B: code_integer] :
% 7.75/5.73 ( ( bit_se1745604003318907178nteger @ N @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 7.75/5.73 = ( bit_se3949692690581998587nteger @ ( bit_se1745604003318907178nteger @ N @ A ) @ ( bit_se1745604003318907178nteger @ N @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_and
% 7.75/5.73 thf(fact_7278_take__bit__and,axiom,
% 7.75/5.73 ! [N: nat,A: nat,B: nat] :
% 7.75/5.73 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 7.75/5.73 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_and
% 7.75/5.73 thf(fact_7279_take__bit__and,axiom,
% 7.75/5.73 ! [N: nat,A: int,B: int] :
% 7.75/5.73 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 7.75/5.73 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % take_bit_and
% 7.75/5.73 thf(fact_7280_tdeletemimi,axiom,
% 7.75/5.73 ! [Deg: nat,Mi3: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Mi3 ) ) @ Deg @ TreeList @ Summary ) @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % tdeletemimi
% 7.75/5.73 thf(fact_7281_tdeletemimi_H,axiom,
% 7.75/5.73 ! [Deg: nat,Mi3: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Mi3 ) ) @ Deg @ TreeList @ Summary ) @ X ) @ one_one_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % tdeletemimi'
% 7.75/5.73 thf(fact_7282_mi__ma__2__deg,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 7.75/5.73 => ( ( ord_less_eq_nat @ Mi3 @ Ma )
% 7.75/5.73 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mi_ma_2_deg
% 7.75/5.73 thf(fact_7283_bit_Oconj__one__right,axiom,
% 7.75/5.73 ! [X: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.73 = X ) ).
% 7.75/5.73
% 7.75/5.73 % bit.conj_one_right
% 7.75/5.73 thf(fact_7284_bit_Oconj__one__right,axiom,
% 7.75/5.73 ! [X: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.73 = X ) ).
% 7.75/5.73
% 7.75/5.73 % bit.conj_one_right
% 7.75/5.73 thf(fact_7285_and_Oright__neutral,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % and.right_neutral
% 7.75/5.73 thf(fact_7286_and_Oright__neutral,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % and.right_neutral
% 7.75/5.73 thf(fact_7287_and_Oleft__neutral,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % and.left_neutral
% 7.75/5.73 thf(fact_7288_and_Oleft__neutral,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 7.75/5.73 = A ) ).
% 7.75/5.73
% 7.75/5.73 % and.left_neutral
% 7.75/5.73 thf(fact_7289_not__Some__eq2,axiom,
% 7.75/5.73 ! [V: option2661157926820139483um_num] :
% 7.75/5.73 ( ( ! [X2: num,Y6: num] :
% 7.75/5.73 ( V
% 7.75/5.73 != ( some_P6201964756284913402um_num @ ( product_Pair_num_num @ X2 @ Y6 ) ) ) )
% 7.75/5.73 = ( V = none_P4394680061957285238um_num ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_Some_eq2
% 7.75/5.73 thf(fact_7290_not__Some__eq2,axiom,
% 7.75/5.73 ! [V: option4624381673175914239nt_int] :
% 7.75/5.73 ( ( ! [X2: int,Y6: int] :
% 7.75/5.73 ( V
% 7.75/5.73 != ( some_P4184893108420464158nt_int @ ( product_Pair_int_int @ X2 @ Y6 ) ) ) )
% 7.75/5.73 = ( V = none_P2377608414092835994nt_int ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_Some_eq2
% 7.75/5.73 thf(fact_7291_not__Some__eq2,axiom,
% 7.75/5.73 ! [V: option5190343406534369742et_nat] :
% 7.75/5.73 ( ( ! [X2: produc3658429121746597890et_nat > $o,Y6: produc3658429121746597890et_nat] :
% 7.75/5.73 ( V
% 7.75/5.73 != ( some_P750831030444334937et_nat @ ( produc5001842942810119800et_nat @ X2 @ Y6 ) ) ) )
% 7.75/5.73 = ( V = none_P4972525538344268765et_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_Some_eq2
% 7.75/5.73 thf(fact_7292_not__Some__eq2,axiom,
% 7.75/5.73 ! [V: option2860828798490689354et_nat] :
% 7.75/5.73 ( ( ! [X2: produc3658429121746597890et_nat > $o,Y6: produc3925858234332021118et_nat] :
% 7.75/5.73 ( V
% 7.75/5.73 != ( some_P1630309045189364437et_nat @ ( produc2245416461498447860et_nat @ X2 @ Y6 ) ) ) )
% 7.75/5.73 = ( V = none_P199884684680593241et_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_Some_eq2
% 7.75/5.73 thf(fact_7293_not__Some__eq2,axiom,
% 7.75/5.73 ! [V: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( ! [X2: nat,Y6: nat] :
% 7.75/5.73 ( V
% 7.75/5.73 != ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ Y6 ) ) ) )
% 7.75/5.73 = ( V = none_P5556105721700978146at_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_Some_eq2
% 7.75/5.73 thf(fact_7294_and__nonnegative__int__iff,axiom,
% 7.75/5.73 ! [K: int,L: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 7.75/5.73 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.75/5.73 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_nonnegative_int_iff
% 7.75/5.73 thf(fact_7295_and__negative__int__iff,axiom,
% 7.75/5.73 ! [K: int,L: int] :
% 7.75/5.73 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 7.75/5.73 = ( ( ord_less_int @ K @ zero_zero_int )
% 7.75/5.73 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_negative_int_iff
% 7.75/5.73 thf(fact_7296_both__member__options__from__complete__tree__to__child,axiom,
% 7.75/5.73 ! [Deg: nat,Mi3: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 7.75/5.73 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 => ( ( 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 ) ) ) ) )
% 7.75/5.73 | ( X = Mi3 )
% 7.75/5.73 | ( X = Ma ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % both_member_options_from_complete_tree_to_child
% 7.75/5.73 thf(fact_7297_less__eq__option__Some__None,axiom,
% 7.75/5.73 ! [X: nat] :
% 7.75/5.73 ~ ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % less_eq_option_Some_None
% 7.75/5.73 thf(fact_7298_less__eq__option__Some__None,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ~ ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ none_num ) ).
% 7.75/5.73
% 7.75/5.73 % less_eq_option_Some_None
% 7.75/5.73 thf(fact_7299_less__option__Some,axiom,
% 7.75/5.73 ! [X: real,Y: real] :
% 7.75/5.73 ( ( ord_less_option_real @ ( some_real @ X ) @ ( some_real @ Y ) )
% 7.75/5.73 = ( ord_less_real @ X @ Y ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_Some
% 7.75/5.73 thf(fact_7300_less__option__Some,axiom,
% 7.75/5.73 ! [X: rat,Y: rat] :
% 7.75/5.73 ( ( ord_less_option_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 7.75/5.73 = ( ord_less_rat @ X @ Y ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_Some
% 7.75/5.73 thf(fact_7301_less__option__Some,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( ord_less_option_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 7.75/5.73 = ( ord_less_num @ X @ Y ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_Some
% 7.75/5.73 thf(fact_7302_less__option__Some,axiom,
% 7.75/5.73 ! [X: nat,Y: nat] :
% 7.75/5.73 ( ( ord_less_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 7.75/5.73 = ( ord_less_nat @ X @ Y ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_Some
% 7.75/5.73 thf(fact_7303_less__option__Some,axiom,
% 7.75/5.73 ! [X: int,Y: int] :
% 7.75/5.73 ( ( ord_less_option_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 7.75/5.73 = ( ord_less_int @ X @ Y ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_Some
% 7.75/5.73 thf(fact_7304_less__option__None__Some__code,axiom,
% 7.75/5.73 ! [X: nat] : ( ord_less_option_nat @ none_nat @ ( some_nat @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_None_Some_code
% 7.75/5.73 thf(fact_7305_less__option__None__Some__code,axiom,
% 7.75/5.73 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_None_Some_code
% 7.75/5.73 thf(fact_7306_member__inv,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 & ( ( X = Mi3 )
% 7.75/5.73 | ( X = Ma )
% 7.75/5.73 | ( ( ord_less_nat @ X @ Ma )
% 7.75/5.73 & ( ord_less_nat @ Mi3 @ X )
% 7.75/5.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.73 & ( 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 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % member_inv
% 7.75/5.73 thf(fact_7307_both__member__options__from__chilf__to__complete__tree,axiom,
% 7.75/5.73 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi3: nat,Ma: nat,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.73 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 7.75/5.73 => ( ( 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 ) ) ) ) )
% 7.75/5.73 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % both_member_options_from_chilf_to_complete_tree
% 7.75/5.73 thf(fact_7308_and__numerals_I8_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 7.75/5.73 = one_one_int ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(8)
% 7.75/5.73 thf(fact_7309_and__numerals_I8_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(8)
% 7.75/5.73 thf(fact_7310_and__numerals_I8_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 7.75/5.73 = one_one_Code_integer ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(8)
% 7.75/5.73 thf(fact_7311_and__numerals_I2_J,axiom,
% 7.75/5.73 ! [Y: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 7.75/5.73 = one_one_int ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(2)
% 7.75/5.73 thf(fact_7312_and__numerals_I2_J,axiom,
% 7.75/5.73 ! [Y: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(2)
% 7.75/5.73 thf(fact_7313_and__numerals_I2_J,axiom,
% 7.75/5.73 ! [Y: num] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 7.75/5.73 = one_one_Code_integer ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(2)
% 7.75/5.73 thf(fact_7314_and__numerals_I1_J,axiom,
% 7.75/5.73 ! [Y: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 7.75/5.73 = zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(1)
% 7.75/5.73 thf(fact_7315_and__numerals_I1_J,axiom,
% 7.75/5.73 ! [Y: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 7.75/5.73 = zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(1)
% 7.75/5.73 thf(fact_7316_and__numerals_I1_J,axiom,
% 7.75/5.73 ! [Y: num] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 7.75/5.73 = zero_z3403309356797280102nteger ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(1)
% 7.75/5.73 thf(fact_7317_and__numerals_I5_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 7.75/5.73 = zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(5)
% 7.75/5.73 thf(fact_7318_and__numerals_I5_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 7.75/5.73 = zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(5)
% 7.75/5.73 thf(fact_7319_and__numerals_I5_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 7.75/5.73 = zero_z3403309356797280102nteger ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(5)
% 7.75/5.73 thf(fact_7320_and__numerals_I3_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 7.75/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(3)
% 7.75/5.73 thf(fact_7321_and__numerals_I3_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 7.75/5.73 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(3)
% 7.75/5.73 thf(fact_7322_and__numerals_I3_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 7.75/5.73 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(3)
% 7.75/5.73 thf(fact_7323_and__minus__numerals_I6_J,axiom,
% 7.75/5.73 ! [N: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 7.75/5.73 = one_one_int ) ).
% 7.75/5.73
% 7.75/5.73 % and_minus_numerals(6)
% 7.75/5.73 thf(fact_7324_and__minus__numerals_I2_J,axiom,
% 7.75/5.73 ! [N: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 7.75/5.73 = one_one_int ) ).
% 7.75/5.73
% 7.75/5.73 % and_minus_numerals(2)
% 7.75/5.73 thf(fact_7325_and__numerals_I4_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 7.75/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(4)
% 7.75/5.73 thf(fact_7326_and__numerals_I4_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 7.75/5.73 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(4)
% 7.75/5.73 thf(fact_7327_and__numerals_I4_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 7.75/5.73 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(4)
% 7.75/5.73 thf(fact_7328_and__numerals_I6_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 7.75/5.73 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(6)
% 7.75/5.73 thf(fact_7329_and__numerals_I6_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 7.75/5.73 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(6)
% 7.75/5.73 thf(fact_7330_and__numerals_I6_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 7.75/5.73 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(6)
% 7.75/5.73 thf(fact_7331_and__minus__numerals_I5_J,axiom,
% 7.75/5.73 ! [N: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 7.75/5.73 = zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % and_minus_numerals(5)
% 7.75/5.73 thf(fact_7332_and__minus__numerals_I1_J,axiom,
% 7.75/5.73 ! [N: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 7.75/5.73 = zero_zero_int ) ).
% 7.75/5.73
% 7.75/5.73 % and_minus_numerals(1)
% 7.75/5.73 thf(fact_7333_and__numerals_I7_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 7.75/5.73 = ( 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 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(7)
% 7.75/5.73 thf(fact_7334_and__numerals_I7_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 7.75/5.73 = ( 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 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(7)
% 7.75/5.73 thf(fact_7335_and__numerals_I7_J,axiom,
% 7.75/5.73 ! [X: num,Y: num] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 7.75/5.73 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_numerals(7)
% 7.75/5.73 thf(fact_7336_of__int__and__eq,axiom,
% 7.75/5.73 ! [K: int,L: int] :
% 7.75/5.73 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 7.75/5.73 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_int_and_eq
% 7.75/5.73 thf(fact_7337_of__int__and__eq,axiom,
% 7.75/5.73 ! [K: int,L: int] :
% 7.75/5.73 ( ( ring_18347121197199848620nteger @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 7.75/5.73 = ( bit_se3949692690581998587nteger @ ( ring_18347121197199848620nteger @ K ) @ ( ring_18347121197199848620nteger @ L ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_int_and_eq
% 7.75/5.73 thf(fact_7338_and_Oleft__commute,axiom,
% 7.75/5.73 ! [B: int,A: int,C: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 7.75/5.73 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.left_commute
% 7.75/5.73 thf(fact_7339_and_Oleft__commute,axiom,
% 7.75/5.73 ! [B: nat,A: nat,C: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 7.75/5.73 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.left_commute
% 7.75/5.73 thf(fact_7340_and_Oleft__commute,axiom,
% 7.75/5.73 ! [B: code_integer,A: code_integer,C: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ B @ ( bit_se3949692690581998587nteger @ A @ C ) )
% 7.75/5.73 = ( bit_se3949692690581998587nteger @ A @ ( bit_se3949692690581998587nteger @ B @ C ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.left_commute
% 7.75/5.73 thf(fact_7341_and_Ocommute,axiom,
% 7.75/5.73 ( bit_se725231765392027082nd_int
% 7.75/5.73 = ( ^ [A3: int,B4: int] : ( bit_se725231765392027082nd_int @ B4 @ A3 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.commute
% 7.75/5.73 thf(fact_7342_and_Ocommute,axiom,
% 7.75/5.73 ( bit_se727722235901077358nd_nat
% 7.75/5.73 = ( ^ [A3: nat,B4: nat] : ( bit_se727722235901077358nd_nat @ B4 @ A3 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.commute
% 7.75/5.73 thf(fact_7343_and_Ocommute,axiom,
% 7.75/5.73 ( bit_se3949692690581998587nteger
% 7.75/5.73 = ( ^ [A3: code_integer,B4: code_integer] : ( bit_se3949692690581998587nteger @ B4 @ A3 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.commute
% 7.75/5.73 thf(fact_7344_and_Oassoc,axiom,
% 7.75/5.73 ! [A: int,B: int,C: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 7.75/5.73 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.assoc
% 7.75/5.73 thf(fact_7345_and_Oassoc,axiom,
% 7.75/5.73 ! [A: nat,B: nat,C: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 7.75/5.73 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.assoc
% 7.75/5.73 thf(fact_7346_and_Oassoc,axiom,
% 7.75/5.73 ! [A: code_integer,B: code_integer,C: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ ( bit_se3949692690581998587nteger @ A @ B ) @ C )
% 7.75/5.73 = ( bit_se3949692690581998587nteger @ A @ ( bit_se3949692690581998587nteger @ B @ C ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and.assoc
% 7.75/5.73 thf(fact_7347_prod__decode__aux_Ocases,axiom,
% 7.75/5.73 ! [X: product_prod_nat_nat] :
% 7.75/5.73 ~ ! [K2: nat,M2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( product_Pair_nat_nat @ K2 @ M2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % prod_decode_aux.cases
% 7.75/5.73 thf(fact_7348_of__nat__and__eq,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 7.75/5.73 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_and_eq
% 7.75/5.73 thf(fact_7349_of__nat__and__eq,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 7.75/5.73 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_and_eq
% 7.75/5.73 thf(fact_7350_of__nat__and__eq,axiom,
% 7.75/5.73 ! [M: nat,N: nat] :
% 7.75/5.73 ( ( semiri4939895301339042750nteger @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 7.75/5.73 = ( bit_se3949692690581998587nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % of_nat_and_eq
% 7.75/5.73 thf(fact_7351_combine__options__cases,axiom,
% 7.75/5.73 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( ( X = none_P5556105721700978146at_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ( ( Y = none_P5556105721700978146at_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ! [A5: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ A5 ) )
% 7.75/5.73 => ( ( Y
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ B2 ) )
% 7.75/5.73 => ( P @ X @ Y ) ) )
% 7.75/5.73 => ( P @ X @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % combine_options_cases
% 7.75/5.73 thf(fact_7352_combine__options__cases,axiom,
% 7.75/5.73 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 7.75/5.73 ( ( ( X = none_P5556105721700978146at_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ( ( Y = none_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ! [A5: product_prod_nat_nat,B2: nat] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ A5 ) )
% 7.75/5.73 => ( ( Y
% 7.75/5.73 = ( some_nat @ B2 ) )
% 7.75/5.73 => ( P @ X @ Y ) ) )
% 7.75/5.73 => ( P @ X @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % combine_options_cases
% 7.75/5.73 thf(fact_7353_combine__options__cases,axiom,
% 7.75/5.73 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 7.75/5.73 ( ( ( X = none_P5556105721700978146at_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ( ( Y = none_num )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ! [A5: product_prod_nat_nat,B2: num] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ A5 ) )
% 7.75/5.73 => ( ( Y
% 7.75/5.73 = ( some_num @ B2 ) )
% 7.75/5.73 => ( P @ X @ Y ) ) )
% 7.75/5.73 => ( P @ X @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % combine_options_cases
% 7.75/5.73 thf(fact_7354_combine__options__cases,axiom,
% 7.75/5.73 ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( ( X = none_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ( ( Y = none_P5556105721700978146at_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ! [A5: nat,B2: product_prod_nat_nat] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( some_nat @ A5 ) )
% 7.75/5.73 => ( ( Y
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ B2 ) )
% 7.75/5.73 => ( P @ X @ Y ) ) )
% 7.75/5.73 => ( P @ X @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % combine_options_cases
% 7.75/5.73 thf(fact_7355_combine__options__cases,axiom,
% 7.75/5.73 ! [X: option_nat,P: option_nat > option_nat > $o,Y: option_nat] :
% 7.75/5.73 ( ( ( X = none_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ( ( Y = none_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ! [A5: nat,B2: nat] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( some_nat @ A5 ) )
% 7.75/5.73 => ( ( Y
% 7.75/5.73 = ( some_nat @ B2 ) )
% 7.75/5.73 => ( P @ X @ Y ) ) )
% 7.75/5.73 => ( P @ X @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % combine_options_cases
% 7.75/5.73 thf(fact_7356_combine__options__cases,axiom,
% 7.75/5.73 ! [X: option_nat,P: option_nat > option_num > $o,Y: option_num] :
% 7.75/5.73 ( ( ( X = none_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ( ( Y = none_num )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ! [A5: nat,B2: num] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( some_nat @ A5 ) )
% 7.75/5.73 => ( ( Y
% 7.75/5.73 = ( some_num @ B2 ) )
% 7.75/5.73 => ( P @ X @ Y ) ) )
% 7.75/5.73 => ( P @ X @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % combine_options_cases
% 7.75/5.73 thf(fact_7357_combine__options__cases,axiom,
% 7.75/5.73 ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( ( X = none_num )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ( ( Y = none_P5556105721700978146at_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ! [A5: num,B2: product_prod_nat_nat] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( some_num @ A5 ) )
% 7.75/5.73 => ( ( Y
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ B2 ) )
% 7.75/5.73 => ( P @ X @ Y ) ) )
% 7.75/5.73 => ( P @ X @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % combine_options_cases
% 7.75/5.73 thf(fact_7358_combine__options__cases,axiom,
% 7.75/5.73 ! [X: option_num,P: option_num > option_nat > $o,Y: option_nat] :
% 7.75/5.73 ( ( ( X = none_num )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ( ( Y = none_nat )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ! [A5: num,B2: nat] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( some_num @ A5 ) )
% 7.75/5.73 => ( ( Y
% 7.75/5.73 = ( some_nat @ B2 ) )
% 7.75/5.73 => ( P @ X @ Y ) ) )
% 7.75/5.73 => ( P @ X @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % combine_options_cases
% 7.75/5.73 thf(fact_7359_combine__options__cases,axiom,
% 7.75/5.73 ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 7.75/5.73 ( ( ( X = none_num )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ( ( Y = none_num )
% 7.75/5.73 => ( P @ X @ Y ) )
% 7.75/5.73 => ( ! [A5: num,B2: num] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( some_num @ A5 ) )
% 7.75/5.73 => ( ( Y
% 7.75/5.73 = ( some_num @ B2 ) )
% 7.75/5.73 => ( P @ X @ Y ) ) )
% 7.75/5.73 => ( P @ X @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % combine_options_cases
% 7.75/5.73 thf(fact_7360_split__option__all,axiom,
% 7.75/5.73 ( ( ^ [P6: option4927543243414619207at_nat > $o] :
% 7.75/5.73 ! [X8: option4927543243414619207at_nat] : ( P6 @ X8 ) )
% 7.75/5.73 = ( ^ [P2: option4927543243414619207at_nat > $o] :
% 7.75/5.73 ( ( P2 @ none_P5556105721700978146at_nat )
% 7.75/5.73 & ! [X2: product_prod_nat_nat] : ( P2 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % split_option_all
% 7.75/5.73 thf(fact_7361_split__option__all,axiom,
% 7.75/5.73 ( ( ^ [P6: option_nat > $o] :
% 7.75/5.73 ! [X8: option_nat] : ( P6 @ X8 ) )
% 7.75/5.73 = ( ^ [P2: option_nat > $o] :
% 7.75/5.73 ( ( P2 @ none_nat )
% 7.75/5.73 & ! [X2: nat] : ( P2 @ ( some_nat @ X2 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % split_option_all
% 7.75/5.73 thf(fact_7362_split__option__all,axiom,
% 7.75/5.73 ( ( ^ [P6: option_num > $o] :
% 7.75/5.73 ! [X8: option_num] : ( P6 @ X8 ) )
% 7.75/5.73 = ( ^ [P2: option_num > $o] :
% 7.75/5.73 ( ( P2 @ none_num )
% 7.75/5.73 & ! [X2: num] : ( P2 @ ( some_num @ X2 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % split_option_all
% 7.75/5.73 thf(fact_7363_split__option__ex,axiom,
% 7.75/5.73 ( ( ^ [P6: option4927543243414619207at_nat > $o] :
% 7.75/5.73 ? [X8: option4927543243414619207at_nat] : ( P6 @ X8 ) )
% 7.75/5.73 = ( ^ [P2: option4927543243414619207at_nat > $o] :
% 7.75/5.73 ( ( P2 @ none_P5556105721700978146at_nat )
% 7.75/5.73 | ? [X2: product_prod_nat_nat] : ( P2 @ ( some_P7363390416028606310at_nat @ X2 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % split_option_ex
% 7.75/5.73 thf(fact_7364_split__option__ex,axiom,
% 7.75/5.73 ( ( ^ [P6: option_nat > $o] :
% 7.75/5.73 ? [X8: option_nat] : ( P6 @ X8 ) )
% 7.75/5.73 = ( ^ [P2: option_nat > $o] :
% 7.75/5.73 ( ( P2 @ none_nat )
% 7.75/5.73 | ? [X2: nat] : ( P2 @ ( some_nat @ X2 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % split_option_ex
% 7.75/5.73 thf(fact_7365_split__option__ex,axiom,
% 7.75/5.73 ( ( ^ [P6: option_num > $o] :
% 7.75/5.73 ? [X8: option_num] : ( P6 @ X8 ) )
% 7.75/5.73 = ( ^ [P2: option_num > $o] :
% 7.75/5.73 ( ( P2 @ none_num )
% 7.75/5.73 | ? [X2: num] : ( P2 @ ( some_num @ X2 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % split_option_ex
% 7.75/5.73 thf(fact_7366_option_Oexhaust,axiom,
% 7.75/5.73 ! [Y: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( Y != none_P5556105721700978146at_nat )
% 7.75/5.73 => ~ ! [X23: product_prod_nat_nat] :
% 7.75/5.73 ( Y
% 7.75/5.73 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.exhaust
% 7.75/5.73 thf(fact_7367_option_Oexhaust,axiom,
% 7.75/5.73 ! [Y: option_nat] :
% 7.75/5.73 ( ( Y != none_nat )
% 7.75/5.73 => ~ ! [X23: nat] :
% 7.75/5.73 ( Y
% 7.75/5.73 != ( some_nat @ X23 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.exhaust
% 7.75/5.73 thf(fact_7368_option_Oexhaust,axiom,
% 7.75/5.73 ! [Y: option_num] :
% 7.75/5.73 ( ( Y != none_num )
% 7.75/5.73 => ~ ! [X23: num] :
% 7.75/5.73 ( Y
% 7.75/5.73 != ( some_num @ X23 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.exhaust
% 7.75/5.73 thf(fact_7369_option_OdiscI,axiom,
% 7.75/5.73 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 7.75/5.73 ( ( Option
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ X22 ) )
% 7.75/5.73 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.discI
% 7.75/5.73 thf(fact_7370_option_OdiscI,axiom,
% 7.75/5.73 ! [Option: option_nat,X22: nat] :
% 7.75/5.73 ( ( Option
% 7.75/5.73 = ( some_nat @ X22 ) )
% 7.75/5.73 => ( Option != none_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.discI
% 7.75/5.73 thf(fact_7371_option_OdiscI,axiom,
% 7.75/5.73 ! [Option: option_num,X22: num] :
% 7.75/5.73 ( ( Option
% 7.75/5.73 = ( some_num @ X22 ) )
% 7.75/5.73 => ( Option != none_num ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.discI
% 7.75/5.73 thf(fact_7372_option_Odistinct_I1_J,axiom,
% 7.75/5.73 ! [X22: product_prod_nat_nat] :
% 7.75/5.73 ( none_P5556105721700978146at_nat
% 7.75/5.73 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.distinct(1)
% 7.75/5.73 thf(fact_7373_option_Odistinct_I1_J,axiom,
% 7.75/5.73 ! [X22: nat] :
% 7.75/5.73 ( none_nat
% 7.75/5.73 != ( some_nat @ X22 ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.distinct(1)
% 7.75/5.73 thf(fact_7374_option_Odistinct_I1_J,axiom,
% 7.75/5.73 ! [X22: num] :
% 7.75/5.73 ( none_num
% 7.75/5.73 != ( some_num @ X22 ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.distinct(1)
% 7.75/5.73 thf(fact_7375_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases,axiom,
% 7.75/5.73 ! [X: vEBT_VEBT] :
% 7.75/5.73 ( ! [A5: $o,B2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.73 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.73 => ~ ! [Mi: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.cases
% 7.75/5.73 thf(fact_7376_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X )
% 7.75/5.73 = ( ( X = Mi3 )
% 7.75/5.73 | ( X = Ma ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.membermima.simps(3)
% 7.75/5.73 thf(fact_7377_and__eq__minus__1__iff,axiom,
% 7.75/5.73 ! [A: int,B: int] :
% 7.75/5.73 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 7.75/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.73 = ( ( A
% 7.75/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 7.75/5.73 & ( B
% 7.75/5.73 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_eq_minus_1_iff
% 7.75/5.73 thf(fact_7378_and__eq__minus__1__iff,axiom,
% 7.75/5.73 ! [A: code_integer,B: code_integer] :
% 7.75/5.73 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 7.75/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.73 = ( ( A
% 7.75/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.75/5.73 & ( B
% 7.75/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_eq_minus_1_iff
% 7.75/5.73 thf(fact_7379_AND__upper2_H,axiom,
% 7.75/5.73 ! [Y: int,Z: int,X: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.73 => ( ( ord_less_eq_int @ Y @ Z )
% 7.75/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % AND_upper2'
% 7.75/5.73 thf(fact_7380_AND__upper1_H,axiom,
% 7.75/5.73 ! [Y: int,Z: int,Ya: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.73 => ( ( ord_less_eq_int @ Y @ Z )
% 7.75/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % AND_upper1'
% 7.75/5.73 thf(fact_7381_AND__upper2,axiom,
% 7.75/5.73 ! [Y: int,X: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 7.75/5.73
% 7.75/5.73 % AND_upper2
% 7.75/5.73 thf(fact_7382_AND__upper1,axiom,
% 7.75/5.73 ! [X: int,Y: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % AND_upper1
% 7.75/5.73 thf(fact_7383_AND__lower,axiom,
% 7.75/5.73 ! [X: int,Y: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.75/5.73 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % AND_lower
% 7.75/5.73 thf(fact_7384_real__sgn__eq,axiom,
% 7.75/5.73 ( sgn_sgn_real
% 7.75/5.73 = ( ^ [X2: real] : ( divide_divide_real @ X2 @ ( abs_abs_real @ X2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % real_sgn_eq
% 7.75/5.73 thf(fact_7385_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I5_J,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(5)
% 7.75/5.73 thf(fact_7386_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I5_J,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(5)
% 7.75/5.73 thf(fact_7387_vebt__insert_Osimps_I4_J,axiom,
% 7.75/5.73 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_insert.simps(4)
% 7.75/5.73 thf(fact_7388_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I6_J,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(6)
% 7.75/5.73 thf(fact_7389_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I6_J,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(6)
% 7.75/5.73 thf(fact_7390_less__option__None__is__Some,axiom,
% 7.75/5.73 ! [X: option_nat] :
% 7.75/5.73 ( ( ord_less_option_nat @ none_nat @ X )
% 7.75/5.73 => ? [Z3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( some_nat @ Z3 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_None_is_Some
% 7.75/5.73 thf(fact_7391_less__option__None__is__Some,axiom,
% 7.75/5.73 ! [X: option_num] :
% 7.75/5.73 ( ( ord_less_option_num @ none_num @ X )
% 7.75/5.73 => ? [Z3: num] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( some_num @ Z3 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_None_is_Some
% 7.75/5.73 thf(fact_7392_less__option__None__Some,axiom,
% 7.75/5.73 ! [X: nat] : ( ord_less_option_nat @ none_nat @ ( some_nat @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_None_Some
% 7.75/5.73 thf(fact_7393_less__option__None__Some,axiom,
% 7.75/5.73 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % less_option_None_Some
% 7.75/5.73 thf(fact_7394_height__node,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 7.75/5.73 => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % height_node
% 7.75/5.73 thf(fact_7395_AND__upper2_H_H,axiom,
% 7.75/5.73 ! [Y: int,Z: int,X: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.73 => ( ( ord_less_int @ Y @ Z )
% 7.75/5.73 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % AND_upper2''
% 7.75/5.73 thf(fact_7396_AND__upper1_H_H,axiom,
% 7.75/5.73 ! [Y: int,Z: int,Ya: int] :
% 7.75/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.75/5.73 => ( ( ord_less_int @ Y @ Z )
% 7.75/5.73 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % AND_upper1''
% 7.75/5.73 thf(fact_7397_and__less__eq,axiom,
% 7.75/5.73 ! [L: int,K: int] :
% 7.75/5.73 ( ( ord_less_int @ L @ zero_zero_int )
% 7.75/5.73 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_less_eq
% 7.75/5.73 thf(fact_7398_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,
% 7.75/5.73 ! [X: vEBT_VEBT] :
% 7.75/5.73 ( ( X
% 7.75/5.73 != ( vEBT_Leaf @ $false @ $false ) )
% 7.75/5.73 => ( ! [Uv2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 7.75/5.73 => ( ! [Uu2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 7.75/5.73 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 7.75/5.73 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.cases
% 7.75/5.73 thf(fact_7399_vebt__member_Osimps_I3_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 7.75/5.73 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_member.simps(3)
% 7.75/5.73 thf(fact_7400_even__and__iff,axiom,
% 7.75/5.73 ! [A: int,B: int] :
% 7.75/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 7.75/5.73 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 7.75/5.73 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % even_and_iff
% 7.75/5.73 thf(fact_7401_even__and__iff,axiom,
% 7.75/5.73 ! [A: nat,B: nat] :
% 7.75/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 7.75/5.73 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 7.75/5.73 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % even_and_iff
% 7.75/5.73 thf(fact_7402_even__and__iff,axiom,
% 7.75/5.73 ! [A: code_integer,B: code_integer] :
% 7.75/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 7.75/5.73 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 7.75/5.73 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % even_and_iff
% 7.75/5.73 thf(fact_7403_option_Osize_I4_J,axiom,
% 7.75/5.73 ! [X22: product_prod_nat_nat] :
% 7.75/5.73 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 7.75/5.73 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.size(4)
% 7.75/5.73 thf(fact_7404_option_Osize_I4_J,axiom,
% 7.75/5.73 ! [X22: nat] :
% 7.75/5.73 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 7.75/5.73 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.size(4)
% 7.75/5.73 thf(fact_7405_option_Osize_I4_J,axiom,
% 7.75/5.73 ! [X22: num] :
% 7.75/5.73 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 7.75/5.73 = ( suc @ zero_zero_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.size(4)
% 7.75/5.73 thf(fact_7406_sgn__real__def,axiom,
% 7.75/5.73 ( sgn_sgn_real
% 7.75/5.73 = ( ^ [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 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_real_def
% 7.75/5.73 thf(fact_7407_even__and__iff__int,axiom,
% 7.75/5.73 ! [K: int,L: int] :
% 7.75/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 7.75/5.73 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 7.75/5.73 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % even_and_iff_int
% 7.75/5.73 thf(fact_7408_vebt__member_Osimps_I4_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT,X: nat] :
% 7.75/5.73 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ X ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_member.simps(4)
% 7.75/5.73 thf(fact_7409_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 7.75/5.73 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(5)
% 7.75/5.73 thf(fact_7410_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I5_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 7.75/5.73 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(5)
% 7.75/5.73 thf(fact_7411_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 7.75/5.73 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Ve )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(4)
% 7.75/5.73 thf(fact_7412_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 7.75/5.73 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Ve )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(4)
% 7.75/5.73 thf(fact_7413_one__and__eq,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 7.75/5.73 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % one_and_eq
% 7.75/5.73 thf(fact_7414_one__and__eq,axiom,
% 7.75/5.73 ! [A: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 7.75/5.73 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % one_and_eq
% 7.75/5.73 thf(fact_7415_one__and__eq,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 7.75/5.73 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % one_and_eq
% 7.75/5.73 thf(fact_7416_and__one__eq,axiom,
% 7.75/5.73 ! [A: int] :
% 7.75/5.73 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 7.75/5.73 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_one_eq
% 7.75/5.73 thf(fact_7417_and__one__eq,axiom,
% 7.75/5.73 ! [A: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 7.75/5.73 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_one_eq
% 7.75/5.73 thf(fact_7418_and__one__eq,axiom,
% 7.75/5.73 ! [A: code_integer] :
% 7.75/5.73 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 7.75/5.73 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_one_eq
% 7.75/5.73 thf(fact_7419_sgn__power__injE,axiom,
% 7.75/5.73 ! [A: real,N: nat,X: real,B: real] :
% 7.75/5.73 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 7.75/5.73 = X )
% 7.75/5.73 => ( ( X
% 7.75/5.73 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 7.75/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.73 => ( A = B ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % sgn_power_injE
% 7.75/5.73 thf(fact_7420_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 7.75/5.73 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(6)
% 7.75/5.73 thf(fact_7421_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I6_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 7.75/5.73 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(6)
% 7.75/5.73 thf(fact_7422_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 7.75/5.73 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(5)
% 7.75/5.73 thf(fact_7423_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 7.75/5.73 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(5)
% 7.75/5.73 thf(fact_7424_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,
% 7.75/5.73 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X )
% 7.75/5.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(3)
% 7.75/5.73 thf(fact_7425_and__int__rec,axiom,
% 7.75/5.73 ( bit_se725231765392027082nd_int
% 7.75/5.73 = ( ^ [K3: int,L2: int] :
% 7.75/5.73 ( plus_plus_int
% 7.75/5.73 @ ( zero_n2684676970156552555ol_int
% 7.75/5.73 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 7.75/5.73 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 7.75/5.73 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_int_rec
% 7.75/5.73 thf(fact_7426_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,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ X )
% 7.75/5.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(4)
% 7.75/5.73 thf(fact_7427_invar__vebt_Ointros_I4_J,axiom,
% 7.75/5.73 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi3: nat,Ma: nat] :
% 7.75/5.73 ( ! [X3: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X3 @ N ) )
% 7.75/5.73 => ( ( vEBT_invar_vebt @ Summary @ M )
% 7.75/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.73 => ( ( M = N )
% 7.75/5.73 => ( ( Deg
% 7.75/5.73 = ( plus_plus_nat @ N @ M ) )
% 7.75/5.73 => ( ! [I3: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.73 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X7 ) )
% 7.75/5.73 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 7.75/5.73 => ( ( ( Mi3 = Ma )
% 7.75/5.73 => ! [X3: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.73 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 7.75/5.73 => ( ( ord_less_eq_nat @ Mi3 @ Ma )
% 7.75/5.73 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 7.75/5.73 => ( ( ( Mi3 != Ma )
% 7.75/5.73 => ! [I3: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.73 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 7.75/5.73 = I3 )
% 7.75/5.73 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 7.75/5.73 & ! [X3: nat] :
% 7.75/5.73 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 7.75/5.73 = I3 )
% 7.75/5.73 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 7.75/5.73 => ( ( ord_less_nat @ Mi3 @ X3 )
% 7.75/5.73 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % invar_vebt.intros(4)
% 7.75/5.73 thf(fact_7428_invar__vebt_Ointros_I5_J,axiom,
% 7.75/5.73 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi3: nat,Ma: nat] :
% 7.75/5.73 ( ! [X3: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ X3 @ N ) )
% 7.75/5.73 => ( ( vEBT_invar_vebt @ Summary @ M )
% 7.75/5.73 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 7.75/5.73 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.73 => ( ( M
% 7.75/5.73 = ( suc @ N ) )
% 7.75/5.73 => ( ( Deg
% 7.75/5.73 = ( plus_plus_nat @ N @ M ) )
% 7.75/5.73 => ( ! [I3: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.73 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X7 ) )
% 7.75/5.73 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 7.75/5.73 => ( ( ( Mi3 = Ma )
% 7.75/5.73 => ! [X3: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 7.75/5.73 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 7.75/5.73 => ( ( ord_less_eq_nat @ Mi3 @ Ma )
% 7.75/5.73 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 7.75/5.73 => ( ( ( Mi3 != Ma )
% 7.75/5.73 => ! [I3: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 7.75/5.73 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 7.75/5.73 = I3 )
% 7.75/5.73 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 7.75/5.73 & ! [X3: nat] :
% 7.75/5.73 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 7.75/5.73 = I3 )
% 7.75/5.73 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 7.75/5.73 => ( ( ord_less_nat @ Mi3 @ X3 )
% 7.75/5.73 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 7.75/5.73 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % invar_vebt.intros(5)
% 7.75/5.73 thf(fact_7429_succ__list__to__short,axiom,
% 7.75/5.73 ! [Deg: nat,Mi3: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ( ord_less_eq_nat @ Mi3 @ X )
% 7.75/5.73 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.73 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = none_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % succ_list_to_short
% 7.75/5.73 thf(fact_7430_pred__list__to__short,axiom,
% 7.75/5.73 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi3: nat,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ( ord_less_eq_nat @ X @ Ma )
% 7.75/5.73 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = none_nat ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % pred_list_to_short
% 7.75/5.73 thf(fact_7431_divmod__step__eq,axiom,
% 7.75/5.73 ! [L: num,R2: nat,Q3: nat] :
% 7.75/5.73 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 7.75/5.73 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 7.75/5.73 = ( 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 ) ) ) ) )
% 7.75/5.73 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 7.75/5.73 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 7.75/5.73 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % divmod_step_eq
% 7.75/5.73 thf(fact_7432_divmod__step__eq,axiom,
% 7.75/5.73 ! [L: num,R2: int,Q3: int] :
% 7.75/5.73 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 7.75/5.73 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.75/5.73 = ( 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 ) ) ) ) )
% 7.75/5.73 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 7.75/5.73 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.75/5.73 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % divmod_step_eq
% 7.75/5.73 thf(fact_7433_divmod__step__eq,axiom,
% 7.75/5.73 ! [L: num,R2: code_integer,Q3: code_integer] :
% 7.75/5.73 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 7.75/5.73 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 7.75/5.73 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 7.75/5.73 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 7.75/5.73 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 7.75/5.73 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % divmod_step_eq
% 7.75/5.73 thf(fact_7434_geqmaxNone,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 7.75/5.73 => ( ( ord_less_eq_nat @ Ma @ X )
% 7.75/5.73 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = none_nat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % geqmaxNone
% 7.75/5.73 thf(fact_7435_del__single__cont,axiom,
% 7.75/5.73 ! [X: nat,Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( ( X = Mi3 )
% 7.75/5.73 & ( X = Ma ) )
% 7.75/5.73 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % del_single_cont
% 7.75/5.73 thf(fact_7436_power__shift,axiom,
% 7.75/5.73 ! [X: nat,Y: nat,Z: nat] :
% 7.75/5.73 ( ( ( power_power_nat @ X @ Y )
% 7.75/5.73 = Z )
% 7.75/5.73 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 7.75/5.73 = ( some_nat @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % power_shift
% 7.75/5.73 thf(fact_7437_delete__pres__valid,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X ) @ N ) ) ).
% 7.75/5.73
% 7.75/5.73 % delete_pres_valid
% 7.75/5.73 thf(fact_7438_dele__bmo__cont__corr,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 7.75/5.73 = ( ( X != Y )
% 7.75/5.73 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % dele_bmo_cont_corr
% 7.75/5.73 thf(fact_7439_dele__member__cont__corr,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 7.75/5.73 = ( ( X != Y )
% 7.75/5.73 & ( vEBT_vebt_member @ T @ Y ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % dele_member_cont_corr
% 7.75/5.73 thf(fact_7440_pred__corr,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_pred @ T @ X )
% 7.75/5.73 = ( some_nat @ Px ) )
% 7.75/5.73 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % pred_corr
% 7.75/5.73 thf(fact_7441_succ__corr,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_succ @ T @ X )
% 7.75/5.73 = ( some_nat @ Sx ) )
% 7.75/5.73 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % succ_corr
% 7.75/5.73 thf(fact_7442_pred__correct,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_pred @ T @ X )
% 7.75/5.73 = ( some_nat @ Sx ) )
% 7.75/5.73 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % pred_correct
% 7.75/5.73 thf(fact_7443_succ__correct,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_succ @ T @ X )
% 7.75/5.73 = ( some_nat @ Sx ) )
% 7.75/5.73 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % succ_correct
% 7.75/5.73 thf(fact_7444_helpyd,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_succ @ T @ X )
% 7.75/5.73 = ( some_nat @ Y ) )
% 7.75/5.73 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % helpyd
% 7.75/5.73 thf(fact_7445_helpypredd,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_pred @ T @ X )
% 7.75/5.73 = ( some_nat @ Y ) )
% 7.75/5.73 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % helpypredd
% 7.75/5.73 thf(fact_7446_delt__out__of__range,axiom,
% 7.75/5.73 ! [X: nat,Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.73 | ( ord_less_nat @ Ma @ X ) )
% 7.75/5.73 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % delt_out_of_range
% 7.75/5.73 thf(fact_7447_succ__min,axiom,
% 7.75/5.73 ! [Deg: nat,X: nat,Mi3: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.73 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = ( some_nat @ Mi3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % succ_min
% 7.75/5.73 thf(fact_7448_pred__max,axiom,
% 7.75/5.73 ! [Deg: nat,Ma: nat,X: nat,Mi3: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ( ord_less_nat @ Ma @ X )
% 7.75/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = ( some_nat @ Ma ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % pred_max
% 7.75/5.73 thf(fact_7449_lesseq__shift,axiom,
% 7.75/5.73 ( ord_less_eq_nat
% 7.75/5.73 = ( ^ [X2: nat,Y6: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X2 ) @ ( some_nat @ Y6 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % lesseq_shift
% 7.75/5.73 thf(fact_7450_and__nat__numerals_I3_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % and_nat_numerals(3)
% 7.75/5.73 thf(fact_7451_and__nat__numerals_I1_J,axiom,
% 7.75/5.73 ! [Y: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 7.75/5.73 = zero_zero_nat ) ).
% 7.75/5.73
% 7.75/5.73 % and_nat_numerals(1)
% 7.75/5.73 thf(fact_7452_and__nat__numerals_I2_J,axiom,
% 7.75/5.73 ! [Y: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % and_nat_numerals(2)
% 7.75/5.73 thf(fact_7453_and__nat__numerals_I4_J,axiom,
% 7.75/5.73 ! [X: num] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = one_one_nat ) ).
% 7.75/5.73
% 7.75/5.73 % and_nat_numerals(4)
% 7.75/5.73 thf(fact_7454_Suc__0__and__eq,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.75/5.73 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % Suc_0_and_eq
% 7.75/5.73 thf(fact_7455_and__Suc__0__eq,axiom,
% 7.75/5.73 ! [N: nat] :
% 7.75/5.73 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_Suc_0_eq
% 7.75/5.73 thf(fact_7456_vebt__pred_Osimps_I2_J,axiom,
% 7.75/5.73 ! [A: $o,Uw: $o] :
% 7.75/5.73 ( ( A
% 7.75/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.73 & ( ~ A
% 7.75/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = none_nat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_pred.simps(2)
% 7.75/5.73 thf(fact_7457_vebt__succ_Osimps_I1_J,axiom,
% 7.75/5.73 ! [B: $o,Uu: $o] :
% 7.75/5.73 ( ( B
% 7.75/5.73 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 7.75/5.73 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.73 & ( ~ B
% 7.75/5.73 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 7.75/5.73 = none_nat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_succ.simps(1)
% 7.75/5.73 thf(fact_7458_vebt__pred_Osimps_I3_J,axiom,
% 7.75/5.73 ! [B: $o,A: $o,Va2: nat] :
% 7.75/5.73 ( ( B
% 7.75/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.73 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.73 & ( ~ B
% 7.75/5.73 => ( ( A
% 7.75/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.73 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.73 & ( ~ A
% 7.75/5.73 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.73 = none_nat ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_pred.simps(3)
% 7.75/5.73 thf(fact_7459_VEBT__internal_Ovalid_H_Ocases,axiom,
% 7.75/5.73 ! [X: produc9072475918466114483BT_nat] :
% 7.75/5.73 ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 7.75/5.73 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.valid'.cases
% 7.75/5.73 thf(fact_7460_vebt__succ_Osimps_I2_J,axiom,
% 7.75/5.73 ! [Uv: $o,Uw: $o,N: nat] :
% 7.75/5.73 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_succ.simps(2)
% 7.75/5.73 thf(fact_7461_vebt__pred_Osimps_I1_J,axiom,
% 7.75/5.73 ! [Uu: $o,Uv: $o] :
% 7.75/5.73 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_pred.simps(1)
% 7.75/5.73 thf(fact_7462_vebt__succ_Osimps_I3_J,axiom,
% 7.75/5.73 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 7.75/5.73 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va2 )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_succ.simps(3)
% 7.75/5.73 thf(fact_7463_vebt__pred_Osimps_I4_J,axiom,
% 7.75/5.73 ! [Uy: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 7.75/5.73 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va2 ) @ Vb )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_pred.simps(4)
% 7.75/5.73 thf(fact_7464_and__nat__def,axiom,
% 7.75/5.73 ( bit_se727722235901077358nd_nat
% 7.75/5.73 = ( ^ [M4: nat,N3: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_nat_def
% 7.75/5.73 thf(fact_7465_xor__num_Ocases,axiom,
% 7.75/5.73 ! [X: product_prod_num_num] :
% 7.75/5.73 ( ( X
% 7.75/5.73 != ( product_Pair_num_num @ one @ one ) )
% 7.75/5.73 => ( ! [N2: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) )
% 7.75/5.73 => ( ! [N2: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) )
% 7.75/5.73 => ( ! [M2: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( product_Pair_num_num @ ( bit0 @ M2 ) @ one ) )
% 7.75/5.73 => ( ! [M2: num,N2: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( product_Pair_num_num @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) ) )
% 7.75/5.73 => ( ! [M2: num,N2: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( product_Pair_num_num @ ( bit0 @ M2 ) @ ( bit1 @ N2 ) ) )
% 7.75/5.73 => ( ! [M2: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( product_Pair_num_num @ ( bit1 @ M2 ) @ one ) )
% 7.75/5.73 => ( ! [M2: num,N2: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( product_Pair_num_num @ ( bit1 @ M2 ) @ ( bit0 @ N2 ) ) )
% 7.75/5.73 => ~ ! [M2: num,N2: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( product_Pair_num_num @ ( bit1 @ M2 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % xor_num.cases
% 7.75/5.73 thf(fact_7466_vebt__pred_Osimps_I5_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 7.75/5.73 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_pred.simps(5)
% 7.75/5.73 thf(fact_7467_vebt__succ_Osimps_I4_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 7.75/5.73 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Ve )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_succ.simps(4)
% 7.75/5.73 thf(fact_7468_VEBT__internal_Onaive__member_Ocases,axiom,
% 7.75/5.73 ! [X: produc9072475918466114483BT_nat] :
% 7.75/5.73 ( ! [A5: $o,B2: $o,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ X3 ) )
% 7.75/5.73 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 7.75/5.73 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) @ X3 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.naive_member.cases
% 7.75/5.73 thf(fact_7469_vebt__succ_Osimps_I5_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 7.75/5.73 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_succ.simps(5)
% 7.75/5.73 thf(fact_7470_vebt__pred_Osimps_I6_J,axiom,
% 7.75/5.73 ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 7.75/5.73 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_pred.simps(6)
% 7.75/5.73 thf(fact_7471_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Ocases,axiom,
% 7.75/5.73 ! [X: produc9072475918466114483BT_nat] :
% 7.75/5.73 ( ! [A5: $o,B2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ zero_zero_nat ) )
% 7.75/5.73 => ( ! [A5: $o,B2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ zero_zero_nat ) ) )
% 7.75/5.73 => ( ! [A5: $o,B2: $o,N2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ ( suc @ N2 ) ) ) )
% 7.75/5.73 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Uu2 ) )
% 7.75/5.73 => ( ! [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ X3 ) )
% 7.75/5.73 => ( ! [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 7.75/5.73 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.cases
% 7.75/5.73 thf(fact_7472_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Ocases,axiom,
% 7.75/5.73 ! [X: produc9072475918466114483BT_nat] :
% 7.75/5.73 ( ! [Uu2: $o,Uv2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 7.75/5.73 => ( ! [A5: $o,Uw2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 7.75/5.73 => ( ! [A5: $o,B2: $o,Va: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ ( suc @ Va ) ) ) )
% 7.75/5.73 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 7.75/5.73 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 7.75/5.73 => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 7.75/5.73 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.cases
% 7.75/5.73 thf(fact_7473_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases,axiom,
% 7.75/5.73 ! [X: produc9072475918466114483BT_nat] :
% 7.75/5.73 ( ! [Uu2: $o,B2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) )
% 7.75/5.73 => ( ! [Uv2: $o,Uw2: $o,N2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) )
% 7.75/5.73 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 7.75/5.73 => ( ! [V3: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 ) )
% 7.75/5.73 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 7.75/5.73 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.cases
% 7.75/5.73 thf(fact_7474_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,
% 7.75/5.73 ! [X: produc9072475918466114483BT_nat] :
% 7.75/5.73 ( ! [A5: $o,B2: $o,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ X3 ) )
% 7.75/5.73 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ X3 ) )
% 7.75/5.73 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X3 ) )
% 7.75/5.73 => ( ! [V3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 7.75/5.73 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.cases
% 7.75/5.73 thf(fact_7475_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,
% 7.75/5.73 ! [X: produc9072475918466114483BT_nat] :
% 7.75/5.73 ( ! [A5: $o,B2: $o,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ X3 ) )
% 7.75/5.73 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X3 ) )
% 7.75/5.73 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X3 ) )
% 7.75/5.73 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ X3 ) )
% 7.75/5.73 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.cases
% 7.75/5.73 thf(fact_7476_VEBT__internal_Omembermima_Ocases,axiom,
% 7.75/5.73 ! [X: produc9072475918466114483BT_nat] :
% 7.75/5.73 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 7.75/5.73 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 7.75/5.73 => ( ! [Mi: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X3 ) )
% 7.75/5.73 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) @ X3 ) )
% 7.75/5.73 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) @ X3 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.membermima.cases
% 7.75/5.73 thf(fact_7477_and__nat__unfold,axiom,
% 7.75/5.73 ( bit_se727722235901077358nd_nat
% 7.75/5.73 = ( ^ [M4: nat,N3: nat] :
% 7.75/5.73 ( if_nat
% 7.75/5.73 @ ( ( M4 = zero_zero_nat )
% 7.75/5.73 | ( N3 = zero_zero_nat ) )
% 7.75/5.73 @ zero_zero_nat
% 7.75/5.73 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M4 @ ( 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 @ M4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_nat_unfold
% 7.75/5.73 thf(fact_7478_and__nat__rec,axiom,
% 7.75/5.73 ( bit_se727722235901077358nd_nat
% 7.75/5.73 = ( ^ [M4: nat,N3: nat] :
% 7.75/5.73 ( plus_plus_nat
% 7.75/5.73 @ ( zero_n2687167440665602831ol_nat
% 7.75/5.73 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 )
% 7.75/5.73 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 7.75/5.73 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % and_nat_rec
% 7.75/5.73 thf(fact_7479_minNull__delete__time__bound,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) )
% 7.75/5.73 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % minNull_delete_time_bound
% 7.75/5.73 thf(fact_7480_mintlistlength,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 7.75/5.73 => ( ( Mi3 != Ma )
% 7.75/5.73 => ( ( ord_less_nat @ Mi3 @ Ma )
% 7.75/5.73 & ? [M2: nat] :
% 7.75/5.73 ( ( ( some_nat @ M2 )
% 7.75/5.73 = ( vEBT_vebt_mint @ Summary ) )
% 7.75/5.73 & ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mintlistlength
% 7.75/5.73 thf(fact_7481_vebt__delete_Osimps_I6_J,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X )
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_delete.simps(6)
% 7.75/5.73 thf(fact_7482_vebt__delete_Osimps_I5_J,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X )
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_delete.simps(5)
% 7.75/5.73 thf(fact_7483_not__min__Null__member,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT] :
% 7.75/5.73 ( ~ ( vEBT_VEBT_minNull @ T )
% 7.75/5.73 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 7.75/5.73
% 7.75/5.73 % not_min_Null_member
% 7.75/5.73 thf(fact_7484_min__Null__member,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( vEBT_VEBT_minNull @ T )
% 7.75/5.73 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % min_Null_member
% 7.75/5.73 thf(fact_7485_minNullmin,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT] :
% 7.75/5.73 ( ( vEBT_VEBT_minNull @ T )
% 7.75/5.73 => ( ( vEBT_vebt_mint @ T )
% 7.75/5.73 = none_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % minNullmin
% 7.75/5.73 thf(fact_7486_minminNull,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT] :
% 7.75/5.73 ( ( ( vEBT_vebt_mint @ T )
% 7.75/5.73 = none_nat )
% 7.75/5.73 => ( vEBT_VEBT_minNull @ T ) ) ).
% 7.75/5.73
% 7.75/5.73 % minminNull
% 7.75/5.73 thf(fact_7487_mint__member,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_mint @ T )
% 7.75/5.73 = ( some_nat @ Maxi ) )
% 7.75/5.73 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mint_member
% 7.75/5.73 thf(fact_7488_mint__corr__help,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_mint @ T )
% 7.75/5.73 = ( some_nat @ Mini ) )
% 7.75/5.73 => ( ( vEBT_vebt_member @ T @ X )
% 7.75/5.73 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mint_corr_help
% 7.75/5.73 thf(fact_7489_mint__sound,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 7.75/5.73 => ( ( vEBT_vebt_mint @ T )
% 7.75/5.73 = ( some_nat @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mint_sound
% 7.75/5.73 thf(fact_7490_mint__corr,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_mint @ T )
% 7.75/5.73 = ( some_nat @ X ) )
% 7.75/5.73 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mint_corr
% 7.75/5.73 thf(fact_7491_minNull__delete__time__bound_H,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) )
% 7.75/5.73 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ T @ X ) @ one_one_nat ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % minNull_delete_time_bound'
% 7.75/5.73 thf(fact_7492_misiz,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( some_nat @ M )
% 7.75/5.73 = ( vEBT_vebt_mint @ T ) )
% 7.75/5.73 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % misiz
% 7.75/5.73 thf(fact_7493_local_Opower__def,axiom,
% 7.75/5.73 ( vEBT_VEBT_power
% 7.75/5.73 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % local.power_def
% 7.75/5.73 thf(fact_7494_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 7.75/5.73 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.minNull.simps(4)
% 7.75/5.73 thf(fact_7495_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 7.75/5.73 ! [X: vEBT_VEBT] :
% 7.75/5.73 ( ( vEBT_VEBT_minNull @ X )
% 7.75/5.73 => ( ( X
% 7.75/5.73 != ( vEBT_Leaf @ $false @ $false ) )
% 7.75/5.73 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.minNull.elims(2)
% 7.75/5.73 thf(fact_7496_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 7.75/5.73 ! [X: vEBT_VEBT,Y: $o] :
% 7.75/5.73 ( ( ( vEBT_VEBT_minNull @ X )
% 7.75/5.73 = Y )
% 7.75/5.73 => ( ( ( X
% 7.75/5.73 = ( vEBT_Leaf @ $false @ $false ) )
% 7.75/5.73 => ~ Y )
% 7.75/5.73 => ( ( ? [Uv2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 7.75/5.73 => Y )
% 7.75/5.73 => ( ( ? [Uu2: $o] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 7.75/5.73 => Y )
% 7.75/5.73 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 7.75/5.73 => ~ Y )
% 7.75/5.73 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc ) )
% 7.75/5.73 => Y ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.minNull.elims(1)
% 7.75/5.73 thf(fact_7497_insertsimp,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( vEBT_VEBT_minNull @ T )
% 7.75/5.73 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % insertsimp
% 7.75/5.73 thf(fact_7498_vebt__delete_Osimps_I3_J,axiom,
% 7.75/5.73 ! [A: $o,B: $o,N: nat] :
% 7.75/5.73 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 7.75/5.73 = ( vEBT_Leaf @ A @ B ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_delete.simps(3)
% 7.75/5.73 thf(fact_7499_vebt__delete_Osimps_I1_J,axiom,
% 7.75/5.73 ! [A: $o,B: $o] :
% 7.75/5.73 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 7.75/5.73 = ( vEBT_Leaf @ $false @ B ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_delete.simps(1)
% 7.75/5.73 thf(fact_7500_vebt__delete_Osimps_I4_J,axiom,
% 7.75/5.73 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 7.75/5.73 ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu )
% 7.75/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_delete.simps(4)
% 7.75/5.73 thf(fact_7501_vebt__delete_Osimps_I2_J,axiom,
% 7.75/5.73 ! [A: $o,B: $o] :
% 7.75/5.73 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 7.75/5.73 = ( vEBT_Leaf @ A @ $false ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_delete.simps(2)
% 7.75/5.73 thf(fact_7502_nested__mint,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va2: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 7.75/5.73 => ( ( N
% 7.75/5.73 = ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.73 => ( ~ ( ord_less_nat @ Ma @ Mi3 )
% 7.75/5.73 => ( ( Ma != Mi3 )
% 7.75/5.73 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nested_mint
% 7.75/5.73 thf(fact_7503_vebt__mint_Oelims,axiom,
% 7.75/5.73 ! [X: vEBT_VEBT,Y: option_nat] :
% 7.75/5.73 ( ( ( vEBT_vebt_mint @ X )
% 7.75/5.73 = Y )
% 7.75/5.73 => ( ! [A5: $o,B2: $o] :
% 7.75/5.73 ( ( X
% 7.75/5.73 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.73 => ~ ( ( A5
% 7.75/5.73 => ( Y
% 7.75/5.73 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.73 & ( ~ A5
% 7.75/5.73 => ( ( B2
% 7.75/5.73 => ( Y
% 7.75/5.73 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.73 & ( ~ B2
% 7.75/5.73 => ( Y = none_nat ) ) ) ) ) )
% 7.75/5.73 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.73 => ( Y != none_nat ) )
% 7.75/5.73 => ~ ! [Mi: nat] :
% 7.75/5.73 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.73 ( X
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.73 => ( Y
% 7.75/5.73 != ( some_nat @ Mi ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_mint.elims
% 7.75/5.73 thf(fact_7504_vebt__mint_Osimps_I1_J,axiom,
% 7.75/5.73 ! [A: $o,B: $o] :
% 7.75/5.73 ( ( A
% 7.75/5.73 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.73 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.73 & ( ~ A
% 7.75/5.73 => ( ( B
% 7.75/5.73 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.73 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.73 & ( ~ B
% 7.75/5.73 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.73 = none_nat ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_mint.simps(1)
% 7.75/5.73 thf(fact_7505_greater__shift,axiom,
% 7.75/5.73 ( ord_less_nat
% 7.75/5.73 = ( ^ [Y6: nat,X2: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X2 ) @ ( some_nat @ Y6 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % greater_shift
% 7.75/5.73 thf(fact_7506_option_Ocollapse,axiom,
% 7.75/5.73 ! [Option: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( Option != none_P5556105721700978146at_nat )
% 7.75/5.73 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 7.75/5.73 = Option ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.collapse
% 7.75/5.73 thf(fact_7507_option_Ocollapse,axiom,
% 7.75/5.73 ! [Option: option_nat] :
% 7.75/5.73 ( ( Option != none_nat )
% 7.75/5.73 => ( ( some_nat @ ( the_nat @ Option ) )
% 7.75/5.73 = Option ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.collapse
% 7.75/5.73 thf(fact_7508_option_Ocollapse,axiom,
% 7.75/5.73 ! [Option: option_num] :
% 7.75/5.73 ( ( Option != none_num )
% 7.75/5.73 => ( ( some_num @ ( the_num @ Option ) )
% 7.75/5.73 = Option ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.collapse
% 7.75/5.73 thf(fact_7509_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 7.75/5.73 ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 7.75/5.73 = none_P5556105721700978146at_nat ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.simps(1)
% 7.75/5.73 thf(fact_7510_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 7.75/5.73 ! [Uu: num > num > num,Uv: option_num] :
% 7.75/5.73 ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 7.75/5.73 = none_num ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.simps(1)
% 7.75/5.73 thf(fact_7511_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 7.75/5.73 ! [Uu: nat > nat > nat,Uv: option_nat] :
% 7.75/5.73 ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.simps(1)
% 7.75/5.73 thf(fact_7512_option_Oexpand,axiom,
% 7.75/5.73 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( ( Option = none_P5556105721700978146at_nat )
% 7.75/5.73 = ( Option2 = none_P5556105721700978146at_nat ) )
% 7.75/5.73 => ( ( ( Option != none_P5556105721700978146at_nat )
% 7.75/5.73 => ( ( Option2 != none_P5556105721700978146at_nat )
% 7.75/5.73 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 7.75/5.73 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 7.75/5.73 => ( Option = Option2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.expand
% 7.75/5.73 thf(fact_7513_option_Oexpand,axiom,
% 7.75/5.73 ! [Option: option_nat,Option2: option_nat] :
% 7.75/5.73 ( ( ( Option = none_nat )
% 7.75/5.73 = ( Option2 = none_nat ) )
% 7.75/5.73 => ( ( ( Option != none_nat )
% 7.75/5.73 => ( ( Option2 != none_nat )
% 7.75/5.73 => ( ( the_nat @ Option )
% 7.75/5.73 = ( the_nat @ Option2 ) ) ) )
% 7.75/5.73 => ( Option = Option2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.expand
% 7.75/5.73 thf(fact_7514_option_Oexpand,axiom,
% 7.75/5.73 ! [Option: option_num,Option2: option_num] :
% 7.75/5.73 ( ( ( Option = none_num )
% 7.75/5.73 = ( Option2 = none_num ) )
% 7.75/5.73 => ( ( ( Option != none_num )
% 7.75/5.73 => ( ( Option2 != none_num )
% 7.75/5.73 => ( ( the_num @ Option )
% 7.75/5.73 = ( the_num @ Option2 ) ) ) )
% 7.75/5.73 => ( Option = Option2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.expand
% 7.75/5.73 thf(fact_7515_option_Oexhaust__sel,axiom,
% 7.75/5.73 ! [Option: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( Option != none_P5556105721700978146at_nat )
% 7.75/5.73 => ( Option
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.exhaust_sel
% 7.75/5.73 thf(fact_7516_option_Oexhaust__sel,axiom,
% 7.75/5.73 ! [Option: option_nat] :
% 7.75/5.73 ( ( Option != none_nat )
% 7.75/5.73 => ( Option
% 7.75/5.73 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.exhaust_sel
% 7.75/5.73 thf(fact_7517_option_Oexhaust__sel,axiom,
% 7.75/5.73 ! [Option: option_num] :
% 7.75/5.73 ( ( Option != none_num )
% 7.75/5.73 => ( Option
% 7.75/5.73 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % option.exhaust_sel
% 7.75/5.73 thf(fact_7518_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 7.75/5.73 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 7.75/5.73 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 7.75/5.73 = none_P5556105721700978146at_nat ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.simps(2)
% 7.75/5.73 thf(fact_7519_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 7.75/5.73 ! [Uw: num > num > num,V: num] :
% 7.75/5.73 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 7.75/5.73 = none_num ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.simps(2)
% 7.75/5.73 thf(fact_7520_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 7.75/5.73 ! [Uw: nat > nat > nat,V: nat] :
% 7.75/5.73 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.simps(2)
% 7.75/5.73 thf(fact_7521_VEBT__internal_Ooption__shift_Oelims,axiom,
% 7.75/5.73 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa3: option4927543243414619207at_nat,Xb3: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 7.75/5.73 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa3 @ Xb3 )
% 7.75/5.73 = Y )
% 7.75/5.73 => ( ( ( Xa3 = none_P5556105721700978146at_nat )
% 7.75/5.73 => ( Y != none_P5556105721700978146at_nat ) )
% 7.75/5.73 => ( ( ? [V3: product_prod_nat_nat] :
% 7.75/5.73 ( Xa3
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ V3 ) )
% 7.75/5.73 => ( ( Xb3 = none_P5556105721700978146at_nat )
% 7.75/5.73 => ( Y != none_P5556105721700978146at_nat ) ) )
% 7.75/5.73 => ~ ! [A5: product_prod_nat_nat] :
% 7.75/5.73 ( ( Xa3
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ A5 ) )
% 7.75/5.73 => ! [B2: product_prod_nat_nat] :
% 7.75/5.73 ( ( Xb3
% 7.75/5.73 = ( some_P7363390416028606310at_nat @ B2 ) )
% 7.75/5.73 => ( Y
% 7.75/5.73 != ( some_P7363390416028606310at_nat @ ( X @ A5 @ B2 ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.elims
% 7.75/5.73 thf(fact_7522_VEBT__internal_Ooption__shift_Oelims,axiom,
% 7.75/5.73 ! [X: num > num > num,Xa3: option_num,Xb3: option_num,Y: option_num] :
% 7.75/5.73 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa3 @ Xb3 )
% 7.75/5.73 = Y )
% 7.75/5.73 => ( ( ( Xa3 = none_num )
% 7.75/5.73 => ( Y != none_num ) )
% 7.75/5.73 => ( ( ? [V3: num] :
% 7.75/5.73 ( Xa3
% 7.75/5.73 = ( some_num @ V3 ) )
% 7.75/5.73 => ( ( Xb3 = none_num )
% 7.75/5.73 => ( Y != none_num ) ) )
% 7.75/5.73 => ~ ! [A5: num] :
% 7.75/5.73 ( ( Xa3
% 7.75/5.73 = ( some_num @ A5 ) )
% 7.75/5.73 => ! [B2: num] :
% 7.75/5.73 ( ( Xb3
% 7.75/5.73 = ( some_num @ B2 ) )
% 7.75/5.73 => ( Y
% 7.75/5.73 != ( some_num @ ( X @ A5 @ B2 ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.elims
% 7.75/5.73 thf(fact_7523_VEBT__internal_Ooption__shift_Oelims,axiom,
% 7.75/5.73 ! [X: nat > nat > nat,Xa3: option_nat,Xb3: option_nat,Y: option_nat] :
% 7.75/5.73 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa3 @ Xb3 )
% 7.75/5.73 = Y )
% 7.75/5.73 => ( ( ( Xa3 = none_nat )
% 7.75/5.73 => ( Y != none_nat ) )
% 7.75/5.73 => ( ( ? [V3: nat] :
% 7.75/5.73 ( Xa3
% 7.75/5.73 = ( some_nat @ V3 ) )
% 7.75/5.73 => ( ( Xb3 = none_nat )
% 7.75/5.73 => ( Y != none_nat ) ) )
% 7.75/5.73 => ~ ! [A5: nat] :
% 7.75/5.73 ( ( Xa3
% 7.75/5.73 = ( some_nat @ A5 ) )
% 7.75/5.73 => ! [B2: nat] :
% 7.75/5.73 ( ( Xb3
% 7.75/5.73 = ( some_nat @ B2 ) )
% 7.75/5.73 => ( Y
% 7.75/5.73 != ( some_nat @ ( X @ A5 @ B2 ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.elims
% 7.75/5.73 thf(fact_7524_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 7.75/5.73 ! [X: produc5491161045314408544at_nat] :
% 7.75/5.73 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 7.75/5.73 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V3: product_prod_nat_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V3 ) @ none_P5556105721700978146at_nat ) ) )
% 7.75/5.73 => ~ ! [F4: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc3994169339658061776at_nat @ F4 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_comp_shift.cases
% 7.75/5.73 thf(fact_7525_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 7.75/5.73 ! [X: produc2233624965454879586on_nat] :
% 7.75/5.73 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 7.75/5.73 => ( ! [Uw2: nat > nat > $o,V3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V3 ) @ none_nat ) ) )
% 7.75/5.73 => ~ ! [F4: nat > nat > $o,X3: nat,Y3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc4035269172776083154on_nat @ F4 @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_comp_shift.cases
% 7.75/5.73 thf(fact_7526_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 7.75/5.73 ! [X: produc7036089656553540234on_num] :
% 7.75/5.73 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 7.75/5.73 => ( ! [Uw2: num > num > $o,V3: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V3 ) @ none_num ) ) )
% 7.75/5.73 => ~ ! [F4: num > num > $o,X3: num,Y3: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc3576312749637752826on_num @ F4 @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_comp_shift.cases
% 7.75/5.73 thf(fact_7527_VEBT__internal_Ooption__shift_Ocases,axiom,
% 7.75/5.73 ! [X: produc5542196010084753463at_nat] :
% 7.75/5.73 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 7.75/5.73 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V3: product_prod_nat_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V3 ) @ none_P5556105721700978146at_nat ) ) )
% 7.75/5.73 => ~ ! [F4: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A5: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc2899441246263362727at_nat @ F4 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A5 ) @ ( some_P7363390416028606310at_nat @ B2 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.cases
% 7.75/5.73 thf(fact_7528_VEBT__internal_Ooption__shift_Ocases,axiom,
% 7.75/5.73 ! [X: produc8306885398267862888on_nat] :
% 7.75/5.73 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 7.75/5.73 => ( ! [Uw2: nat > nat > nat,V3: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V3 ) @ none_nat ) ) )
% 7.75/5.73 => ~ ! [F4: nat > nat > nat,A5: nat,B2: nat] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc8929957630744042906on_nat @ F4 @ ( produc5098337634421038937on_nat @ ( some_nat @ A5 ) @ ( some_nat @ B2 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.cases
% 7.75/5.73 thf(fact_7529_VEBT__internal_Ooption__shift_Ocases,axiom,
% 7.75/5.73 ! [X: produc1193250871479095198on_num] :
% 7.75/5.73 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 7.75/5.73 => ( ! [Uw2: num > num > num,V3: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V3 ) @ none_num ) ) )
% 7.75/5.73 => ~ ! [F4: num > num > num,A5: num,B2: num] :
% 7.75/5.73 ( X
% 7.75/5.73 != ( produc5778274026573060048on_num @ F4 @ ( produc8585076106096196333on_num @ ( some_num @ A5 ) @ ( some_num @ B2 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % VEBT_internal.option_shift.cases
% 7.75/5.73 thf(fact_7530_vebt__mint_Osimps_I2_J,axiom,
% 7.75/5.73 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 7.75/5.73 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 7.75/5.73 = none_nat ) ).
% 7.75/5.73
% 7.75/5.73 % vebt_mint.simps(2)
% 7.75/5.73 thf(fact_7531_summaxma,axiom,
% 7.75/5.73 ! [Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 7.75/5.73 => ( ( Mi3 != Ma )
% 7.75/5.73 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 7.75/5.73 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % summaxma
% 7.75/5.73 thf(fact_7532_mul__def,axiom,
% 7.75/5.73 ( vEBT_VEBT_mul
% 7.75/5.73 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % mul_def
% 7.75/5.73 thf(fact_7533_add__def,axiom,
% 7.75/5.73 ( vEBT_VEBT_add
% 7.75/5.73 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 7.75/5.73
% 7.75/5.73 % add_def
% 7.75/5.73 thf(fact_7534_mul__shift,axiom,
% 7.75/5.73 ! [X: nat,Y: nat,Z: nat] :
% 7.75/5.73 ( ( ( times_times_nat @ X @ Y )
% 7.75/5.73 = Z )
% 7.75/5.73 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 7.75/5.73 = ( some_nat @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % mul_shift
% 7.75/5.73 thf(fact_7535_maxbmo,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,X: nat] :
% 7.75/5.73 ( ( ( vEBT_vebt_maxt @ T )
% 7.75/5.73 = ( some_nat @ X ) )
% 7.75/5.73 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 7.75/5.73
% 7.75/5.73 % maxbmo
% 7.75/5.73 thf(fact_7536_add__shift,axiom,
% 7.75/5.73 ! [X: nat,Y: nat,Z: nat] :
% 7.75/5.73 ( ( ( plus_plus_nat @ X @ Y )
% 7.75/5.73 = Z )
% 7.75/5.73 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 7.75/5.73 = ( some_nat @ Z ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % add_shift
% 7.75/5.73 thf(fact_7537_maxt__member,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_maxt @ T )
% 7.75/5.73 = ( some_nat @ Maxi ) )
% 7.75/5.73 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % maxt_member
% 7.75/5.73 thf(fact_7538_list__update__overwrite,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 7.75/5.73 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ I @ Y )
% 7.75/5.73 = ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ Y ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_overwrite
% 7.75/5.73 thf(fact_7539_list__update__overwrite,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi,Y: vEBT_VEBTi] :
% 7.75/5.73 ( ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X ) @ I @ Y )
% 7.75/5.73 = ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ Y ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_overwrite
% 7.75/5.73 thf(fact_7540_maxt__corr__help,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_maxt @ T )
% 7.75/5.73 = ( some_nat @ Maxi ) )
% 7.75/5.73 => ( ( vEBT_vebt_member @ T @ X )
% 7.75/5.73 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % maxt_corr_help
% 7.75/5.73 thf(fact_7541_maxt__sound,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 7.75/5.73 => ( ( vEBT_vebt_maxt @ T )
% 7.75/5.73 = ( some_nat @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % maxt_sound
% 7.75/5.73 thf(fact_7542_maxt__corr,axiom,
% 7.75/5.73 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.73 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.73 => ( ( ( vEBT_vebt_maxt @ T )
% 7.75/5.73 = ( some_nat @ X ) )
% 7.75/5.73 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % maxt_corr
% 7.75/5.73 thf(fact_7543_length__list__update,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 7.75/5.73 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) )
% 7.75/5.73 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % length_list_update
% 7.75/5.73 thf(fact_7544_length__list__update,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] :
% 7.75/5.73 ( ( size_s7982070591426661849_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X ) )
% 7.75/5.73 = ( size_s7982070591426661849_VEBTi @ Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % length_list_update
% 7.75/5.73 thf(fact_7545_length__list__update,axiom,
% 7.75/5.73 ! [Xs2: list_real,I: nat,X: real] :
% 7.75/5.73 ( ( size_size_list_real @ ( list_update_real @ Xs2 @ I @ X ) )
% 7.75/5.73 = ( size_size_list_real @ Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % length_list_update
% 7.75/5.73 thf(fact_7546_length__list__update,axiom,
% 7.75/5.73 ! [Xs2: list_o,I: nat,X: $o] :
% 7.75/5.73 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I @ X ) )
% 7.75/5.73 = ( size_size_list_o @ Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % length_list_update
% 7.75/5.73 thf(fact_7547_length__list__update,axiom,
% 7.75/5.73 ! [Xs2: list_nat,I: nat,X: nat] :
% 7.75/5.73 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I @ X ) )
% 7.75/5.73 = ( size_size_list_nat @ Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % length_list_update
% 7.75/5.73 thf(fact_7548_length__list__update,axiom,
% 7.75/5.73 ! [Xs2: list_int,I: nat,X: int] :
% 7.75/5.73 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I @ X ) )
% 7.75/5.73 = ( size_size_list_int @ Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % length_list_update
% 7.75/5.73 thf(fact_7549_list__update__id,axiom,
% 7.75/5.73 ! [Xs2: list_nat,I: nat] :
% 7.75/5.73 ( ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ I ) )
% 7.75/5.73 = Xs2 ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_id
% 7.75/5.73 thf(fact_7550_list__update__id,axiom,
% 7.75/5.73 ! [Xs2: list_int,I: nat] :
% 7.75/5.73 ( ( list_update_int @ Xs2 @ I @ ( nth_int @ Xs2 @ I ) )
% 7.75/5.73 = Xs2 ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_id
% 7.75/5.73 thf(fact_7551_list__update__id,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBT,I: nat] :
% 7.75/5.73 ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 7.75/5.73 = Xs2 ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_id
% 7.75/5.73 thf(fact_7552_list__update__id,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBTi,I: nat] :
% 7.75/5.73 ( ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ ( nth_VEBT_VEBTi @ Xs2 @ I ) )
% 7.75/5.73 = Xs2 ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_id
% 7.75/5.73 thf(fact_7553_nth__list__update__neq,axiom,
% 7.75/5.73 ! [I: nat,J: nat,Xs2: list_nat,X: nat] :
% 7.75/5.73 ( ( I != J )
% 7.75/5.73 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X ) @ J )
% 7.75/5.73 = ( nth_nat @ Xs2 @ J ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_neq
% 7.75/5.73 thf(fact_7554_nth__list__update__neq,axiom,
% 7.75/5.73 ! [I: nat,J: nat,Xs2: list_int,X: int] :
% 7.75/5.73 ( ( I != J )
% 7.75/5.73 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X ) @ J )
% 7.75/5.73 = ( nth_int @ Xs2 @ J ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_neq
% 7.75/5.73 thf(fact_7555_nth__list__update__neq,axiom,
% 7.75/5.73 ! [I: nat,J: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 7.75/5.73 ( ( I != J )
% 7.75/5.73 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ J )
% 7.75/5.73 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_neq
% 7.75/5.73 thf(fact_7556_nth__list__update__neq,axiom,
% 7.75/5.73 ! [I: nat,J: nat,Xs2: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 7.75/5.73 ( ( I != J )
% 7.75/5.73 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X ) @ J )
% 7.75/5.73 = ( nth_VEBT_VEBTi @ Xs2 @ J ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_neq
% 7.75/5.73 thf(fact_7557_list__update__beyond,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I )
% 7.75/5.73 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_beyond
% 7.75/5.73 thf(fact_7558_list__update__beyond,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( size_s7982070591426661849_VEBTi @ Xs2 ) @ I )
% 7.75/5.73 => ( ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_beyond
% 7.75/5.73 thf(fact_7559_list__update__beyond,axiom,
% 7.75/5.73 ! [Xs2: list_real,I: nat,X: real] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs2 ) @ I )
% 7.75/5.73 => ( ( list_update_real @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_beyond
% 7.75/5.73 thf(fact_7560_list__update__beyond,axiom,
% 7.75/5.73 ! [Xs2: list_o,I: nat,X: $o] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I )
% 7.75/5.73 => ( ( list_update_o @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_beyond
% 7.75/5.73 thf(fact_7561_list__update__beyond,axiom,
% 7.75/5.73 ! [Xs2: list_nat,I: nat,X: nat] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I )
% 7.75/5.73 => ( ( list_update_nat @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_beyond
% 7.75/5.73 thf(fact_7562_list__update__beyond,axiom,
% 7.75/5.73 ! [Xs2: list_int,I: nat,X: int] :
% 7.75/5.73 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I )
% 7.75/5.73 => ( ( list_update_int @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_beyond
% 7.75/5.73 thf(fact_7563_nth__update__invalid,axiom,
% 7.75/5.73 ! [I: nat,L: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 7.75/5.73 ( ~ ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 7.75/5.73 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ J @ X ) @ I )
% 7.75/5.73 = ( nth_VEBT_VEBT @ L @ I ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_update_invalid
% 7.75/5.73 thf(fact_7564_nth__update__invalid,axiom,
% 7.75/5.73 ! [I: nat,L: list_VEBT_VEBTi,J: nat,X: vEBT_VEBTi] :
% 7.75/5.73 ( ~ ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 7.75/5.73 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ J @ X ) @ I )
% 7.75/5.73 = ( nth_VEBT_VEBTi @ L @ I ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_update_invalid
% 7.75/5.73 thf(fact_7565_nth__update__invalid,axiom,
% 7.75/5.73 ! [I: nat,L: list_real,J: nat,X: real] :
% 7.75/5.73 ( ~ ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 7.75/5.73 => ( ( nth_real @ ( list_update_real @ L @ J @ X ) @ I )
% 7.75/5.73 = ( nth_real @ L @ I ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_update_invalid
% 7.75/5.73 thf(fact_7566_nth__update__invalid,axiom,
% 7.75/5.73 ! [I: nat,L: list_o,J: nat,X: $o] :
% 7.75/5.73 ( ~ ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 7.75/5.73 => ( ( nth_o @ ( list_update_o @ L @ J @ X ) @ I )
% 7.75/5.73 = ( nth_o @ L @ I ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_update_invalid
% 7.75/5.73 thf(fact_7567_nth__update__invalid,axiom,
% 7.75/5.73 ! [I: nat,L: list_nat,J: nat,X: nat] :
% 7.75/5.73 ( ~ ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 7.75/5.73 => ( ( nth_nat @ ( list_update_nat @ L @ J @ X ) @ I )
% 7.75/5.73 = ( nth_nat @ L @ I ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_update_invalid
% 7.75/5.73 thf(fact_7568_nth__update__invalid,axiom,
% 7.75/5.73 ! [I: nat,L: list_int,J: nat,X: int] :
% 7.75/5.73 ( ~ ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 7.75/5.73 => ( ( nth_int @ ( list_update_int @ L @ J @ X ) @ I )
% 7.75/5.73 = ( nth_int @ L @ I ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_update_invalid
% 7.75/5.73 thf(fact_7569_nth__list__update__eq,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.73 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ I )
% 7.75/5.73 = X ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_eq
% 7.75/5.73 thf(fact_7570_nth__list__update__eq,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.73 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X ) @ I )
% 7.75/5.73 = X ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_eq
% 7.75/5.73 thf(fact_7571_nth__list__update__eq,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_real,X: real] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.73 => ( ( nth_real @ ( list_update_real @ Xs2 @ I @ X ) @ I )
% 7.75/5.73 = X ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_eq
% 7.75/5.73 thf(fact_7572_nth__list__update__eq,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_o,X: $o] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.73 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X ) @ I )
% 7.75/5.73 = X ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_eq
% 7.75/5.73 thf(fact_7573_nth__list__update__eq,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_nat,X: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.73 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X ) @ I )
% 7.75/5.73 = X ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_eq
% 7.75/5.73 thf(fact_7574_nth__list__update__eq,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_int,X: int] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.73 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X ) @ I )
% 7.75/5.73 = X ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update_eq
% 7.75/5.73 thf(fact_7575_set__swap,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.73 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.73 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) )
% 7.75/5.73 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_swap
% 7.75/5.73 thf(fact_7576_set__swap,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_VEBT_VEBTi,J: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.73 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.73 => ( ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ ( nth_VEBT_VEBTi @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBTi @ Xs2 @ I ) ) )
% 7.75/5.73 = ( set_VEBT_VEBTi2 @ Xs2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_swap
% 7.75/5.73 thf(fact_7577_set__swap,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_real,J: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.73 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.73 => ( ( set_real2 @ ( list_update_real @ ( list_update_real @ Xs2 @ I @ ( nth_real @ Xs2 @ J ) ) @ J @ ( nth_real @ Xs2 @ I ) ) )
% 7.75/5.73 = ( set_real2 @ Xs2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_swap
% 7.75/5.73 thf(fact_7578_set__swap,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_o,J: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.73 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.73 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I ) ) )
% 7.75/5.73 = ( set_o2 @ Xs2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_swap
% 7.75/5.73 thf(fact_7579_set__swap,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_nat,J: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.73 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.73 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I ) ) )
% 7.75/5.73 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_swap
% 7.75/5.73 thf(fact_7580_set__swap,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_int,J: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.73 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.73 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I ) ) )
% 7.75/5.73 = ( set_int2 @ Xs2 ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_swap
% 7.75/5.73 thf(fact_7581_del__x__not__mi__newnode__not__nil,axiom,
% 7.75/5.73 ! [Mi3: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.73 ( ( ( ord_less_nat @ Mi3 @ X )
% 7.75/5.73 & ( ord_less_eq_nat @ X @ Ma ) )
% 7.75/5.73 => ( ( Mi3 != Ma )
% 7.75/5.73 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.73 = H2 )
% 7.75/5.73 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.73 = L )
% 7.75/5.73 => ( ( Newnode
% 7.75/5.73 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.73 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 7.75/5.73 => ( ( Newlist
% 7.75/5.73 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 7.75/5.73 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.73 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % del_x_not_mi_newnode_not_nil
% 7.75/5.73 thf(fact_7582_del__x__mi__lets__in__not__minNull,axiom,
% 7.75/5.73 ! [X: nat,Mi3: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 7.75/5.73 ( ( ( X = Mi3 )
% 7.75/5.73 & ( ord_less_nat @ X @ Ma ) )
% 7.75/5.73 => ( ( Mi3 != Ma )
% 7.75/5.73 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.73 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.73 = H2 )
% 7.75/5.73 => ( ( Xn
% 7.75/5.73 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 7.75/5.73 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.73 = L )
% 7.75/5.73 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.73 => ( ( Newnode
% 7.75/5.73 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.73 => ( ( Newlist
% 7.75/5.73 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 7.75/5.73 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 7.75/5.73 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % del_x_mi_lets_in_not_minNull
% 7.75/5.73 thf(fact_7583_list__update__swap,axiom,
% 7.75/5.73 ! [I: nat,I5: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT,X6: vEBT_VEBT] :
% 7.75/5.73 ( ( I != I5 )
% 7.75/5.73 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ I5 @ X6 )
% 7.75/5.73 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I5 @ X6 ) @ I @ X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_swap
% 7.75/5.73 thf(fact_7584_list__update__swap,axiom,
% 7.75/5.73 ! [I: nat,I5: nat,Xs2: list_VEBT_VEBTi,X: vEBT_VEBTi,X6: vEBT_VEBTi] :
% 7.75/5.73 ( ( I != I5 )
% 7.75/5.73 => ( ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X ) @ I5 @ X6 )
% 7.75/5.73 = ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I5 @ X6 ) @ I @ X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_swap
% 7.75/5.73 thf(fact_7585_set__update__subsetI,axiom,
% 7.75/5.73 ! [Xs2: list_complex,A2: set_complex,X: complex,I: nat] :
% 7.75/5.73 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 7.75/5.73 => ( ( member_complex @ X @ A2 )
% 7.75/5.73 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_subsetI
% 7.75/5.73 thf(fact_7586_set__update__subsetI,axiom,
% 7.75/5.73 ! [Xs2: list_real,A2: set_real,X: real,I: nat] :
% 7.75/5.73 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A2 )
% 7.75/5.73 => ( ( member_real @ X @ A2 )
% 7.75/5.73 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_subsetI
% 7.75/5.73 thf(fact_7587_set__update__subsetI,axiom,
% 7.75/5.73 ! [Xs2: list_int,A2: set_int,X: int,I: nat] :
% 7.75/5.73 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 7.75/5.73 => ( ( member_int @ X @ A2 )
% 7.75/5.73 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_subsetI
% 7.75/5.73 thf(fact_7588_set__update__subsetI,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I: nat] :
% 7.75/5.73 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 7.75/5.73 => ( ( member_VEBT_VEBT @ X @ A2 )
% 7.75/5.73 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_subsetI
% 7.75/5.73 thf(fact_7589_set__update__subsetI,axiom,
% 7.75/5.73 ! [Xs2: list_VEBT_VEBTi,A2: set_VEBT_VEBTi,X: vEBT_VEBTi,I: nat] :
% 7.75/5.73 ( ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ Xs2 ) @ A2 )
% 7.75/5.73 => ( ( member_VEBT_VEBTi @ X @ A2 )
% 7.75/5.73 => ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_subsetI
% 7.75/5.73 thf(fact_7590_set__update__subsetI,axiom,
% 7.75/5.73 ! [Xs2: list_nat,A2: set_nat,X: nat,I: nat] :
% 7.75/5.73 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 7.75/5.73 => ( ( member_nat @ X @ A2 )
% 7.75/5.73 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I @ X ) ) @ A2 ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_subsetI
% 7.75/5.73 thf(fact_7591_in__set__upd__eq,axiom,
% 7.75/5.73 ! [I: nat,L: list_complex,X: complex,Y: complex] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s3451745648224563538omplex @ L ) )
% 7.75/5.73 => ( ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ( ( member_complex @ X @ ( set_complex2 @ L ) )
% 7.75/5.73 & ! [Y6: complex] : ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ L @ I @ Y6 ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq
% 7.75/5.73 thf(fact_7592_in__set__upd__eq,axiom,
% 7.75/5.73 ! [I: nat,L: list_VEBT_VEBT,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 7.75/5.73 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ L ) )
% 7.75/5.73 & ! [Y6: vEBT_VEBT] : ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y6 ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq
% 7.75/5.73 thf(fact_7593_in__set__upd__eq,axiom,
% 7.75/5.73 ! [I: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi,Y: vEBT_VEBTi] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 7.75/5.73 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ L ) )
% 7.75/5.73 & ! [Y6: vEBT_VEBTi] : ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y6 ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq
% 7.75/5.73 thf(fact_7594_in__set__upd__eq,axiom,
% 7.75/5.73 ! [I: nat,L: list_real,X: real,Y: real] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 7.75/5.73 => ( ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ( ( member_real @ X @ ( set_real2 @ L ) )
% 7.75/5.73 & ! [Y6: real] : ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y6 ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq
% 7.75/5.73 thf(fact_7595_in__set__upd__eq,axiom,
% 7.75/5.73 ! [I: nat,L: list_o,X: $o,Y: $o] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 7.75/5.73 => ( ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ( ( member_o @ X @ ( set_o2 @ L ) )
% 7.75/5.73 & ! [Y6: $o] : ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y6 ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq
% 7.75/5.73 thf(fact_7596_in__set__upd__eq,axiom,
% 7.75/5.73 ! [I: nat,L: list_nat,X: nat,Y: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 7.75/5.73 => ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ( ( member_nat @ X @ ( set_nat2 @ L ) )
% 7.75/5.73 & ! [Y6: nat] : ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y6 ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq
% 7.75/5.73 thf(fact_7597_in__set__upd__eq,axiom,
% 7.75/5.73 ! [I: nat,L: list_int,X: int,Y: int] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 7.75/5.73 => ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ( ( member_int @ X @ ( set_int2 @ L ) )
% 7.75/5.73 & ! [Y6: int] : ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y6 ) ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq
% 7.75/5.73 thf(fact_7598_set__update__memI,axiom,
% 7.75/5.73 ! [N: nat,Xs2: list_complex,X: complex] :
% 7.75/5.73 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 7.75/5.73 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_memI
% 7.75/5.73 thf(fact_7599_set__update__memI,axiom,
% 7.75/5.73 ! [N: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.73 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_memI
% 7.75/5.73 thf(fact_7600_set__update__memI,axiom,
% 7.75/5.73 ! [N: nat,Xs2: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 7.75/5.73 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.73 => ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs2 @ N @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_memI
% 7.75/5.73 thf(fact_7601_set__update__memI,axiom,
% 7.75/5.73 ! [N: nat,Xs2: list_real,X: real] :
% 7.75/5.73 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.73 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_memI
% 7.75/5.73 thf(fact_7602_set__update__memI,axiom,
% 7.75/5.73 ! [N: nat,Xs2: list_o,X: $o] :
% 7.75/5.73 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.73 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_memI
% 7.75/5.73 thf(fact_7603_set__update__memI,axiom,
% 7.75/5.73 ! [N: nat,Xs2: list_nat,X: nat] :
% 7.75/5.73 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.73 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_memI
% 7.75/5.73 thf(fact_7604_set__update__memI,axiom,
% 7.75/5.73 ! [N: nat,Xs2: list_int,X: int] :
% 7.75/5.73 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.73 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % set_update_memI
% 7.75/5.73 thf(fact_7605_in__set__upd__cases,axiom,
% 7.75/5.73 ! [X: complex,L: list_complex,I: nat,Y: complex] :
% 7.75/5.73 ( ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ L @ I @ Y ) ) )
% 7.75/5.73 => ( ( ( ord_less_nat @ I @ ( size_s3451745648224563538omplex @ L ) )
% 7.75/5.73 => ( X != Y ) )
% 7.75/5.73 => ( member_complex @ X @ ( set_complex2 @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_cases
% 7.75/5.73 thf(fact_7606_in__set__upd__cases,axiom,
% 7.75/5.73 ! [X: vEBT_VEBT,L: list_VEBT_VEBT,I: nat,Y: vEBT_VEBT] :
% 7.75/5.73 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) )
% 7.75/5.73 => ( ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 7.75/5.73 => ( X != Y ) )
% 7.75/5.73 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_cases
% 7.75/5.73 thf(fact_7607_in__set__upd__cases,axiom,
% 7.75/5.73 ! [X: vEBT_VEBTi,L: list_VEBT_VEBTi,I: nat,Y: vEBT_VEBTi] :
% 7.75/5.73 ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) )
% 7.75/5.73 => ( ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 7.75/5.73 => ( X != Y ) )
% 7.75/5.73 => ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_cases
% 7.75/5.73 thf(fact_7608_in__set__upd__cases,axiom,
% 7.75/5.73 ! [X: real,L: list_real,I: nat,Y: real] :
% 7.75/5.73 ( ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) )
% 7.75/5.73 => ( ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 7.75/5.73 => ( X != Y ) )
% 7.75/5.73 => ( member_real @ X @ ( set_real2 @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_cases
% 7.75/5.73 thf(fact_7609_in__set__upd__cases,axiom,
% 7.75/5.73 ! [X: $o,L: list_o,I: nat,Y: $o] :
% 7.75/5.73 ( ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) )
% 7.75/5.73 => ( ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 7.75/5.73 => ( X = ~ Y ) )
% 7.75/5.73 => ( member_o @ X @ ( set_o2 @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_cases
% 7.75/5.73 thf(fact_7610_in__set__upd__cases,axiom,
% 7.75/5.73 ! [X: nat,L: list_nat,I: nat,Y: nat] :
% 7.75/5.73 ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 7.75/5.73 => ( ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 7.75/5.73 => ( X != Y ) )
% 7.75/5.73 => ( member_nat @ X @ ( set_nat2 @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_cases
% 7.75/5.73 thf(fact_7611_in__set__upd__cases,axiom,
% 7.75/5.73 ! [X: int,L: list_int,I: nat,Y: int] :
% 7.75/5.73 ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 7.75/5.73 => ( ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 7.75/5.73 => ( X != Y ) )
% 7.75/5.73 => ( member_int @ X @ ( set_int2 @ L ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_cases
% 7.75/5.73 thf(fact_7612_in__set__upd__eq__aux,axiom,
% 7.75/5.73 ! [I: nat,L: list_complex,X: complex,Y: complex] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s3451745648224563538omplex @ L ) )
% 7.75/5.73 => ( ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ! [Y6: complex] : ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ L @ I @ Y6 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq_aux
% 7.75/5.73 thf(fact_7613_in__set__upd__eq__aux,axiom,
% 7.75/5.73 ! [I: nat,L: list_VEBT_VEBT,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 7.75/5.73 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ! [Y6: vEBT_VEBT] : ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y6 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq_aux
% 7.75/5.73 thf(fact_7614_in__set__upd__eq__aux,axiom,
% 7.75/5.73 ! [I: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi,Y: vEBT_VEBTi] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 7.75/5.73 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ! [Y6: vEBT_VEBTi] : ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y6 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq_aux
% 7.75/5.73 thf(fact_7615_in__set__upd__eq__aux,axiom,
% 7.75/5.73 ! [I: nat,L: list_real,X: real,Y: real] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 7.75/5.73 => ( ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ! [Y6: real] : ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y6 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq_aux
% 7.75/5.73 thf(fact_7616_in__set__upd__eq__aux,axiom,
% 7.75/5.73 ! [I: nat,L: list_o,X: $o,Y: $o] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 7.75/5.73 => ( ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ! [Y6: $o] : ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y6 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq_aux
% 7.75/5.73 thf(fact_7617_in__set__upd__eq__aux,axiom,
% 7.75/5.73 ! [I: nat,L: list_nat,X: nat,Y: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 7.75/5.73 => ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ! [Y6: nat] : ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y6 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq_aux
% 7.75/5.73 thf(fact_7618_in__set__upd__eq__aux,axiom,
% 7.75/5.73 ! [I: nat,L: list_int,X: int,Y: int] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 7.75/5.73 => ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 7.75/5.73 = ( ( X = Y )
% 7.75/5.73 | ! [Y6: int] : ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y6 ) ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % in_set_upd_eq_aux
% 7.75/5.73 thf(fact_7619_list__update__same__conv,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.73 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 )
% 7.75/5.73 = ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 7.75/5.73 = X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_same_conv
% 7.75/5.73 thf(fact_7620_list__update__same__conv,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.73 => ( ( ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 )
% 7.75/5.73 = ( ( nth_VEBT_VEBTi @ Xs2 @ I )
% 7.75/5.73 = X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_same_conv
% 7.75/5.73 thf(fact_7621_list__update__same__conv,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_real,X: real] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.73 => ( ( ( list_update_real @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 )
% 7.75/5.73 = ( ( nth_real @ Xs2 @ I )
% 7.75/5.73 = X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_same_conv
% 7.75/5.73 thf(fact_7622_list__update__same__conv,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_o,X: $o] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.73 => ( ( ( list_update_o @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 )
% 7.75/5.73 = ( ( nth_o @ Xs2 @ I )
% 7.75/5.73 = X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_same_conv
% 7.75/5.73 thf(fact_7623_list__update__same__conv,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_nat,X: nat] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.73 => ( ( ( list_update_nat @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 )
% 7.75/5.73 = ( ( nth_nat @ Xs2 @ I )
% 7.75/5.73 = X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_same_conv
% 7.75/5.73 thf(fact_7624_list__update__same__conv,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_int,X: int] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.73 => ( ( ( list_update_int @ Xs2 @ I @ X )
% 7.75/5.73 = Xs2 )
% 7.75/5.73 = ( ( nth_int @ Xs2 @ I )
% 7.75/5.73 = X ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % list_update_same_conv
% 7.75/5.73 thf(fact_7625_nth__list__update_H,axiom,
% 7.75/5.73 ! [I: nat,J: nat,L: list_VEBT_VEBT,X: vEBT_VEBT] :
% 7.75/5.73 ( ( ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 7.75/5.73 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) @ J )
% 7.75/5.73 = X ) )
% 7.75/5.73 & ( ~ ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 7.75/5.73 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) @ J )
% 7.75/5.73 = ( nth_VEBT_VEBT @ L @ J ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update'
% 7.75/5.73 thf(fact_7626_nth__list__update_H,axiom,
% 7.75/5.73 ! [I: nat,J: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 7.75/5.73 ( ( ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 7.75/5.73 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) @ J )
% 7.75/5.73 = X ) )
% 7.75/5.73 & ( ~ ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 7.75/5.73 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) @ J )
% 7.75/5.73 = ( nth_VEBT_VEBTi @ L @ J ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update'
% 7.75/5.73 thf(fact_7627_nth__list__update_H,axiom,
% 7.75/5.73 ! [I: nat,J: nat,L: list_real,X: real] :
% 7.75/5.73 ( ( ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_size_list_real @ L ) ) )
% 7.75/5.73 => ( ( nth_real @ ( list_update_real @ L @ I @ X ) @ J )
% 7.75/5.73 = X ) )
% 7.75/5.73 & ( ~ ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_size_list_real @ L ) ) )
% 7.75/5.73 => ( ( nth_real @ ( list_update_real @ L @ I @ X ) @ J )
% 7.75/5.73 = ( nth_real @ L @ J ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update'
% 7.75/5.73 thf(fact_7628_nth__list__update_H,axiom,
% 7.75/5.73 ! [L: list_o,I: nat,X: $o,J: nat] :
% 7.75/5.73 ( ( nth_o @ ( list_update_o @ L @ I @ X ) @ J )
% 7.75/5.73 = ( ( ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_size_list_o @ L ) ) )
% 7.75/5.73 => X )
% 7.75/5.73 & ( ~ ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_size_list_o @ L ) ) )
% 7.75/5.73 => ( nth_o @ L @ J ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update'
% 7.75/5.73 thf(fact_7629_nth__list__update_H,axiom,
% 7.75/5.73 ! [I: nat,J: nat,L: list_nat,X: nat] :
% 7.75/5.73 ( ( ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 7.75/5.73 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X ) @ J )
% 7.75/5.73 = X ) )
% 7.75/5.73 & ( ~ ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 7.75/5.73 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X ) @ J )
% 7.75/5.73 = ( nth_nat @ L @ J ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update'
% 7.75/5.73 thf(fact_7630_nth__list__update_H,axiom,
% 7.75/5.73 ! [I: nat,J: nat,L: list_int,X: int] :
% 7.75/5.73 ( ( ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_size_list_int @ L ) ) )
% 7.75/5.73 => ( ( nth_int @ ( list_update_int @ L @ I @ X ) @ J )
% 7.75/5.73 = X ) )
% 7.75/5.73 & ( ~ ( ( I = J )
% 7.75/5.73 & ( ord_less_nat @ I @ ( size_size_list_int @ L ) ) )
% 7.75/5.73 => ( ( nth_int @ ( list_update_int @ L @ I @ X ) @ J )
% 7.75/5.73 = ( nth_int @ L @ J ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update'
% 7.75/5.73 thf(fact_7631_nth__list__update,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.75/5.73 => ( ( ( I = J )
% 7.75/5.73 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ J )
% 7.75/5.73 = X ) )
% 7.75/5.73 & ( ( I != J )
% 7.75/5.73 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X ) @ J )
% 7.75/5.73 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 7.75/5.73
% 7.75/5.73 % nth_list_update
% 7.75/5.73 thf(fact_7632_nth__list__update,axiom,
% 7.75/5.73 ! [I: nat,Xs2: list_VEBT_VEBTi,J: nat,X: vEBT_VEBTi] :
% 7.75/5.73 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.75/5.73 => ( ( ( I = J )
% 7.75/5.73 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X ) @ J )
% 7.75/5.73 = X ) )
% 7.75/5.73 & ( ( I != J )
% 7.75/5.73 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X ) @ J )
% 7.75/5.74 = ( nth_VEBT_VEBTi @ Xs2 @ J ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nth_list_update
% 7.75/5.74 thf(fact_7633_nth__list__update,axiom,
% 7.75/5.74 ! [I: nat,Xs2: list_real,J: nat,X: real] :
% 7.75/5.74 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs2 ) )
% 7.75/5.74 => ( ( ( I = J )
% 7.75/5.74 => ( ( nth_real @ ( list_update_real @ Xs2 @ I @ X ) @ J )
% 7.75/5.74 = X ) )
% 7.75/5.74 & ( ( I != J )
% 7.75/5.74 => ( ( nth_real @ ( list_update_real @ Xs2 @ I @ X ) @ J )
% 7.75/5.74 = ( nth_real @ Xs2 @ J ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nth_list_update
% 7.75/5.74 thf(fact_7634_nth__list__update,axiom,
% 7.75/5.74 ! [I: nat,Xs2: list_o,X: $o,J: nat] :
% 7.75/5.74 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 7.75/5.74 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X ) @ J )
% 7.75/5.74 = ( ( ( I = J )
% 7.75/5.74 => X )
% 7.75/5.74 & ( ( I != J )
% 7.75/5.74 => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nth_list_update
% 7.75/5.74 thf(fact_7635_nth__list__update,axiom,
% 7.75/5.74 ! [I: nat,Xs2: list_nat,J: nat,X: nat] :
% 7.75/5.74 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.74 => ( ( ( I = J )
% 7.75/5.74 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X ) @ J )
% 7.75/5.74 = X ) )
% 7.75/5.74 & ( ( I != J )
% 7.75/5.74 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X ) @ J )
% 7.75/5.74 = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nth_list_update
% 7.75/5.74 thf(fact_7636_nth__list__update,axiom,
% 7.75/5.74 ! [I: nat,Xs2: list_int,J: nat,X: int] :
% 7.75/5.74 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 7.75/5.74 => ( ( ( I = J )
% 7.75/5.74 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X ) @ J )
% 7.75/5.74 = X ) )
% 7.75/5.74 & ( ( I != J )
% 7.75/5.74 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X ) @ J )
% 7.75/5.74 = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nth_list_update
% 7.75/5.74 thf(fact_7637_vebt__maxt_Osimps_I2_J,axiom,
% 7.75/5.74 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 7.75/5.74 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 7.75/5.74 = none_nat ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_maxt.simps(2)
% 7.75/5.74 thf(fact_7638_vebt__maxt_Osimps_I1_J,axiom,
% 7.75/5.74 ! [B: $o,A: $o] :
% 7.75/5.74 ( ( B
% 7.75/5.74 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.74 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.74 & ( ~ B
% 7.75/5.74 => ( ( A
% 7.75/5.74 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.74 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.74 & ( ~ A
% 7.75/5.74 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.74 = none_nat ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_maxt.simps(1)
% 7.75/5.74 thf(fact_7639_vebt__maxt_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Y: option_nat] :
% 7.75/5.74 ( ( ( vEBT_vebt_maxt @ X )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ~ ( ( B2
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.74 & ( ~ B2
% 7.75/5.74 => ( ( A5
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.74 & ( ~ A5
% 7.75/5.74 => ( Y = none_nat ) ) ) ) ) )
% 7.75/5.74 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( Y != none_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat] :
% 7.75/5.74 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_maxt.elims
% 7.75/5.74 thf(fact_7640_insert__simp__norm,axiom,
% 7.75/5.74 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi3: nat,Ma: nat,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( ord_less_nat @ Mi3 @ X )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( X != Ma )
% 7.75/5.74 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ ( 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 ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % insert_simp_norm
% 7.75/5.74 thf(fact_7641_insert__simp__excp,axiom,
% 7.75/5.74 ! [Mi3: nat,Deg: nat,TreeList: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( X != Ma )
% 7.75/5.74 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi3 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % insert_simp_excp
% 7.75/5.74 thf(fact_7642_less__shift,axiom,
% 7.75/5.74 ( ord_less_nat
% 7.75/5.74 = ( ^ [X2: nat,Y6: nat] : ( vEBT_VEBT_less @ ( some_nat @ X2 ) @ ( some_nat @ Y6 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_shift
% 7.75/5.74 thf(fact_7643_max__Suc__Suc,axiom,
% 7.75/5.74 ! [M: nat,N: nat] :
% 7.75/5.74 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 7.75/5.74 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_Suc_Suc
% 7.75/5.74 thf(fact_7644_max__nat_Oeq__neutr__iff,axiom,
% 7.75/5.74 ! [A: nat,B: nat] :
% 7.75/5.74 ( ( ( ord_max_nat @ A @ B )
% 7.75/5.74 = zero_zero_nat )
% 7.75/5.74 = ( ( A = zero_zero_nat )
% 7.75/5.74 & ( B = zero_zero_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_nat.eq_neutr_iff
% 7.75/5.74 thf(fact_7645_max__nat_Oleft__neutral,axiom,
% 7.75/5.74 ! [A: nat] :
% 7.75/5.74 ( ( ord_max_nat @ zero_zero_nat @ A )
% 7.75/5.74 = A ) ).
% 7.75/5.74
% 7.75/5.74 % max_nat.left_neutral
% 7.75/5.74 thf(fact_7646_max__nat_Oneutr__eq__iff,axiom,
% 7.75/5.74 ! [A: nat,B: nat] :
% 7.75/5.74 ( ( zero_zero_nat
% 7.75/5.74 = ( ord_max_nat @ A @ B ) )
% 7.75/5.74 = ( ( A = zero_zero_nat )
% 7.75/5.74 & ( B = zero_zero_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_nat.neutr_eq_iff
% 7.75/5.74 thf(fact_7647_max__nat_Oright__neutral,axiom,
% 7.75/5.74 ! [A: nat] :
% 7.75/5.74 ( ( ord_max_nat @ A @ zero_zero_nat )
% 7.75/5.74 = A ) ).
% 7.75/5.74
% 7.75/5.74 % max_nat.right_neutral
% 7.75/5.74 thf(fact_7648_max__0L,axiom,
% 7.75/5.74 ! [N: nat] :
% 7.75/5.74 ( ( ord_max_nat @ zero_zero_nat @ N )
% 7.75/5.74 = N ) ).
% 7.75/5.74
% 7.75/5.74 % max_0L
% 7.75/5.74 thf(fact_7649_max__0R,axiom,
% 7.75/5.74 ! [N: nat] :
% 7.75/5.74 ( ( ord_max_nat @ N @ zero_zero_nat )
% 7.75/5.74 = N ) ).
% 7.75/5.74
% 7.75/5.74 % max_0R
% 7.75/5.74 thf(fact_7650_of__bool__or__iff,axiom,
% 7.75/5.74 ! [P: $o,Q: $o] :
% 7.75/5.74 ( ( zero_n2687167440665602831ol_nat
% 7.75/5.74 @ ( P
% 7.75/5.74 | Q ) )
% 7.75/5.74 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_bool_or_iff
% 7.75/5.74 thf(fact_7651_of__bool__or__iff,axiom,
% 7.75/5.74 ! [P: $o,Q: $o] :
% 7.75/5.74 ( ( zero_n2684676970156552555ol_int
% 7.75/5.74 @ ( P
% 7.75/5.74 | Q ) )
% 7.75/5.74 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_bool_or_iff
% 7.75/5.74 thf(fact_7652_of__bool__or__iff,axiom,
% 7.75/5.74 ! [P: $o,Q: $o] :
% 7.75/5.74 ( ( zero_n356916108424825756nteger
% 7.75/5.74 @ ( P
% 7.75/5.74 | Q ) )
% 7.75/5.74 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_bool_or_iff
% 7.75/5.74 thf(fact_7653_max__0__1_I3_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 7.75/5.74 = ( numera1916890842035813515d_enat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(3)
% 7.75/5.74 thf(fact_7654_max__0__1_I3_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 7.75/5.74 = ( numeral_numeral_real @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(3)
% 7.75/5.74 thf(fact_7655_max__0__1_I3_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 7.75/5.74 = ( numeral_numeral_rat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(3)
% 7.75/5.74 thf(fact_7656_max__0__1_I3_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 7.75/5.74 = ( numeral_numeral_nat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(3)
% 7.75/5.74 thf(fact_7657_max__0__1_I3_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 7.75/5.74 = ( numeral_numeral_int @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(3)
% 7.75/5.74 thf(fact_7658_max__0__1_I4_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 7.75/5.74 = ( numera1916890842035813515d_enat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(4)
% 7.75/5.74 thf(fact_7659_max__0__1_I4_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 7.75/5.74 = ( numeral_numeral_real @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(4)
% 7.75/5.74 thf(fact_7660_max__0__1_I4_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 7.75/5.74 = ( numeral_numeral_rat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(4)
% 7.75/5.74 thf(fact_7661_max__0__1_I4_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 7.75/5.74 = ( numeral_numeral_nat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(4)
% 7.75/5.74 thf(fact_7662_max__0__1_I4_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 7.75/5.74 = ( numeral_numeral_int @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(4)
% 7.75/5.74 thf(fact_7663_max__number__of_I1_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 7.75/5.74 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 7.75/5.74 = ( numera1916890842035813515d_enat @ V ) ) )
% 7.75/5.74 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 7.75/5.74 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 7.75/5.74 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(1)
% 7.75/5.74 thf(fact_7664_max__number__of_I1_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.74 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.74 = ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.74 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.74 = ( numeral_numeral_real @ U ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(1)
% 7.75/5.74 thf(fact_7665_max__number__of_I1_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.74 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.74 = ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.74 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.74 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(1)
% 7.75/5.74 thf(fact_7666_max__number__of_I1_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 7.75/5.74 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 7.75/5.74 = ( numeral_numeral_nat @ V ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 7.75/5.74 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 7.75/5.74 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(1)
% 7.75/5.74 thf(fact_7667_max__number__of_I1_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.74 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.74 = ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.74 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.74 = ( numeral_numeral_int @ U ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(1)
% 7.75/5.74 thf(fact_7668_max__0__1_I2_J,axiom,
% 7.75/5.74 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 7.75/5.74 = one_one_real ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(2)
% 7.75/5.74 thf(fact_7669_max__0__1_I2_J,axiom,
% 7.75/5.74 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 7.75/5.74 = one_one_rat ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(2)
% 7.75/5.74 thf(fact_7670_max__0__1_I2_J,axiom,
% 7.75/5.74 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(2)
% 7.75/5.74 thf(fact_7671_max__0__1_I2_J,axiom,
% 7.75/5.74 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 7.75/5.74 = one_on7984719198319812577d_enat ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(2)
% 7.75/5.74 thf(fact_7672_max__0__1_I2_J,axiom,
% 7.75/5.74 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 7.75/5.74 = one_one_int ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(2)
% 7.75/5.74 thf(fact_7673_max__0__1_I1_J,axiom,
% 7.75/5.74 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 7.75/5.74 = one_one_real ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(1)
% 7.75/5.74 thf(fact_7674_max__0__1_I1_J,axiom,
% 7.75/5.74 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 7.75/5.74 = one_one_rat ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(1)
% 7.75/5.74 thf(fact_7675_max__0__1_I1_J,axiom,
% 7.75/5.74 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(1)
% 7.75/5.74 thf(fact_7676_max__0__1_I1_J,axiom,
% 7.75/5.74 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 7.75/5.74 = one_on7984719198319812577d_enat ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(1)
% 7.75/5.74 thf(fact_7677_max__0__1_I1_J,axiom,
% 7.75/5.74 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 7.75/5.74 = one_one_int ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(1)
% 7.75/5.74 thf(fact_7678_max__0__1_I5_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 7.75/5.74 = ( numera1916890842035813515d_enat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(5)
% 7.75/5.74 thf(fact_7679_max__0__1_I5_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 7.75/5.74 = ( numeral_numeral_real @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(5)
% 7.75/5.74 thf(fact_7680_max__0__1_I5_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 7.75/5.74 = ( numeral_numeral_rat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(5)
% 7.75/5.74 thf(fact_7681_max__0__1_I5_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 7.75/5.74 = ( numeral_numeral_nat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(5)
% 7.75/5.74 thf(fact_7682_max__0__1_I5_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 7.75/5.74 = ( numeral_numeral_int @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(5)
% 7.75/5.74 thf(fact_7683_max__0__1_I6_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 7.75/5.74 = ( numera1916890842035813515d_enat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(6)
% 7.75/5.74 thf(fact_7684_max__0__1_I6_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 7.75/5.74 = ( numeral_numeral_real @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(6)
% 7.75/5.74 thf(fact_7685_max__0__1_I6_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 7.75/5.74 = ( numeral_numeral_rat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(6)
% 7.75/5.74 thf(fact_7686_max__0__1_I6_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 7.75/5.74 = ( numeral_numeral_nat @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(6)
% 7.75/5.74 thf(fact_7687_max__0__1_I6_J,axiom,
% 7.75/5.74 ! [X: num] :
% 7.75/5.74 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 7.75/5.74 = ( numeral_numeral_int @ X ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_0_1(6)
% 7.75/5.74 thf(fact_7688_max__number__of_I4_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(4)
% 7.75/5.74 thf(fact_7689_max__number__of_I4_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 7.75/5.74 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 7.75/5.74 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 7.75/5.74 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 7.75/5.74 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 7.75/5.74 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(4)
% 7.75/5.74 thf(fact_7690_max__number__of_I4_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(4)
% 7.75/5.74 thf(fact_7691_max__number__of_I4_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(4)
% 7.75/5.74 thf(fact_7692_max__number__of_I3_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.74 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.74 = ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.74 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 7.75/5.74 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(3)
% 7.75/5.74 thf(fact_7693_max__number__of_I3_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 7.75/5.74 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 7.75/5.74 = ( numera6620942414471956472nteger @ V ) ) )
% 7.75/5.74 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 7.75/5.74 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 7.75/5.74 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(3)
% 7.75/5.74 thf(fact_7694_max__number__of_I3_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.74 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.74 = ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.74 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 7.75/5.74 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(3)
% 7.75/5.74 thf(fact_7695_max__number__of_I3_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.74 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.74 = ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.74 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 7.75/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(3)
% 7.75/5.74 thf(fact_7696_max__number__of_I2_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 7.75/5.74 = ( numeral_numeral_real @ U ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(2)
% 7.75/5.74 thf(fact_7697_max__number__of_I2_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 7.75/5.74 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 7.75/5.74 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 7.75/5.74 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 7.75/5.74 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 7.75/5.74 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(2)
% 7.75/5.74 thf(fact_7698_max__number__of_I2_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 7.75/5.74 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(2)
% 7.75/5.74 thf(fact_7699_max__number__of_I2_J,axiom,
% 7.75/5.74 ! [U: num,V: num] :
% 7.75/5.74 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 7.75/5.74 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 7.75/5.74 = ( numeral_numeral_int @ U ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_number_of(2)
% 7.75/5.74 thf(fact_7700_max__Suc__numeral,axiom,
% 7.75/5.74 ! [N: nat,K: num] :
% 7.75/5.74 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 7.75/5.74 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_Suc_numeral
% 7.75/5.74 thf(fact_7701_max__numeral__Suc,axiom,
% 7.75/5.74 ! [K: num,N: nat] :
% 7.75/5.74 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 7.75/5.74 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_numeral_Suc
% 7.75/5.74 thf(fact_7702_of__nat__max,axiom,
% 7.75/5.74 ! [X: nat,Y: nat] :
% 7.75/5.74 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y ) )
% 7.75/5.74 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_nat_max
% 7.75/5.74 thf(fact_7703_of__nat__max,axiom,
% 7.75/5.74 ! [X: nat,Y: nat] :
% 7.75/5.74 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 7.75/5.74 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_nat_max
% 7.75/5.74 thf(fact_7704_of__nat__max,axiom,
% 7.75/5.74 ! [X: nat,Y: nat] :
% 7.75/5.74 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 7.75/5.74 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_nat_max
% 7.75/5.74 thf(fact_7705_of__nat__max,axiom,
% 7.75/5.74 ! [X: nat,Y: nat] :
% 7.75/5.74 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 7.75/5.74 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_nat_max
% 7.75/5.74 thf(fact_7706_max__diff__distrib__left,axiom,
% 7.75/5.74 ! [X: real,Y: real,Z: real] :
% 7.75/5.74 ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 7.75/5.74 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_diff_distrib_left
% 7.75/5.74 thf(fact_7707_max__diff__distrib__left,axiom,
% 7.75/5.74 ! [X: int,Y: int,Z: int] :
% 7.75/5.74 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 7.75/5.74 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_diff_distrib_left
% 7.75/5.74 thf(fact_7708_max__add__distrib__left,axiom,
% 7.75/5.74 ! [X: real,Y: real,Z: real] :
% 7.75/5.74 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 7.75/5.74 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_add_distrib_left
% 7.75/5.74 thf(fact_7709_max__add__distrib__left,axiom,
% 7.75/5.74 ! [X: rat,Y: rat,Z: rat] :
% 7.75/5.74 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 7.75/5.74 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_add_distrib_left
% 7.75/5.74 thf(fact_7710_max__add__distrib__left,axiom,
% 7.75/5.74 ! [X: nat,Y: nat,Z: nat] :
% 7.75/5.74 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 7.75/5.74 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_add_distrib_left
% 7.75/5.74 thf(fact_7711_max__add__distrib__left,axiom,
% 7.75/5.74 ! [X: int,Y: int,Z: int] :
% 7.75/5.74 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 7.75/5.74 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_add_distrib_left
% 7.75/5.74 thf(fact_7712_max__add__distrib__right,axiom,
% 7.75/5.74 ! [X: real,Y: real,Z: real] :
% 7.75/5.74 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 7.75/5.74 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_add_distrib_right
% 7.75/5.74 thf(fact_7713_max__add__distrib__right,axiom,
% 7.75/5.74 ! [X: rat,Y: rat,Z: rat] :
% 7.75/5.74 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 7.75/5.74 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_add_distrib_right
% 7.75/5.74 thf(fact_7714_max__add__distrib__right,axiom,
% 7.75/5.74 ! [X: nat,Y: nat,Z: nat] :
% 7.75/5.74 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 7.75/5.74 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_add_distrib_right
% 7.75/5.74 thf(fact_7715_max__add__distrib__right,axiom,
% 7.75/5.74 ! [X: int,Y: int,Z: int] :
% 7.75/5.74 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 7.75/5.74 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_add_distrib_right
% 7.75/5.74 thf(fact_7716_nat__mult__max__right,axiom,
% 7.75/5.74 ! [M: nat,N: nat,Q3: nat] :
% 7.75/5.74 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 7.75/5.74 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_mult_max_right
% 7.75/5.74 thf(fact_7717_nat__mult__max__left,axiom,
% 7.75/5.74 ! [M: nat,N: nat,Q3: nat] :
% 7.75/5.74 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 7.75/5.74 = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_mult_max_left
% 7.75/5.74 thf(fact_7718_nat__add__max__left,axiom,
% 7.75/5.74 ! [M: nat,N: nat,Q3: nat] :
% 7.75/5.74 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 7.75/5.74 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N @ Q3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_add_max_left
% 7.75/5.74 thf(fact_7719_nat__add__max__right,axiom,
% 7.75/5.74 ! [M: nat,N: nat,Q3: nat] :
% 7.75/5.74 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 7.75/5.74 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_add_max_right
% 7.75/5.74 thf(fact_7720_nat__minus__add__max,axiom,
% 7.75/5.74 ! [N: nat,M: nat] :
% 7.75/5.74 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 7.75/5.74 = ( ord_max_nat @ N @ M ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_minus_add_max
% 7.75/5.74 thf(fact_7721_max__less__iff__conj,axiom,
% 7.75/5.74 ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 7.75/5.74 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y ) @ Z )
% 7.75/5.74 = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 7.75/5.74 & ( ord_le72135733267957522d_enat @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_less_iff_conj
% 7.75/5.74 thf(fact_7722_max__less__iff__conj,axiom,
% 7.75/5.74 ! [X: real,Y: real,Z: real] :
% 7.75/5.74 ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 7.75/5.74 = ( ( ord_less_real @ X @ Z )
% 7.75/5.74 & ( ord_less_real @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_less_iff_conj
% 7.75/5.74 thf(fact_7723_max__less__iff__conj,axiom,
% 7.75/5.74 ! [X: rat,Y: rat,Z: rat] :
% 7.75/5.74 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 7.75/5.74 = ( ( ord_less_rat @ X @ Z )
% 7.75/5.74 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_less_iff_conj
% 7.75/5.74 thf(fact_7724_max__less__iff__conj,axiom,
% 7.75/5.74 ! [X: num,Y: num,Z: num] :
% 7.75/5.74 ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 7.75/5.74 = ( ( ord_less_num @ X @ Z )
% 7.75/5.74 & ( ord_less_num @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_less_iff_conj
% 7.75/5.74 thf(fact_7725_max__less__iff__conj,axiom,
% 7.75/5.74 ! [X: nat,Y: nat,Z: nat] :
% 7.75/5.74 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 7.75/5.74 = ( ( ord_less_nat @ X @ Z )
% 7.75/5.74 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_less_iff_conj
% 7.75/5.74 thf(fact_7726_max__less__iff__conj,axiom,
% 7.75/5.74 ! [X: int,Y: int,Z: int] :
% 7.75/5.74 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 7.75/5.74 = ( ( ord_less_int @ X @ Z )
% 7.75/5.74 & ( ord_less_int @ Y @ Z ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_less_iff_conj
% 7.75/5.74 thf(fact_7727_max_Oabsorb4,axiom,
% 7.75/5.74 ! [A: extended_enat,B: extended_enat] :
% 7.75/5.74 ( ( ord_le72135733267957522d_enat @ A @ B )
% 7.75/5.74 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 7.75/5.74 = B ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb4
% 7.75/5.74 thf(fact_7728_max_Oabsorb4,axiom,
% 7.75/5.74 ! [A: real,B: real] :
% 7.75/5.74 ( ( ord_less_real @ A @ B )
% 7.75/5.74 => ( ( ord_max_real @ A @ B )
% 7.75/5.74 = B ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb4
% 7.75/5.74 thf(fact_7729_max_Oabsorb4,axiom,
% 7.75/5.74 ! [A: rat,B: rat] :
% 7.75/5.74 ( ( ord_less_rat @ A @ B )
% 7.75/5.74 => ( ( ord_max_rat @ A @ B )
% 7.75/5.74 = B ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb4
% 7.75/5.74 thf(fact_7730_max_Oabsorb4,axiom,
% 7.75/5.74 ! [A: num,B: num] :
% 7.75/5.74 ( ( ord_less_num @ A @ B )
% 7.75/5.74 => ( ( ord_max_num @ A @ B )
% 7.75/5.74 = B ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb4
% 7.75/5.74 thf(fact_7731_max_Oabsorb4,axiom,
% 7.75/5.74 ! [A: nat,B: nat] :
% 7.75/5.74 ( ( ord_less_nat @ A @ B )
% 7.75/5.74 => ( ( ord_max_nat @ A @ B )
% 7.75/5.74 = B ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb4
% 7.75/5.74 thf(fact_7732_max_Oabsorb4,axiom,
% 7.75/5.74 ! [A: int,B: int] :
% 7.75/5.74 ( ( ord_less_int @ A @ B )
% 7.75/5.74 => ( ( ord_max_int @ A @ B )
% 7.75/5.74 = B ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb4
% 7.75/5.74 thf(fact_7733_max_Oabsorb3,axiom,
% 7.75/5.74 ! [B: extended_enat,A: extended_enat] :
% 7.75/5.74 ( ( ord_le72135733267957522d_enat @ B @ A )
% 7.75/5.74 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 7.75/5.74 = A ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb3
% 7.75/5.74 thf(fact_7734_max_Oabsorb3,axiom,
% 7.75/5.74 ! [B: real,A: real] :
% 7.75/5.74 ( ( ord_less_real @ B @ A )
% 7.75/5.74 => ( ( ord_max_real @ A @ B )
% 7.75/5.74 = A ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb3
% 7.75/5.74 thf(fact_7735_max_Oabsorb3,axiom,
% 7.75/5.74 ! [B: rat,A: rat] :
% 7.75/5.74 ( ( ord_less_rat @ B @ A )
% 7.75/5.74 => ( ( ord_max_rat @ A @ B )
% 7.75/5.74 = A ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb3
% 7.75/5.74 thf(fact_7736_max_Oabsorb3,axiom,
% 7.75/5.74 ! [B: num,A: num] :
% 7.75/5.74 ( ( ord_less_num @ B @ A )
% 7.75/5.74 => ( ( ord_max_num @ A @ B )
% 7.75/5.74 = A ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb3
% 7.75/5.74 thf(fact_7737_max_Oabsorb3,axiom,
% 7.75/5.74 ! [B: nat,A: nat] :
% 7.75/5.74 ( ( ord_less_nat @ B @ A )
% 7.75/5.74 => ( ( ord_max_nat @ A @ B )
% 7.75/5.74 = A ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb3
% 7.75/5.74 thf(fact_7738_max_Oabsorb3,axiom,
% 7.75/5.74 ! [B: int,A: int] :
% 7.75/5.74 ( ( ord_less_int @ B @ A )
% 7.75/5.74 => ( ( ord_max_int @ A @ B )
% 7.75/5.74 = A ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.absorb3
% 7.75/5.74 thf(fact_7739_succ__greatereq__min,axiom,
% 7.75/5.74 ! [Deg: nat,Mi3: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ord_less_eq_nat @ Mi3 @ X )
% 7.75/5.74 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( 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 ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( 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 ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ none_nat
% 7.75/5.74 @ ( 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 ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ none_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % succ_greatereq_min
% 7.75/5.74 thf(fact_7740_succ__less__length__list,axiom,
% 7.75/5.74 ! [Deg: nat,Mi3: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ord_less_eq_nat @ Mi3 @ X )
% 7.75/5.74 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( 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 ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( 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 ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ none_nat
% 7.75/5.74 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % succ_less_length_list
% 7.75/5.74 thf(fact_7741_set__vebt_H__def,axiom,
% 7.75/5.74 ( vEBT_VEBT_set_vebt
% 7.75/5.74 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % set_vebt'_def
% 7.75/5.74 thf(fact_7742_max__enat__simps_I2_J,axiom,
% 7.75/5.74 ! [Q3: extended_enat] :
% 7.75/5.74 ( ( ord_ma741700101516333627d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 7.75/5.74 = Q3 ) ).
% 7.75/5.74
% 7.75/5.74 % max_enat_simps(2)
% 7.75/5.74 thf(fact_7743_max__enat__simps_I3_J,axiom,
% 7.75/5.74 ! [Q3: extended_enat] :
% 7.75/5.74 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 7.75/5.74 = Q3 ) ).
% 7.75/5.74
% 7.75/5.74 % max_enat_simps(3)
% 7.75/5.74 thf(fact_7744_finite__interval__int4,axiom,
% 7.75/5.74 ! [A: int,B: int] :
% 7.75/5.74 ( finite_finite_int
% 7.75/5.74 @ ( collect_int
% 7.75/5.74 @ ^ [I2: int] :
% 7.75/5.74 ( ( ord_less_int @ A @ I2 )
% 7.75/5.74 & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_interval_int4
% 7.75/5.74 thf(fact_7745_finite__nth__roots,axiom,
% 7.75/5.74 ! [N: nat,C: complex] :
% 7.75/5.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.75/5.74 => ( finite3207457112153483333omplex
% 7.75/5.74 @ ( collect_complex
% 7.75/5.74 @ ^ [Z6: complex] :
% 7.75/5.74 ( ( power_power_complex @ Z6 @ N )
% 7.75/5.74 = C ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_nth_roots
% 7.75/5.74 thf(fact_7746_finite__interval__int3,axiom,
% 7.75/5.74 ! [A: int,B: int] :
% 7.75/5.74 ( finite_finite_int
% 7.75/5.74 @ ( collect_int
% 7.75/5.74 @ ^ [I2: int] :
% 7.75/5.74 ( ( ord_less_int @ A @ I2 )
% 7.75/5.74 & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_interval_int3
% 7.75/5.74 thf(fact_7747_finite__interval__int2,axiom,
% 7.75/5.74 ! [A: int,B: int] :
% 7.75/5.74 ( finite_finite_int
% 7.75/5.74 @ ( collect_int
% 7.75/5.74 @ ^ [I2: int] :
% 7.75/5.74 ( ( ord_less_eq_int @ A @ I2 )
% 7.75/5.74 & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_interval_int2
% 7.75/5.74 thf(fact_7748_del__x__not__mi,axiom,
% 7.75/5.74 ! [Mi3: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( ord_less_nat @ Mi3 @ X )
% 7.75/5.74 & ( ord_less_eq_nat @ X @ Ma ) )
% 7.75/5.74 => ( ( Mi3 != Ma )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = H2 )
% 7.75/5.74 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = L )
% 7.75/5.74 => ( ( Newnode
% 7.75/5.74 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.74 => ( ( Newlist
% 7.75/5.74 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 7.75/5.74 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ Mi3
% 7.75/5.74 @ ( if_nat @ ( X = Ma )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ Mi3
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ Newlist
% 7.75/5.74 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 7.75/5.74 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % del_x_not_mi
% 7.75/5.74 thf(fact_7749_del__x__not__mi__new__node__nil,axiom,
% 7.75/5.74 ! [Mi3: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 7.75/5.74 ( ( ( ord_less_nat @ Mi3 @ X )
% 7.75/5.74 & ( ord_less_eq_nat @ X @ Ma ) )
% 7.75/5.74 => ( ( Mi3 != Ma )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = H2 )
% 7.75/5.74 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = L )
% 7.75/5.74 => ( ( Newnode
% 7.75/5.74 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.74 => ( ( vEBT_VEBT_minNull @ Newnode )
% 7.75/5.74 => ( ( Sn
% 7.75/5.74 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 7.75/5.74 => ( ( Newlist
% 7.75/5.74 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 7.75/5.74 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ Mi3
% 7.75/5.74 @ ( if_nat @ ( X = Ma )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ Sn )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ Mi3
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ Newlist
% 7.75/5.74 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % del_x_not_mi_new_node_nil
% 7.75/5.74 thf(fact_7750_del__x__not__mia,axiom,
% 7.75/5.74 ! [Mi3: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( ord_less_nat @ Mi3 @ X )
% 7.75/5.74 & ( ord_less_eq_nat @ X @ Ma ) )
% 7.75/5.74 => ( ( Mi3 != Ma )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = H2 )
% 7.75/5.74 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = L )
% 7.75/5.74 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ Mi3
% 7.75/5.74 @ ( if_nat @ ( X = Ma )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ Mi3
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.74 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % del_x_not_mia
% 7.75/5.74 thf(fact_7751_del__x__mia,axiom,
% 7.75/5.74 ! [X: nat,Mi3: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( X = Mi3 )
% 7.75/5.74 & ( ord_less_nat @ X @ Ma ) )
% 7.75/5.74 => ( ( Mi3 != Ma )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 = Ma )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 = Ma )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ Summary ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % del_x_mia
% 7.75/5.74 thf(fact_7752_del__x__mi__lets__in__minNull,axiom,
% 7.75/5.74 ! [X: nat,Mi3: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 7.75/5.74 ( ( ( X = Mi3 )
% 7.75/5.74 & ( ord_less_nat @ X @ Ma ) )
% 7.75/5.74 => ( ( Mi3 != Ma )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = H2 )
% 7.75/5.74 => ( ( Xn
% 7.75/5.74 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 7.75/5.74 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = L )
% 7.75/5.74 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( Newnode
% 7.75/5.74 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.74 => ( ( Newlist
% 7.75/5.74 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 7.75/5.74 => ( ( vEBT_VEBT_minNull @ Newnode )
% 7.75/5.74 => ( ( Sn
% 7.75/5.74 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ Xn
% 7.75/5.74 @ ( if_nat @ ( Xn = Ma )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ Sn )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ Xn
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ Newlist
% 7.75/5.74 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % del_x_mi_lets_in_minNull
% 7.75/5.74 thf(fact_7753_del__x__mi__lets__in,axiom,
% 7.75/5.74 ! [X: nat,Mi3: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 7.75/5.74 ( ( ( X = Mi3 )
% 7.75/5.74 & ( ord_less_nat @ X @ Ma ) )
% 7.75/5.74 => ( ( Mi3 != Ma )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = H2 )
% 7.75/5.74 => ( ( Xn
% 7.75/5.74 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 7.75/5.74 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = L )
% 7.75/5.74 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( Newnode
% 7.75/5.74 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.74 => ( ( Newlist
% 7.75/5.74 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 7.75/5.74 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ Xn
% 7.75/5.74 @ ( if_nat @ ( Xn = Ma )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ Xn
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ Newlist
% 7.75/5.74 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 7.75/5.74 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % del_x_mi_lets_in
% 7.75/5.74 thf(fact_7754_del__x__mi,axiom,
% 7.75/5.74 ! [X: nat,Mi3: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat] :
% 7.75/5.74 ( ( ( X = Mi3 )
% 7.75/5.74 & ( ord_less_nat @ X @ Ma ) )
% 7.75/5.74 => ( ( Mi3 != Ma )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = H2 )
% 7.75/5.74 => ( ( Xn
% 7.75/5.74 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 7.75/5.74 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 = L )
% 7.75/5.74 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ Xn
% 7.75/5.74 @ ( if_nat @ ( Xn = Ma )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ Xn
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.75/5.74 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % del_x_mi
% 7.75/5.74 thf(fact_7755_del__in__range,axiom,
% 7.75/5.74 ! [Mi3: nat,X: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( ord_less_eq_nat @ Mi3 @ X )
% 7.75/5.74 & ( ord_less_eq_nat @ X @ Ma ) )
% 7.75/5.74 => ( ( Mi3 != Ma )
% 7.75/5.74 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( X = Mi3 )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 = Ma ) )
% 7.75/5.74 & ( ( X != Mi3 )
% 7.75/5.74 => ( X = Ma ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( X = Mi3 )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 = Ma ) )
% 7.75/5.74 & ( ( X != Mi3 )
% 7.75/5.74 => ( X = Ma ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ Deg
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ Summary ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % del_in_range
% 7.75/5.74 thf(fact_7756_pred__lesseq__max,axiom,
% 7.75/5.74 ! [Deg: nat,X: nat,Ma: nat,Mi3: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ord_less_eq_nat @ X @ Ma )
% 7.75/5.74 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( 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 ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( 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 ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( if_option_nat @ ( ord_less_nat @ Mi3 @ X ) @ ( some_nat @ Mi3 ) @ none_nat )
% 7.75/5.74 @ ( 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 ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ none_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % pred_lesseq_max
% 7.75/5.74 thf(fact_7757_pred__less__length__list,axiom,
% 7.75/5.74 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi3: nat,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 7.75/5.74 => ( ( ord_less_eq_nat @ X @ Ma )
% 7.75/5.74 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( 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 ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( 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 ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( if_option_nat @ ( ord_less_nat @ Mi3 @ X ) @ ( some_nat @ Mi3 ) @ none_nat )
% 7.75/5.74 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % pred_less_length_list
% 7.75/5.74 thf(fact_7758_max__def__raw,axiom,
% 7.75/5.74 ( ord_ma741700101516333627d_enat
% 7.75/5.74 = ( ^ [A3: extended_enat,B4: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_def_raw
% 7.75/5.74 thf(fact_7759_max__def__raw,axiom,
% 7.75/5.74 ( ord_max_set_nat
% 7.75/5.74 = ( ^ [A3: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_def_raw
% 7.75/5.74 thf(fact_7760_max__def__raw,axiom,
% 7.75/5.74 ( ord_max_rat
% 7.75/5.74 = ( ^ [A3: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_def_raw
% 7.75/5.74 thf(fact_7761_max__def__raw,axiom,
% 7.75/5.74 ( ord_max_num
% 7.75/5.74 = ( ^ [A3: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_def_raw
% 7.75/5.74 thf(fact_7762_max__def__raw,axiom,
% 7.75/5.74 ( ord_max_nat
% 7.75/5.74 = ( ^ [A3: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_def_raw
% 7.75/5.74 thf(fact_7763_max__def__raw,axiom,
% 7.75/5.74 ( ord_max_int
% 7.75/5.74 = ( ^ [A3: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B4 ) @ B4 @ A3 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max_def_raw
% 7.75/5.74 thf(fact_7764_numeral__code_I2_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 7.75/5.74 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(2)
% 7.75/5.74 thf(fact_7765_numeral__code_I2_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 7.75/5.74 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(2)
% 7.75/5.74 thf(fact_7766_numeral__code_I2_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 7.75/5.74 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(2)
% 7.75/5.74 thf(fact_7767_numeral__code_I2_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 7.75/5.74 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(2)
% 7.75/5.74 thf(fact_7768_numeral__code_I2_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 7.75/5.74 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(2)
% 7.75/5.74 thf(fact_7769_set__vebt__def,axiom,
% 7.75/5.74 ( vEBT_set_vebt
% 7.75/5.74 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % set_vebt_def
% 7.75/5.74 thf(fact_7770_strict__subset__divisors__dvd,axiom,
% 7.75/5.74 ! [A: complex,B: complex] :
% 7.75/5.74 ( ( ord_less_set_complex
% 7.75/5.74 @ ( collect_complex
% 7.75/5.74 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ A ) )
% 7.75/5.74 @ ( collect_complex
% 7.75/5.74 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ B ) ) )
% 7.75/5.74 = ( ( dvd_dvd_complex @ A @ B )
% 7.75/5.74 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % strict_subset_divisors_dvd
% 7.75/5.74 thf(fact_7771_strict__subset__divisors__dvd,axiom,
% 7.75/5.74 ! [A: nat,B: nat] :
% 7.75/5.74 ( ( ord_less_set_nat
% 7.75/5.74 @ ( collect_nat
% 7.75/5.74 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 7.75/5.74 @ ( collect_nat
% 7.75/5.74 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 7.75/5.74 = ( ( dvd_dvd_nat @ A @ B )
% 7.75/5.74 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % strict_subset_divisors_dvd
% 7.75/5.74 thf(fact_7772_strict__subset__divisors__dvd,axiom,
% 7.75/5.74 ! [A: int,B: int] :
% 7.75/5.74 ( ( ord_less_set_int
% 7.75/5.74 @ ( collect_int
% 7.75/5.74 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 7.75/5.74 @ ( collect_int
% 7.75/5.74 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 7.75/5.74 = ( ( dvd_dvd_int @ A @ B )
% 7.75/5.74 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % strict_subset_divisors_dvd
% 7.75/5.74 thf(fact_7773_lambda__one,axiom,
% 7.75/5.74 ( ( ^ [X2: rat] : X2 )
% 7.75/5.74 = ( times_times_rat @ one_one_rat ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_one
% 7.75/5.74 thf(fact_7774_lambda__one,axiom,
% 7.75/5.74 ( ( ^ [X2: assn] : X2 )
% 7.75/5.74 = ( times_times_assn @ one_one_assn ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_one
% 7.75/5.74 thf(fact_7775_lambda__one,axiom,
% 7.75/5.74 ( ( ^ [X2: real] : X2 )
% 7.75/5.74 = ( times_times_real @ one_one_real ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_one
% 7.75/5.74 thf(fact_7776_lambda__one,axiom,
% 7.75/5.74 ( ( ^ [X2: nat] : X2 )
% 7.75/5.74 = ( times_times_nat @ one_one_nat ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_one
% 7.75/5.74 thf(fact_7777_lambda__one,axiom,
% 7.75/5.74 ( ( ^ [X2: int] : X2 )
% 7.75/5.74 = ( times_times_int @ one_one_int ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_one
% 7.75/5.74 thf(fact_7778_lambda__one,axiom,
% 7.75/5.74 ( ( ^ [X2: code_integer] : X2 )
% 7.75/5.74 = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_one
% 7.75/5.74 thf(fact_7779_lambda__one,axiom,
% 7.75/5.74 ( ( ^ [X2: complex] : X2 )
% 7.75/5.74 = ( times_times_complex @ one_one_complex ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_one
% 7.75/5.74 thf(fact_7780_lambda__zero,axiom,
% 7.75/5.74 ( ( ^ [H: rat] : zero_zero_rat )
% 7.75/5.74 = ( times_times_rat @ zero_zero_rat ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_zero
% 7.75/5.74 thf(fact_7781_lambda__zero,axiom,
% 7.75/5.74 ( ( ^ [H: real] : zero_zero_real )
% 7.75/5.74 = ( times_times_real @ zero_zero_real ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_zero
% 7.75/5.74 thf(fact_7782_lambda__zero,axiom,
% 7.75/5.74 ( ( ^ [H: nat] : zero_zero_nat )
% 7.75/5.74 = ( times_times_nat @ zero_zero_nat ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_zero
% 7.75/5.74 thf(fact_7783_lambda__zero,axiom,
% 7.75/5.74 ( ( ^ [H: int] : zero_zero_int )
% 7.75/5.74 = ( times_times_int @ zero_zero_int ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_zero
% 7.75/5.74 thf(fact_7784_lambda__zero,axiom,
% 7.75/5.74 ( ( ^ [H: code_integer] : zero_z3403309356797280102nteger )
% 7.75/5.74 = ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_zero
% 7.75/5.74 thf(fact_7785_lambda__zero,axiom,
% 7.75/5.74 ( ( ^ [H: complex] : zero_zero_complex )
% 7.75/5.74 = ( times_times_complex @ zero_zero_complex ) ) ).
% 7.75/5.74
% 7.75/5.74 % lambda_zero
% 7.75/5.74 thf(fact_7786_mult__commute__abs,axiom,
% 7.75/5.74 ! [C: assn] :
% 7.75/5.74 ( ( ^ [X2: assn] : ( times_times_assn @ X2 @ C ) )
% 7.75/5.74 = ( times_times_assn @ C ) ) ).
% 7.75/5.74
% 7.75/5.74 % mult_commute_abs
% 7.75/5.74 thf(fact_7787_mult__commute__abs,axiom,
% 7.75/5.74 ! [C: real] :
% 7.75/5.74 ( ( ^ [X2: real] : ( times_times_real @ X2 @ C ) )
% 7.75/5.74 = ( times_times_real @ C ) ) ).
% 7.75/5.74
% 7.75/5.74 % mult_commute_abs
% 7.75/5.74 thf(fact_7788_mult__commute__abs,axiom,
% 7.75/5.74 ! [C: nat] :
% 7.75/5.74 ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
% 7.75/5.74 = ( times_times_nat @ C ) ) ).
% 7.75/5.74
% 7.75/5.74 % mult_commute_abs
% 7.75/5.74 thf(fact_7789_mult__commute__abs,axiom,
% 7.75/5.74 ! [C: int] :
% 7.75/5.74 ( ( ^ [X2: int] : ( times_times_int @ X2 @ C ) )
% 7.75/5.74 = ( times_times_int @ C ) ) ).
% 7.75/5.74
% 7.75/5.74 % mult_commute_abs
% 7.75/5.74 thf(fact_7790_mult__commute__abs,axiom,
% 7.75/5.74 ! [C: code_integer] :
% 7.75/5.74 ( ( ^ [X2: code_integer] : ( times_3573771949741848930nteger @ X2 @ C ) )
% 7.75/5.74 = ( times_3573771949741848930nteger @ C ) ) ).
% 7.75/5.74
% 7.75/5.74 % mult_commute_abs
% 7.75/5.74 thf(fact_7791_mult__commute__abs,axiom,
% 7.75/5.74 ! [C: complex] :
% 7.75/5.74 ( ( ^ [X2: complex] : ( times_times_complex @ X2 @ C ) )
% 7.75/5.74 = ( times_times_complex @ C ) ) ).
% 7.75/5.74
% 7.75/5.74 % mult_commute_abs
% 7.75/5.74 thf(fact_7792_subset__divisors__dvd,axiom,
% 7.75/5.74 ! [A: complex,B: complex] :
% 7.75/5.74 ( ( ord_le211207098394363844omplex
% 7.75/5.74 @ ( collect_complex
% 7.75/5.74 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ A ) )
% 7.75/5.74 @ ( collect_complex
% 7.75/5.74 @ ^ [C4: complex] : ( dvd_dvd_complex @ C4 @ B ) ) )
% 7.75/5.74 = ( dvd_dvd_complex @ A @ B ) ) ).
% 7.75/5.74
% 7.75/5.74 % subset_divisors_dvd
% 7.75/5.74 thf(fact_7793_subset__divisors__dvd,axiom,
% 7.75/5.74 ! [A: int,B: int] :
% 7.75/5.74 ( ( ord_less_eq_set_int
% 7.75/5.74 @ ( collect_int
% 7.75/5.74 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 7.75/5.74 @ ( collect_int
% 7.75/5.74 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 7.75/5.74 = ( dvd_dvd_int @ A @ B ) ) ).
% 7.75/5.74
% 7.75/5.74 % subset_divisors_dvd
% 7.75/5.74 thf(fact_7794_subset__divisors__dvd,axiom,
% 7.75/5.74 ! [A: nat,B: nat] :
% 7.75/5.74 ( ( ord_less_eq_set_nat
% 7.75/5.74 @ ( collect_nat
% 7.75/5.74 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 7.75/5.74 @ ( collect_nat
% 7.75/5.74 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 7.75/5.74 = ( dvd_dvd_nat @ A @ B ) ) ).
% 7.75/5.74
% 7.75/5.74 % subset_divisors_dvd
% 7.75/5.74 thf(fact_7795_less__set__def,axiom,
% 7.75/5.74 ( ord_less_set_nat
% 7.75/5.74 = ( ^ [A6: set_nat,B7: set_nat] :
% 7.75/5.74 ( ord_less_nat_o
% 7.75/5.74 @ ^ [X2: nat] : ( member_nat @ X2 @ A6 )
% 7.75/5.74 @ ^ [X2: nat] : ( member_nat @ X2 @ B7 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_set_def
% 7.75/5.74 thf(fact_7796_less__set__def,axiom,
% 7.75/5.74 ( ord_less_set_real
% 7.75/5.74 = ( ^ [A6: set_real,B7: set_real] :
% 7.75/5.74 ( ord_less_real_o
% 7.75/5.74 @ ^ [X2: real] : ( member_real @ X2 @ A6 )
% 7.75/5.74 @ ^ [X2: real] : ( member_real @ X2 @ B7 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_set_def
% 7.75/5.74 thf(fact_7797_less__set__def,axiom,
% 7.75/5.74 ( ord_less_set_int
% 7.75/5.74 = ( ^ [A6: set_int,B7: set_int] :
% 7.75/5.74 ( ord_less_int_o
% 7.75/5.74 @ ^ [X2: int] : ( member_int @ X2 @ A6 )
% 7.75/5.74 @ ^ [X2: int] : ( member_int @ X2 @ B7 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_set_def
% 7.75/5.74 thf(fact_7798_less__set__def,axiom,
% 7.75/5.74 ( ord_le3480810397992357184T_VEBT
% 7.75/5.74 = ( ^ [A6: set_VEBT_VEBT,B7: set_VEBT_VEBT] :
% 7.75/5.74 ( ord_less_VEBT_VEBT_o
% 7.75/5.74 @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ A6 )
% 7.75/5.74 @ ^ [X2: vEBT_VEBT] : ( member_VEBT_VEBT @ X2 @ B7 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_set_def
% 7.75/5.74 thf(fact_7799_less__set__def,axiom,
% 7.75/5.74 ( ord_less_set_complex
% 7.75/5.74 = ( ^ [A6: set_complex,B7: set_complex] :
% 7.75/5.74 ( ord_less_complex_o
% 7.75/5.74 @ ^ [X2: complex] : ( member_complex @ X2 @ A6 )
% 7.75/5.74 @ ^ [X2: complex] : ( member_complex @ X2 @ B7 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_set_def
% 7.75/5.74 thf(fact_7800_finite__divisors__int,axiom,
% 7.75/5.74 ! [I: int] :
% 7.75/5.74 ( ( I != zero_zero_int )
% 7.75/5.74 => ( finite_finite_int
% 7.75/5.74 @ ( collect_int
% 7.75/5.74 @ ^ [D: int] : ( dvd_dvd_int @ D @ I ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_divisors_int
% 7.75/5.74 thf(fact_7801_finite__M__bounded__by__nat,axiom,
% 7.75/5.74 ! [P: nat > $o,I: nat] :
% 7.75/5.74 ( finite_finite_nat
% 7.75/5.74 @ ( collect_nat
% 7.75/5.74 @ ^ [K3: nat] :
% 7.75/5.74 ( ( P @ K3 )
% 7.75/5.74 & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_M_bounded_by_nat
% 7.75/5.74 thf(fact_7802_nat__less__as__int,axiom,
% 7.75/5.74 ( ord_less_nat
% 7.75/5.74 = ( ^ [A3: nat,B4: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_less_as_int
% 7.75/5.74 thf(fact_7803_nat__leq__as__int,axiom,
% 7.75/5.74 ( ord_less_eq_nat
% 7.75/5.74 = ( ^ [A3: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_leq_as_int
% 7.75/5.74 thf(fact_7804_numeral__code_I3_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 7.75/5.74 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(3)
% 7.75/5.74 thf(fact_7805_numeral__code_I3_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 7.75/5.74 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(3)
% 7.75/5.74 thf(fact_7806_numeral__code_I3_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 7.75/5.74 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(3)
% 7.75/5.74 thf(fact_7807_numeral__code_I3_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 7.75/5.74 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(3)
% 7.75/5.74 thf(fact_7808_numeral__code_I3_J,axiom,
% 7.75/5.74 ! [N: num] :
% 7.75/5.74 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 7.75/5.74 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 7.75/5.74
% 7.75/5.74 % numeral_code(3)
% 7.75/5.74 thf(fact_7809_power__numeral__even,axiom,
% 7.75/5.74 ! [Z: assn,W: num] :
% 7.75/5.74 ( ( power_power_assn @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 7.75/5.74 = ( times_times_assn @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_even
% 7.75/5.74 thf(fact_7810_power__numeral__even,axiom,
% 7.75/5.74 ! [Z: real,W: num] :
% 7.75/5.74 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 7.75/5.74 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_even
% 7.75/5.74 thf(fact_7811_power__numeral__even,axiom,
% 7.75/5.74 ! [Z: nat,W: num] :
% 7.75/5.74 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 7.75/5.74 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_even
% 7.75/5.74 thf(fact_7812_power__numeral__even,axiom,
% 7.75/5.74 ! [Z: int,W: num] :
% 7.75/5.74 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 7.75/5.74 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_even
% 7.75/5.74 thf(fact_7813_power__numeral__even,axiom,
% 7.75/5.74 ! [Z: code_integer,W: num] :
% 7.75/5.74 ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 7.75/5.74 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_even
% 7.75/5.74 thf(fact_7814_power__numeral__even,axiom,
% 7.75/5.74 ! [Z: complex,W: num] :
% 7.75/5.74 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 7.75/5.74 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_even
% 7.75/5.74 thf(fact_7815_power__numeral__odd,axiom,
% 7.75/5.74 ! [Z: assn,W: num] :
% 7.75/5.74 ( ( power_power_assn @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 7.75/5.74 = ( times_times_assn @ ( times_times_assn @ Z @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_odd
% 7.75/5.74 thf(fact_7816_power__numeral__odd,axiom,
% 7.75/5.74 ! [Z: real,W: num] :
% 7.75/5.74 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 7.75/5.74 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_odd
% 7.75/5.74 thf(fact_7817_power__numeral__odd,axiom,
% 7.75/5.74 ! [Z: nat,W: num] :
% 7.75/5.74 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 7.75/5.74 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_odd
% 7.75/5.74 thf(fact_7818_power__numeral__odd,axiom,
% 7.75/5.74 ! [Z: int,W: num] :
% 7.75/5.74 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 7.75/5.74 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_odd
% 7.75/5.74 thf(fact_7819_power__numeral__odd,axiom,
% 7.75/5.74 ! [Z: code_integer,W: num] :
% 7.75/5.74 ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 7.75/5.74 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ Z @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_odd
% 7.75/5.74 thf(fact_7820_power__numeral__odd,axiom,
% 7.75/5.74 ! [Z: complex,W: num] :
% 7.75/5.74 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 7.75/5.74 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % power_numeral_odd
% 7.75/5.74 thf(fact_7821_nat__plus__as__int,axiom,
% 7.75/5.74 ( plus_plus_nat
% 7.75/5.74 = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_plus_as_int
% 7.75/5.74 thf(fact_7822_finite__divisors__nat,axiom,
% 7.75/5.74 ! [M: nat] :
% 7.75/5.74 ( ( ord_less_nat @ zero_zero_nat @ M )
% 7.75/5.74 => ( finite_finite_nat
% 7.75/5.74 @ ( collect_nat
% 7.75/5.74 @ ^ [D: nat] : ( dvd_dvd_nat @ D @ M ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_divisors_nat
% 7.75/5.74 thf(fact_7823_nat__times__as__int,axiom,
% 7.75/5.74 ( times_times_nat
% 7.75/5.74 = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_times_as_int
% 7.75/5.74 thf(fact_7824_nat__minus__as__int,axiom,
% 7.75/5.74 ( minus_minus_nat
% 7.75/5.74 = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_minus_as_int
% 7.75/5.74 thf(fact_7825_nat__div__as__int,axiom,
% 7.75/5.74 ( divide_divide_nat
% 7.75/5.74 = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_div_as_int
% 7.75/5.74 thf(fact_7826_nat__mod__as__int,axiom,
% 7.75/5.74 ( modulo_modulo_nat
% 7.75/5.74 = ( ^ [A3: nat,B4: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % nat_mod_as_int
% 7.75/5.74 thf(fact_7827_finite__roots__unity,axiom,
% 7.75/5.74 ! [N: nat] :
% 7.75/5.74 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 7.75/5.74 => ( finite_finite_real
% 7.75/5.74 @ ( collect_real
% 7.75/5.74 @ ^ [Z6: real] :
% 7.75/5.74 ( ( power_power_real @ Z6 @ N )
% 7.75/5.74 = one_one_real ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_roots_unity
% 7.75/5.74 thf(fact_7828_finite__roots__unity,axiom,
% 7.75/5.74 ! [N: nat] :
% 7.75/5.74 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 7.75/5.74 => ( finite3207457112153483333omplex
% 7.75/5.74 @ ( collect_complex
% 7.75/5.74 @ ^ [Z6: complex] :
% 7.75/5.74 ( ( power_power_complex @ Z6 @ N )
% 7.75/5.74 = one_one_complex ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_roots_unity
% 7.75/5.74 thf(fact_7829_finite__lists__length__eq,axiom,
% 7.75/5.74 ! [A2: set_VEBT_VEBT,N: nat] :
% 7.75/5.74 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.74 => ( finite3004134309566078307T_VEBT
% 7.75/5.74 @ ( collec5608196760682091941T_VEBT
% 7.75/5.74 @ ^ [Xs: list_VEBT_VEBT] :
% 7.75/5.74 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 7.75/5.74 = N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_eq
% 7.75/5.74 thf(fact_7830_finite__lists__length__eq,axiom,
% 7.75/5.74 ! [A2: set_complex,N: nat] :
% 7.75/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.74 => ( finite8712137658972009173omplex
% 7.75/5.74 @ ( collect_list_complex
% 7.75/5.74 @ ^ [Xs: list_complex] :
% 7.75/5.74 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ( size_s3451745648224563538omplex @ Xs )
% 7.75/5.74 = N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_eq
% 7.75/5.74 thf(fact_7831_finite__lists__length__eq,axiom,
% 7.75/5.74 ! [A2: set_Code_integer,N: nat] :
% 7.75/5.74 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.74 => ( finite1283093830868386564nteger
% 7.75/5.74 @ ( collec3483841146883906114nteger
% 7.75/5.74 @ ^ [Xs: list_Code_integer] :
% 7.75/5.74 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ( size_s3445333598471063425nteger @ Xs )
% 7.75/5.74 = N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_eq
% 7.75/5.74 thf(fact_7832_finite__lists__length__eq,axiom,
% 7.75/5.74 ! [A2: set_real,N: nat] :
% 7.75/5.74 ( ( finite_finite_real @ A2 )
% 7.75/5.74 => ( finite306553202115118035t_real
% 7.75/5.74 @ ( collect_list_real
% 7.75/5.74 @ ^ [Xs: list_real] :
% 7.75/5.74 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ( size_size_list_real @ Xs )
% 7.75/5.74 = N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_eq
% 7.75/5.74 thf(fact_7833_finite__lists__length__eq,axiom,
% 7.75/5.74 ! [A2: set_o,N: nat] :
% 7.75/5.74 ( ( finite_finite_o @ A2 )
% 7.75/5.74 => ( finite_finite_list_o
% 7.75/5.74 @ ( collect_list_o
% 7.75/5.74 @ ^ [Xs: list_o] :
% 7.75/5.74 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ( size_size_list_o @ Xs )
% 7.75/5.74 = N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_eq
% 7.75/5.74 thf(fact_7834_finite__lists__length__eq,axiom,
% 7.75/5.74 ! [A2: set_int,N: nat] :
% 7.75/5.74 ( ( finite_finite_int @ A2 )
% 7.75/5.74 => ( finite3922522038869484883st_int
% 7.75/5.74 @ ( collect_list_int
% 7.75/5.74 @ ^ [Xs: list_int] :
% 7.75/5.74 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ( size_size_list_int @ Xs )
% 7.75/5.74 = N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_eq
% 7.75/5.74 thf(fact_7835_finite__lists__length__eq,axiom,
% 7.75/5.74 ! [A2: set_nat,N: nat] :
% 7.75/5.74 ( ( finite_finite_nat @ A2 )
% 7.75/5.74 => ( finite8100373058378681591st_nat
% 7.75/5.74 @ ( collect_list_nat
% 7.75/5.74 @ ^ [Xs: list_nat] :
% 7.75/5.74 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ( size_size_list_nat @ Xs )
% 7.75/5.74 = N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_eq
% 7.75/5.74 thf(fact_7836_diff__nat__eq__if,axiom,
% 7.75/5.74 ! [Z5: int,Z: int] :
% 7.75/5.74 ( ( ( ord_less_int @ Z5 @ zero_zero_int )
% 7.75/5.74 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) )
% 7.75/5.74 = ( nat2 @ Z ) ) )
% 7.75/5.74 & ( ~ ( ord_less_int @ Z5 @ zero_zero_int )
% 7.75/5.74 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) )
% 7.75/5.74 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z5 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z5 ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % diff_nat_eq_if
% 7.75/5.74 thf(fact_7837_finite__lists__length__le,axiom,
% 7.75/5.74 ! [A2: set_VEBT_VEBT,N: nat] :
% 7.75/5.74 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.74 => ( finite3004134309566078307T_VEBT
% 7.75/5.74 @ ( collec5608196760682091941T_VEBT
% 7.75/5.74 @ ^ [Xs: list_VEBT_VEBT] :
% 7.75/5.74 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_le
% 7.75/5.74 thf(fact_7838_finite__lists__length__le,axiom,
% 7.75/5.74 ! [A2: set_complex,N: nat] :
% 7.75/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.74 => ( finite8712137658972009173omplex
% 7.75/5.74 @ ( collect_list_complex
% 7.75/5.74 @ ^ [Xs: list_complex] :
% 7.75/5.74 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_le
% 7.75/5.74 thf(fact_7839_finite__lists__length__le,axiom,
% 7.75/5.74 ! [A2: set_Code_integer,N: nat] :
% 7.75/5.74 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.74 => ( finite1283093830868386564nteger
% 7.75/5.74 @ ( collec3483841146883906114nteger
% 7.75/5.74 @ ^ [Xs: list_Code_integer] :
% 7.75/5.74 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ord_less_eq_nat @ ( size_s3445333598471063425nteger @ Xs ) @ N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_le
% 7.75/5.74 thf(fact_7840_finite__lists__length__le,axiom,
% 7.75/5.74 ! [A2: set_real,N: nat] :
% 7.75/5.74 ( ( finite_finite_real @ A2 )
% 7.75/5.74 => ( finite306553202115118035t_real
% 7.75/5.74 @ ( collect_list_real
% 7.75/5.74 @ ^ [Xs: list_real] :
% 7.75/5.74 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_le
% 7.75/5.74 thf(fact_7841_finite__lists__length__le,axiom,
% 7.75/5.74 ! [A2: set_o,N: nat] :
% 7.75/5.74 ( ( finite_finite_o @ A2 )
% 7.75/5.74 => ( finite_finite_list_o
% 7.75/5.74 @ ( collect_list_o
% 7.75/5.74 @ ^ [Xs: list_o] :
% 7.75/5.74 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_le
% 7.75/5.74 thf(fact_7842_finite__lists__length__le,axiom,
% 7.75/5.74 ! [A2: set_int,N: nat] :
% 7.75/5.74 ( ( finite_finite_int @ A2 )
% 7.75/5.74 => ( finite3922522038869484883st_int
% 7.75/5.74 @ ( collect_list_int
% 7.75/5.74 @ ^ [Xs: list_int] :
% 7.75/5.74 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_le
% 7.75/5.74 thf(fact_7843_finite__lists__length__le,axiom,
% 7.75/5.74 ! [A2: set_nat,N: nat] :
% 7.75/5.74 ( ( finite_finite_nat @ A2 )
% 7.75/5.74 => ( finite8100373058378681591st_nat
% 7.75/5.74 @ ( collect_list_nat
% 7.75/5.74 @ ^ [Xs: list_nat] :
% 7.75/5.74 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 7.75/5.74 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_lists_length_le
% 7.75/5.74 thf(fact_7844_set__decode__def,axiom,
% 7.75/5.74 ( nat_set_decode
% 7.75/5.74 = ( ^ [X2: nat] :
% 7.75/5.74 ( collect_nat
% 7.75/5.74 @ ^ [N3: nat] :
% 7.75/5.74 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % set_decode_def
% 7.75/5.74 thf(fact_7845_pochhammer__code,axiom,
% 7.75/5.74 ( comm_s4028243227959126397er_rat
% 7.75/5.74 = ( ^ [A3: rat,N3: nat] :
% 7.75/5.74 ( if_rat @ ( N3 = zero_zero_nat ) @ one_one_rat
% 7.75/5.74 @ ( set_fo1949268297981939178at_rat
% 7.75/5.74 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 7.75/5.74 @ zero_zero_nat
% 7.75/5.74 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 7.75/5.74 @ one_one_rat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % pochhammer_code
% 7.75/5.74 thf(fact_7846_pochhammer__code,axiom,
% 7.75/5.74 ( comm_s8582702949713902594nteger
% 7.75/5.74 = ( ^ [A3: code_integer,N3: nat] :
% 7.75/5.74 ( if_Code_integer @ ( N3 = zero_zero_nat ) @ one_one_Code_integer
% 7.75/5.74 @ ( set_fo1084959871951514735nteger
% 7.75/5.74 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A3 @ ( semiri4939895301339042750nteger @ O ) ) )
% 7.75/5.74 @ zero_zero_nat
% 7.75/5.74 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 7.75/5.74 @ one_one_Code_integer ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % pochhammer_code
% 7.75/5.74 thf(fact_7847_pochhammer__code,axiom,
% 7.75/5.74 ( comm_s7457072308508201937r_real
% 7.75/5.74 = ( ^ [A3: real,N3: nat] :
% 7.75/5.74 ( if_real @ ( N3 = zero_zero_nat ) @ one_one_real
% 7.75/5.74 @ ( set_fo3111899725591712190t_real
% 7.75/5.74 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 7.75/5.74 @ zero_zero_nat
% 7.75/5.74 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 7.75/5.74 @ one_one_real ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % pochhammer_code
% 7.75/5.74 thf(fact_7848_pochhammer__code,axiom,
% 7.75/5.74 ( comm_s4660882817536571857er_int
% 7.75/5.74 = ( ^ [A3: int,N3: nat] :
% 7.75/5.74 ( if_int @ ( N3 = zero_zero_nat ) @ one_one_int
% 7.75/5.74 @ ( set_fo2581907887559384638at_int
% 7.75/5.74 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 7.75/5.74 @ zero_zero_nat
% 7.75/5.74 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 7.75/5.74 @ one_one_int ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % pochhammer_code
% 7.75/5.74 thf(fact_7849_pochhammer__code,axiom,
% 7.75/5.74 ( comm_s2602460028002588243omplex
% 7.75/5.74 = ( ^ [A3: complex,N3: nat] :
% 7.75/5.74 ( if_complex @ ( N3 = zero_zero_nat ) @ one_one_complex
% 7.75/5.74 @ ( set_fo1517530859248394432omplex
% 7.75/5.74 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 7.75/5.74 @ zero_zero_nat
% 7.75/5.74 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 7.75/5.74 @ one_one_complex ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % pochhammer_code
% 7.75/5.74 thf(fact_7850_pochhammer__code,axiom,
% 7.75/5.74 ( comm_s4663373288045622133er_nat
% 7.75/5.74 = ( ^ [A3: nat,N3: nat] :
% 7.75/5.74 ( if_nat @ ( N3 = zero_zero_nat ) @ one_one_nat
% 7.75/5.74 @ ( set_fo2584398358068434914at_nat
% 7.75/5.74 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 7.75/5.74 @ zero_zero_nat
% 7.75/5.74 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 7.75/5.74 @ one_one_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % pochhammer_code
% 7.75/5.74 thf(fact_7851_vebt__buildup_Osimps_I3_J,axiom,
% 7.75/5.74 ! [Va2: nat] :
% 7.75/5.74 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_buildup.simps(3)
% 7.75/5.74 thf(fact_7852_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I3_J,axiom,
% 7.75/5.74 ! [Va2: nat] :
% 7.75/5.74 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 7.75/5.74 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(3)
% 7.75/5.74 thf(fact_7853_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I3_J,axiom,
% 7.75/5.74 ! [Va2: nat] :
% 7.75/5.74 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 7.75/5.74 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va2 ) ) )
% 7.75/5.74 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(3)
% 7.75/5.74 thf(fact_7854_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 7.75/5.74 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ X )
% 7.75/5.74 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( 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 ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.naive_member.simps(3)
% 7.75/5.74 thf(fact_7855_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Oelims,axiom,
% 7.75/5.74 ! [X: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_V8346862874174094_d_u_p @ X )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ( X = zero_zero_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 7.75/5.74 => ( ( ( X
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 7.75/5.74 => ~ ! [Va: nat] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 7.75/5.74 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.elims
% 7.75/5.74 thf(fact_7856_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Oelims,axiom,
% 7.75/5.74 ! [X: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_V8646137997579335489_i_l_d @ X )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ( X = zero_zero_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 => ( ( ( X
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 => ~ ! [Va: nat] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 7.75/5.74 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.elims
% 7.75/5.74 thf(fact_7857_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 7.75/5.74 ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X )
% 7.75/5.74 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( 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 ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.membermima.simps(5)
% 7.75/5.74 thf(fact_7858_vebt__buildup_Oelims,axiom,
% 7.75/5.74 ! [X: nat,Y: vEBT_VEBT] :
% 7.75/5.74 ( ( ( vEBT_vebt_buildup @ X )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ( X = zero_zero_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Leaf @ $false @ $false ) ) )
% 7.75/5.74 => ( ( ( X
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Leaf @ $false @ $false ) ) )
% 7.75/5.74 => ~ ! [Va: nat] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( 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 ) ) ) ) ) ) )
% 7.75/5.74 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_buildup.elims
% 7.75/5.74 thf(fact_7859_vebt__member_Osimps_I5_J,axiom,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( ( X != Mi3 )
% 7.75/5.74 => ( ( X != Ma )
% 7.75/5.74 => ( ~ ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 & ( ~ ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Ma @ X )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma @ X )
% 7.75/5.74 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_member.simps(5)
% 7.75/5.74 thf(fact_7860_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ X )
% 7.75/5.74 = ( ( X = Mi3 )
% 7.75/5.74 | ( X = Ma )
% 7.75/5.74 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 => ( 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 ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.membermima.simps(4)
% 7.75/5.74 thf(fact_7861_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.74 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa3 )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) )
% 7.75/5.74 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [S2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 7.75/5.74 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.naive_member.elims(3)
% 7.75/5.74 thf(fact_7862_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.74 ( ( vEBT_V5719532721284313246member @ X @ Xa3 )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ~ ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) )
% 7.75/5.74 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [S2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 7.75/5.74 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.naive_member.elims(2)
% 7.75/5.74 thf(fact_7863_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: $o] :
% 7.75/5.74 ( ( ( vEBT_V5719532721284313246member @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( ~ ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) ) ) )
% 7.75/5.74 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 7.75/5.74 => Y )
% 7.75/5.74 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [S2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.naive_member.elims(1)
% 7.75/5.74 thf(fact_7864_less__max__iff__disj,axiom,
% 7.75/5.74 ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 7.75/5.74 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 7.75/5.74 = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 7.75/5.74 | ( ord_le72135733267957522d_enat @ Z @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_max_iff_disj
% 7.75/5.74 thf(fact_7865_less__max__iff__disj,axiom,
% 7.75/5.74 ! [Z: real,X: real,Y: real] :
% 7.75/5.74 ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 7.75/5.74 = ( ( ord_less_real @ Z @ X )
% 7.75/5.74 | ( ord_less_real @ Z @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_max_iff_disj
% 7.75/5.74 thf(fact_7866_less__max__iff__disj,axiom,
% 7.75/5.74 ! [Z: rat,X: rat,Y: rat] :
% 7.75/5.74 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 7.75/5.74 = ( ( ord_less_rat @ Z @ X )
% 7.75/5.74 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_max_iff_disj
% 7.75/5.74 thf(fact_7867_less__max__iff__disj,axiom,
% 7.75/5.74 ! [Z: num,X: num,Y: num] :
% 7.75/5.74 ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 7.75/5.74 = ( ( ord_less_num @ Z @ X )
% 7.75/5.74 | ( ord_less_num @ Z @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_max_iff_disj
% 7.75/5.74 thf(fact_7868_less__max__iff__disj,axiom,
% 7.75/5.74 ! [Z: nat,X: nat,Y: nat] :
% 7.75/5.74 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 7.75/5.74 = ( ( ord_less_nat @ Z @ X )
% 7.75/5.74 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_max_iff_disj
% 7.75/5.74 thf(fact_7869_less__max__iff__disj,axiom,
% 7.75/5.74 ! [Z: int,X: int,Y: int] :
% 7.75/5.74 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 7.75/5.74 = ( ( ord_less_int @ Z @ X )
% 7.75/5.74 | ( ord_less_int @ Z @ Y ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % less_max_iff_disj
% 7.75/5.74 thf(fact_7870_max_Ostrict__boundedE,axiom,
% 7.75/5.74 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 7.75/5.74 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 7.75/5.74 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 7.75/5.74 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_boundedE
% 7.75/5.74 thf(fact_7871_max_Ostrict__boundedE,axiom,
% 7.75/5.74 ! [B: real,C: real,A: real] :
% 7.75/5.74 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 7.75/5.74 => ~ ( ( ord_less_real @ B @ A )
% 7.75/5.74 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_boundedE
% 7.75/5.74 thf(fact_7872_max_Ostrict__boundedE,axiom,
% 7.75/5.74 ! [B: rat,C: rat,A: rat] :
% 7.75/5.74 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 7.75/5.74 => ~ ( ( ord_less_rat @ B @ A )
% 7.75/5.74 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_boundedE
% 7.75/5.74 thf(fact_7873_max_Ostrict__boundedE,axiom,
% 7.75/5.74 ! [B: num,C: num,A: num] :
% 7.75/5.74 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 7.75/5.74 => ~ ( ( ord_less_num @ B @ A )
% 7.75/5.74 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_boundedE
% 7.75/5.74 thf(fact_7874_max_Ostrict__boundedE,axiom,
% 7.75/5.74 ! [B: nat,C: nat,A: nat] :
% 7.75/5.74 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 7.75/5.74 => ~ ( ( ord_less_nat @ B @ A )
% 7.75/5.74 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_boundedE
% 7.75/5.74 thf(fact_7875_max_Ostrict__boundedE,axiom,
% 7.75/5.74 ! [B: int,C: int,A: int] :
% 7.75/5.74 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 7.75/5.74 => ~ ( ( ord_less_int @ B @ A )
% 7.75/5.74 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_boundedE
% 7.75/5.74 thf(fact_7876_max_Ostrict__order__iff,axiom,
% 7.75/5.74 ( ord_le72135733267957522d_enat
% 7.75/5.74 = ( ^ [B4: extended_enat,A3: extended_enat] :
% 7.75/5.74 ( ( A3
% 7.75/5.74 = ( ord_ma741700101516333627d_enat @ A3 @ B4 ) )
% 7.75/5.74 & ( A3 != B4 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_order_iff
% 7.75/5.74 thf(fact_7877_max_Ostrict__order__iff,axiom,
% 7.75/5.74 ( ord_less_real
% 7.75/5.74 = ( ^ [B4: real,A3: real] :
% 7.75/5.74 ( ( A3
% 7.75/5.74 = ( ord_max_real @ A3 @ B4 ) )
% 7.75/5.74 & ( A3 != B4 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_order_iff
% 7.75/5.74 thf(fact_7878_max_Ostrict__order__iff,axiom,
% 7.75/5.74 ( ord_less_rat
% 7.75/5.74 = ( ^ [B4: rat,A3: rat] :
% 7.75/5.74 ( ( A3
% 7.75/5.74 = ( ord_max_rat @ A3 @ B4 ) )
% 7.75/5.74 & ( A3 != B4 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_order_iff
% 7.75/5.74 thf(fact_7879_max_Ostrict__order__iff,axiom,
% 7.75/5.74 ( ord_less_num
% 7.75/5.74 = ( ^ [B4: num,A3: num] :
% 7.75/5.74 ( ( A3
% 7.75/5.74 = ( ord_max_num @ A3 @ B4 ) )
% 7.75/5.74 & ( A3 != B4 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_order_iff
% 7.75/5.74 thf(fact_7880_max_Ostrict__order__iff,axiom,
% 7.75/5.74 ( ord_less_nat
% 7.75/5.74 = ( ^ [B4: nat,A3: nat] :
% 7.75/5.74 ( ( A3
% 7.75/5.74 = ( ord_max_nat @ A3 @ B4 ) )
% 7.75/5.74 & ( A3 != B4 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_order_iff
% 7.75/5.74 thf(fact_7881_max_Ostrict__order__iff,axiom,
% 7.75/5.74 ( ord_less_int
% 7.75/5.74 = ( ^ [B4: int,A3: int] :
% 7.75/5.74 ( ( A3
% 7.75/5.74 = ( ord_max_int @ A3 @ B4 ) )
% 7.75/5.74 & ( A3 != B4 ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_order_iff
% 7.75/5.74 thf(fact_7882_max_Ostrict__coboundedI1,axiom,
% 7.75/5.74 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 7.75/5.74 ( ( ord_le72135733267957522d_enat @ C @ A )
% 7.75/5.74 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI1
% 7.75/5.74 thf(fact_7883_max_Ostrict__coboundedI1,axiom,
% 7.75/5.74 ! [C: real,A: real,B: real] :
% 7.75/5.74 ( ( ord_less_real @ C @ A )
% 7.75/5.74 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI1
% 7.75/5.74 thf(fact_7884_max_Ostrict__coboundedI1,axiom,
% 7.75/5.74 ! [C: rat,A: rat,B: rat] :
% 7.75/5.74 ( ( ord_less_rat @ C @ A )
% 7.75/5.74 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI1
% 7.75/5.74 thf(fact_7885_max_Ostrict__coboundedI1,axiom,
% 7.75/5.74 ! [C: num,A: num,B: num] :
% 7.75/5.74 ( ( ord_less_num @ C @ A )
% 7.75/5.74 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI1
% 7.75/5.74 thf(fact_7886_max_Ostrict__coboundedI1,axiom,
% 7.75/5.74 ! [C: nat,A: nat,B: nat] :
% 7.75/5.74 ( ( ord_less_nat @ C @ A )
% 7.75/5.74 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI1
% 7.75/5.74 thf(fact_7887_max_Ostrict__coboundedI1,axiom,
% 7.75/5.74 ! [C: int,A: int,B: int] :
% 7.75/5.74 ( ( ord_less_int @ C @ A )
% 7.75/5.74 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI1
% 7.75/5.74 thf(fact_7888_max_Ostrict__coboundedI2,axiom,
% 7.75/5.74 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 7.75/5.74 ( ( ord_le72135733267957522d_enat @ C @ B )
% 7.75/5.74 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI2
% 7.75/5.74 thf(fact_7889_max_Ostrict__coboundedI2,axiom,
% 7.75/5.74 ! [C: real,B: real,A: real] :
% 7.75/5.74 ( ( ord_less_real @ C @ B )
% 7.75/5.74 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI2
% 7.75/5.74 thf(fact_7890_max_Ostrict__coboundedI2,axiom,
% 7.75/5.74 ! [C: rat,B: rat,A: rat] :
% 7.75/5.74 ( ( ord_less_rat @ C @ B )
% 7.75/5.74 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI2
% 7.75/5.74 thf(fact_7891_max_Ostrict__coboundedI2,axiom,
% 7.75/5.74 ! [C: num,B: num,A: num] :
% 7.75/5.74 ( ( ord_less_num @ C @ B )
% 7.75/5.74 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI2
% 7.75/5.74 thf(fact_7892_max_Ostrict__coboundedI2,axiom,
% 7.75/5.74 ! [C: nat,B: nat,A: nat] :
% 7.75/5.74 ( ( ord_less_nat @ C @ B )
% 7.75/5.74 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI2
% 7.75/5.74 thf(fact_7893_max_Ostrict__coboundedI2,axiom,
% 7.75/5.74 ! [C: int,B: int,A: int] :
% 7.75/5.74 ( ( ord_less_int @ C @ B )
% 7.75/5.74 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % max.strict_coboundedI2
% 7.75/5.74 thf(fact_7894_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.74 ( ( vEBT_VEBT_membermima @ X @ Xa3 )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat] :
% 7.75/5.74 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 7.75/5.74 => ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Vc: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 7.75/5.74 => ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 )
% 7.75/5.74 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 7.75/5.74 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Vd2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) )
% 7.75/5.74 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.membermima.elims(2)
% 7.75/5.74 thf(fact_7895_vebt__member_Oelims_I2_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.74 ( ( vEBT_vebt_member @ X @ Xa3 )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ~ ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ~ ( ( Xa3 != Mi )
% 7.75/5.74 => ( ( Xa3 != Ma2 )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_member.elims(2)
% 7.75/5.74 thf(fact_7896_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: $o] :
% 7.75/5.74 ( ( ( vEBT_VEBT_membermima @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [Uu2: $o,Uv2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.74 => Y )
% 7.75/5.74 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 7.75/5.74 => Y )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat] :
% 7.75/5.74 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 ) ) ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Vc: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 )
% 7.75/5.74 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 7.75/5.74 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Vd2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.membermima.elims(1)
% 7.75/5.74 thf(fact_7897_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.74 ( ~ ( vEBT_VEBT_membermima @ X @ Xa3 )
% 7.75/5.74 => ( ! [Uu2: $o,Uv2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.74 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat] :
% 7.75/5.74 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 7.75/5.74 => ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Vc: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 7.75/5.74 => ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 )
% 7.75/5.74 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 7.75/5.74 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Vd2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) )
% 7.75/5.74 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.membermima.elims(3)
% 7.75/5.74 thf(fact_7898_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,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = Mi3 ) @ 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 @ Mi3 ) @ 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 @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(5)
% 7.75/5.74 thf(fact_7899_vebt__insert_Osimps_I5_J,axiom,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_VEBT_VEBT
% 7.75/5.74 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 & ~ ( ( X = Mi3 )
% 7.75/5.74 | ( X = Ma ) ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ X @ Mi3 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_insert.simps(5)
% 7.75/5.74 thf(fact_7900_vebt__member_Oelims_I1_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: $o] :
% 7.75/5.74 ( ( ( vEBT_vebt_member @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( ~ ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) ) ) )
% 7.75/5.74 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => Y )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 7.75/5.74 => Y )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) )
% 7.75/5.74 => Y )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( ~ ( ( Xa3 != Mi )
% 7.75/5.74 => ( ( Xa3 != Ma2 )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_member.elims(1)
% 7.75/5.74 thf(fact_7901_vebt__member_Oelims_I3_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.74 ( ~ ( vEBT_vebt_member @ X @ Xa3 )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) )
% 7.75/5.74 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Xa3 != Mi )
% 7.75/5.74 => ( ( Xa3 != Ma2 )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_member.elims(3)
% 7.75/5.74 thf(fact_7902_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,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa3 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 7.75/5.74 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa3 = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa3 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa3 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.elims
% 7.75/5.74 thf(fact_7903_vebt__insert_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: vEBT_VEBT] :
% 7.75/5.74 ( ( ( vEBT_vebt_insert @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ~ ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 7.75/5.74 & ( ( Xa3 != one_one_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) ) ) ) ) ) )
% 7.75/5.74 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) ) )
% 7.75/5.74 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) )
% 7.75/5.74 => ( ! [V3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa3 @ Xa3 ) ) @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( if_VEBT_VEBT
% 7.75/5.74 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 & ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Xa3 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_insert.elims
% 7.75/5.74 thf(fact_7904_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I7_J,axiom,
% 7.75/5.74 ! [Ma: nat,X: nat,Mi3: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( ord_less_nat @ Ma @ X )
% 7.75/5.74 => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma @ X )
% 7.75/5.74 => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(7)
% 7.75/5.74 thf(fact_7905_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I6_J,axiom,
% 7.75/5.74 ! [X: nat,Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(6)
% 7.75/5.74 thf(fact_7906_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I7_J,axiom,
% 7.75/5.74 ! [X: nat,Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 | ( ord_less_nat @ Ma @ X ) )
% 7.75/5.74 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 | ( ord_less_nat @ Ma @ X ) )
% 7.75/5.74 => ( ( ( ( X = Mi3 )
% 7.75/5.74 & ( X = Ma ) )
% 7.75/5.74 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ( X = Mi3 )
% 7.75/5.74 & ( X = Ma ) )
% 7.75/5.74 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(7)
% 7.75/5.74 thf(fact_7907_vebt__pred_Osimps_I7_J,axiom,
% 7.75/5.74 ! [Ma: nat,X: nat,Mi3: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( ord_less_nat @ Ma @ X )
% 7.75/5.74 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( some_nat @ Ma ) ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma @ X )
% 7.75/5.74 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( if_option_nat @ ( ord_less_nat @ Mi3 @ X ) @ ( some_nat @ Mi3 ) @ none_nat )
% 7.75/5.74 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ none_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_pred.simps(7)
% 7.75/5.74 thf(fact_7908_vebt__succ_Osimps_I6_J,axiom,
% 7.75/5.74 ! [X: nat,Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( some_nat @ Mi3 ) ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ none_nat
% 7.75/5.74 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ none_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_succ.simps(6)
% 7.75/5.74 thf(fact_7909_vebt__delete_Osimps_I7_J,axiom,
% 7.75/5.74 ! [X: nat,Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.75/5.74 ( ( ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 | ( ord_less_nat @ Ma @ X ) )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) )
% 7.75/5.74 & ( ~ ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 | ( ord_less_nat @ Ma @ X ) )
% 7.75/5.74 => ( ( ( ( X = Mi3 )
% 7.75/5.74 & ( X = Ma ) )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) )
% 7.75/5.74 & ( ~ ( ( X = Mi3 )
% 7.75/5.74 & ( X = Ma ) )
% 7.75/5.74 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( X = Mi3 )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 = Ma ) )
% 7.75/5.74 & ( ( X != Mi3 )
% 7.75/5.74 => ( X = Ma ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ ( suc @ ( suc @ Va2 ) )
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( X = Mi3 )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 = Ma ) )
% 7.75/5.74 & ( ( X != Mi3 )
% 7.75/5.74 => ( X = Ma ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma ) ) )
% 7.75/5.74 @ ( suc @ ( suc @ Va2 ) )
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ Summary ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_delete.simps(7)
% 7.75/5.74 thf(fact_7910_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [Uu2: $o,Uv2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [A5: $o,Uw2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ? [Va: nat] :
% 7.75/5.74 ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( Y = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.elims
% 7.75/5.74 thf(fact_7911_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [Uu2: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [Uv2: $o,Uw2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( ? [N2: nat] :
% 7.75/5.74 ( Xa3
% 7.75/5.74 = ( suc @ N2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ~ ( ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( Y = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.elims
% 7.75/5.74 thf(fact_7912_vebt__delete_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: vEBT_VEBT] :
% 7.75/5.74 ( ( ( vEBT_vebt_delete @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Leaf @ $false @ B2 ) ) ) )
% 7.75/5.74 => ( ! [A5: $o] :
% 7.75/5.74 ( ? [B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Leaf @ A5 @ $false ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ? [N2: nat] :
% 7.75/5.74 ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ N2 ) ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 7.75/5.74 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ~ ( ( ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 7.75/5.74 & ( ~ ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 => ( ( ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 7.75/5.74 & ( ~ ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa3 = Mi ) @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ Mi )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( Xa3 = Mi )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 7.75/5.74 = Ma2 ) )
% 7.75/5.74 & ( ( Xa3 != Mi )
% 7.75/5.74 => ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( if_nat @ ( Xa3 = Mi ) @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ Mi )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma2 ) ) )
% 7.75/5.74 @ ( suc @ ( suc @ Va ) )
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa3 = Mi ) @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ Mi )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( Xa3 = Mi )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 7.75/5.74 = Ma2 ) )
% 7.75/5.74 & ( ( Xa3 != Mi )
% 7.75/5.74 => ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma2 ) ) )
% 7.75/5.74 @ ( suc @ ( suc @ Va ) )
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ Summary2 ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_delete.elims
% 7.75/5.74 thf(fact_7913_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_V1232361888498592333_e_t_e @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ? [N2: nat] :
% 7.75/5.74 ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ N2 ) ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ~ ( ( ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 => ( Y = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 => ( ( ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 => ( Y = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.elims
% 7.75/5.74 thf(fact_7914_vebt__pred_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: option_nat] :
% 7.75/5.74 ( ( ( vEBT_vebt_pred @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [Uu2: $o,Uv2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y != none_nat ) ) )
% 7.75/5.74 => ( ! [A5: $o] :
% 7.75/5.74 ( ? [Uw2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ~ ( ( A5
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.74 & ( ~ A5
% 7.75/5.74 => ( Y = none_nat ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ? [Va: nat] :
% 7.75/5.74 ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ~ ( ( B2
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.74 & ( ~ B2
% 7.75/5.74 => ( ( A5
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.74 & ( ~ A5
% 7.75/5.74 => ( Y = none_nat ) ) ) ) ) ) )
% 7.75/5.74 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 7.75/5.74 => ( Y != none_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 7.75/5.74 => ( Y != none_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 7.75/5.74 => ( Y != none_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ Ma2 ) ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( 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 @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( if_option_nat @ ( ord_less_nat @ Mi @ Xa3 ) @ ( some_nat @ Mi ) @ none_nat )
% 7.75/5.74 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_pred.elims
% 7.75/5.74 thf(fact_7915_vebt__succ_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: option_nat] :
% 7.75/5.74 ( ( ( vEBT_vebt_succ @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ! [Uu2: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ~ ( ( B2
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.74 & ( ~ B2
% 7.75/5.74 => ( Y = none_nat ) ) ) ) )
% 7.75/5.74 => ( ( ? [Uv2: $o,Uw2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( ? [N2: nat] :
% 7.75/5.74 ( Xa3
% 7.75/5.74 = ( suc @ N2 ) )
% 7.75/5.74 => ( Y != none_nat ) ) )
% 7.75/5.74 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( Y != none_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) )
% 7.75/5.74 => ( Y != none_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 7.75/5.74 => ( Y != none_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ~ ( ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ Mi ) ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( 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 @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ none_nat
% 7.75/5.74 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_succ.elims
% 7.75/5.74 thf(fact_7916_of__int__code__if,axiom,
% 7.75/5.74 ( ring_1_of_int_int
% 7.75/5.74 = ( ^ [K3: int] :
% 7.75/5.74 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 7.75/5.74 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 7.75/5.74 @ ( if_int
% 7.75/5.74 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.74 = zero_zero_int )
% 7.75/5.74 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_int_code_if
% 7.75/5.74 thf(fact_7917_of__int__code__if,axiom,
% 7.75/5.74 ( ring_1_of_int_real
% 7.75/5.74 = ( ^ [K3: int] :
% 7.75/5.74 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 7.75/5.74 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 7.75/5.74 @ ( if_real
% 7.75/5.74 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.74 = zero_zero_int )
% 7.75/5.74 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_int_code_if
% 7.75/5.74 thf(fact_7918_of__int__code__if,axiom,
% 7.75/5.74 ( ring_18347121197199848620nteger
% 7.75/5.74 = ( ^ [K3: int] :
% 7.75/5.74 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 7.75/5.74 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 7.75/5.74 @ ( if_Code_integer
% 7.75/5.74 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.74 = zero_zero_int )
% 7.75/5.74 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_int_code_if
% 7.75/5.74 thf(fact_7919_of__int__code__if,axiom,
% 7.75/5.74 ( ring_17405671764205052669omplex
% 7.75/5.74 = ( ^ [K3: int] :
% 7.75/5.74 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 7.75/5.74 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 7.75/5.74 @ ( if_complex
% 7.75/5.74 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.74 = zero_zero_int )
% 7.75/5.74 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_int_code_if
% 7.75/5.74 thf(fact_7920_of__int__code__if,axiom,
% 7.75/5.74 ( ring_1_of_int_rat
% 7.75/5.74 = ( ^ [K3: int] :
% 7.75/5.74 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 7.75/5.74 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 7.75/5.74 @ ( if_rat
% 7.75/5.74 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.75/5.74 = zero_zero_int )
% 7.75/5.74 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % of_int_code_if
% 7.75/5.74 thf(fact_7921_lowi__hT,axiom,
% 7.75/5.74 ! [X: nat,N: nat] :
% 7.75/5.74 ( time_htt_nat @ one_one_assn @ ( vEBT_VEBT_lowi @ X @ N )
% 7.75/5.74 @ ^ [R5: nat] :
% 7.75/5.74 ( pure_assn
% 7.75/5.74 @ ( R5
% 7.75/5.74 = ( vEBT_VEBT_low @ X @ N ) ) )
% 7.75/5.74 @ one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % lowi_hT
% 7.75/5.74 thf(fact_7922_highi__hT,axiom,
% 7.75/5.74 ! [X: nat,N: nat] :
% 7.75/5.74 ( time_htt_nat @ one_one_assn @ ( vEBT_VEBT_highi @ X @ N )
% 7.75/5.74 @ ^ [R5: nat] :
% 7.75/5.74 ( pure_assn
% 7.75/5.74 @ ( R5
% 7.75/5.74 = ( vEBT_VEBT_high @ X @ N ) ) )
% 7.75/5.74 @ one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % highi_hT
% 7.75/5.74 thf(fact_7923_div__half__nat,axiom,
% 7.75/5.74 ! [Y: nat,X: nat] :
% 7.75/5.74 ( ( Y != zero_zero_nat )
% 7.75/5.74 => ( ( product_Pair_nat_nat @ ( divide_divide_nat @ X @ Y ) @ ( modulo_modulo_nat @ X @ Y ) )
% 7.75/5.74 = ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ Y @ ( minus_minus_nat @ X @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ Y ) ) ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( minus_minus_nat @ X @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ Y ) ) @ Y ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ ( minus_minus_nat @ X @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ Y ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % div_half_nat
% 7.75/5.74 thf(fact_7924_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,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa3 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 7.75/5.74 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 & ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.elims
% 7.75/5.74 thf(fact_7925_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,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 7.75/5.74 ( ? [Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat @ ( Xa3 = Mi ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat @ ( Xa3 = Ma2 ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa3 ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ Mi @ Xa3 )
% 7.75/5.74 & ( ord_less_nat @ Xa3 @ Ma2 ) )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 7.75/5.74 @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.elims
% 7.75/5.74 thf(fact_7926_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,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 & ~ ( ( X = Mi3 )
% 7.75/5.74 | ( X = Ma ) ) )
% 7.75/5.74 @ ( 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 @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(5)
% 7.75/5.74 thf(fact_7927_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,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 & ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.elims
% 7.75/5.74 thf(fact_7928_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,
% 7.75/5.74 ! [A: $o,B: $o,X: nat] :
% 7.75/5.74 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(1)
% 7.75/5.74 thf(fact_7929_minNull__bound,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % minNull_bound
% 7.75/5.74 thf(fact_7930_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,
% 7.75/5.74 ! [Uu: $o] :
% 7.75/5.74 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ Uu @ $true ) )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(3)
% 7.75/5.74 thf(fact_7931_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,
% 7.75/5.74 ! [Uv: $o] :
% 7.75/5.74 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $true @ Uv ) )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(2)
% 7.75/5.74 thf(fact_7932_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,
% 7.75/5.74 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $false @ $false ) )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(1)
% 7.75/5.74 thf(fact_7933_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,
% 7.75/5.74 ! [A: $o,B: $o,X: nat] :
% 7.75/5.74 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(1)
% 7.75/5.74 thf(fact_7934_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,
% 7.75/5.74 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(2)
% 7.75/5.74 thf(fact_7935_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,
% 7.75/5.74 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 7.75/5.74 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc2 ) )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(5)
% 7.75/5.74 thf(fact_7936_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,
% 7.75/5.74 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 7.75/5.74 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(4)
% 7.75/5.74 thf(fact_7937_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,
% 7.75/5.74 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(2)
% 7.75/5.74 thf(fact_7938_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,
% 7.75/5.74 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(3)
% 7.75/5.74 thf(fact_7939_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,
% 7.75/5.74 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(4)
% 7.75/5.74 thf(fact_7940_insersimp_H,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT,N: nat,Y: nat] :
% 7.75/5.74 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.74 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 7.75/5.74 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y ) @ one_one_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % insersimp'
% 7.75/5.74 thf(fact_7941_insertsimp_H,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 7.75/5.74 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.74 => ( ( vEBT_VEBT_minNull @ T )
% 7.75/5.74 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L ) @ one_one_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % insertsimp'
% 7.75/5.74 thf(fact_7942_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,
% 7.75/5.74 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(3)
% 7.75/5.74 thf(fact_7943_insert_H__bound__height,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.74 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.74 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % insert'_bound_height
% 7.75/5.74 thf(fact_7944_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,
% 7.75/5.74 ! [X: vEBT_VEBT,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ $false @ $false ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Uv2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Uu2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.elims
% 7.75/5.74 thf(fact_7945_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,
% 7.75/5.74 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc2 ) @ X )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(4)
% 7.75/5.74 thf(fact_7946_member__bound__height_H,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.74 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.74 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % member_bound_height'
% 7.75/5.74 thf(fact_7947_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,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 & ~ ( ( X = Mi3 )
% 7.75/5.74 | ( X = Ma ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(5)
% 7.75/5.74 thf(fact_7948_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,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat @ ( X = Mi3 ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat @ ( X = Ma ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ Mi3 @ X )
% 7.75/5.74 & ( ord_less_nat @ X @ Ma ) )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 7.75/5.74 @ zero_zero_nat ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(5)
% 7.75/5.74 thf(fact_7949_finite__Collect__less__nat,axiom,
% 7.75/5.74 ! [K: nat] :
% 7.75/5.74 ( finite_finite_nat
% 7.75/5.74 @ ( collect_nat
% 7.75/5.74 @ ^ [N3: nat] : ( ord_less_nat @ N3 @ K ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_Collect_less_nat
% 7.75/5.74 thf(fact_7950_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [A5: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ? [N2: nat] :
% 7.75/5.74 ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ N2 ) ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( Xa3 = Mi )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 7.75/5.74 = Ma2 ) )
% 7.75/5.74 & ( ( Xa3 != Mi )
% 7.75/5.74 => ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( Xa3 = Mi )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 7.75/5.74 = Ma2 ) )
% 7.75/5.74 & ( ( Xa3 != Mi )
% 7.75/5.74 => ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.elims
% 7.75/5.74 thf(fact_7951_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I7_J,axiom,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ X @ Mi3 )
% 7.75/5.74 | ( ord_less_nat @ Ma @ X ) )
% 7.75/5.74 @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( X = Mi3 )
% 7.75/5.74 & ( X = Ma ) )
% 7.75/5.74 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( X = Mi3 )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 = Ma ) )
% 7.75/5.74 & ( ( X != Mi3 )
% 7.75/5.74 => ( X = Ma ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( X = Mi3 )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 7.75/5.74 = Ma ) )
% 7.75/5.74 & ( ( X != Mi3 )
% 7.75/5.74 => ( X = Ma ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(7)
% 7.75/5.74 thf(fact_7952_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_s_u_c_c @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [Uu2: $o,B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 7.75/5.74 => ( ( ? [Uv2: $o,Uw2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( ? [N2: nat] :
% 7.75/5.74 ( Xa3
% 7.75/5.74 = ( suc @ N2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.elims
% 7.75/5.74 thf(fact_7953_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J,axiom,
% 7.75/5.74 ! [A: $o,B: $o] :
% 7.75/5.74 ( ( vEBT_T_m_a_x_t @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(1)
% 7.75/5.74 thf(fact_7954_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J,axiom,
% 7.75/5.74 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 7.75/5.74 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(2)
% 7.75/5.74 thf(fact_7955_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J,axiom,
% 7.75/5.74 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 7.75/5.74 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(2)
% 7.75/5.74 thf(fact_7956_maxt__bound,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % maxt_bound
% 7.75/5.74 thf(fact_7957_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J,axiom,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 7.75/5.74 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(3)
% 7.75/5.74 thf(fact_7958_mint__bound,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % mint_bound
% 7.75/5.74 thf(fact_7959_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 7.75/5.74 ! [A: $o,B: $o] :
% 7.75/5.74 ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(1)
% 7.75/5.74 thf(fact_7960_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J,axiom,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 7.75/5.74 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 7.75/5.74 = one_one_nat ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(3)
% 7.75/5.74 thf(fact_7961_finite__psubset__induct,axiom,
% 7.75/5.74 ! [A2: set_nat,P: set_nat > $o] :
% 7.75/5.74 ( ( finite_finite_nat @ A2 )
% 7.75/5.74 => ( ! [A8: set_nat] :
% 7.75/5.74 ( ( finite_finite_nat @ A8 )
% 7.75/5.74 => ( ! [B8: set_nat] :
% 7.75/5.74 ( ( ord_less_set_nat @ B8 @ A8 )
% 7.75/5.74 => ( P @ B8 ) )
% 7.75/5.74 => ( P @ A8 ) ) )
% 7.75/5.74 => ( P @ A2 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_psubset_induct
% 7.75/5.74 thf(fact_7962_finite__psubset__induct,axiom,
% 7.75/5.74 ! [A2: set_int,P: set_int > $o] :
% 7.75/5.74 ( ( finite_finite_int @ A2 )
% 7.75/5.74 => ( ! [A8: set_int] :
% 7.75/5.74 ( ( finite_finite_int @ A8 )
% 7.75/5.74 => ( ! [B8: set_int] :
% 7.75/5.74 ( ( ord_less_set_int @ B8 @ A8 )
% 7.75/5.74 => ( P @ B8 ) )
% 7.75/5.74 => ( P @ A8 ) ) )
% 7.75/5.74 => ( P @ A2 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_psubset_induct
% 7.75/5.74 thf(fact_7963_finite__psubset__induct,axiom,
% 7.75/5.74 ! [A2: set_complex,P: set_complex > $o] :
% 7.75/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.74 => ( ! [A8: set_complex] :
% 7.75/5.74 ( ( finite3207457112153483333omplex @ A8 )
% 7.75/5.74 => ( ! [B8: set_complex] :
% 7.75/5.74 ( ( ord_less_set_complex @ B8 @ A8 )
% 7.75/5.74 => ( P @ B8 ) )
% 7.75/5.74 => ( P @ A8 ) ) )
% 7.75/5.74 => ( P @ A2 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_psubset_induct
% 7.75/5.74 thf(fact_7964_finite__psubset__induct,axiom,
% 7.75/5.74 ! [A2: set_Code_integer,P: set_Code_integer > $o] :
% 7.75/5.74 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.74 => ( ! [A8: set_Code_integer] :
% 7.75/5.74 ( ( finite6017078050557962740nteger @ A8 )
% 7.75/5.74 => ( ! [B8: set_Code_integer] :
% 7.75/5.74 ( ( ord_le1307284697595431911nteger @ B8 @ A8 )
% 7.75/5.74 => ( P @ B8 ) )
% 7.75/5.74 => ( P @ A8 ) ) )
% 7.75/5.74 => ( P @ A2 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % finite_psubset_induct
% 7.75/5.74 thf(fact_7965_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_m_a_x_t @ X )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B2 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 7.75/5.74 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ( ? [Mi: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.elims
% 7.75/5.74 thf(fact_7966_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_m_i_n_t @ X )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ! [A5: $o] :
% 7.75/5.74 ( ? [B2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 7.75/5.74 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ( ? [Mi: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.elims
% 7.75/5.74 thf(fact_7967_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I7_J,axiom,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(7)
% 7.75/5.74 thf(fact_7968_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I6_J,axiom,
% 7.75/5.74 ! [Mi3: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 7.75/5.74 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(6)
% 7.75/5.74 thf(fact_7969_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Oelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_p_r_e_d @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( ? [Uu2: $o,Uv2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y != one_one_nat ) ) )
% 7.75/5.74 => ( ( ? [A5: $o,Uw2: $o] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ? [Va: nat] :
% 7.75/5.74 ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B2 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ) )
% 7.75/5.74 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ( ( ? [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 7.75/5.74 ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 7.75/5.74 => ( Y != one_one_nat ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 != ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa3 ) @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.elims
% 7.75/5.74 thf(fact_7970_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ! [N2: nat] :
% 7.75/5.74 ( ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ N2 ) ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 7.75/5.74 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( Xa3 = Mi )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 7.75/5.74 = Ma2 ) )
% 7.75/5.74 & ( ( Xa3 != Mi )
% 7.75/5.74 => ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( Xa3 = Mi )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 7.75/5.74 = Ma2 ) )
% 7.75/5.74 & ( ( Xa3 != Mi )
% 7.75/5.74 => ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.pelims
% 7.75/5.74 thf(fact_7971_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_s_u_c_c @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [Uu2: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 7.75/5.74 => ( ! [Uv2: $o,Uw2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ! [N2: nat] :
% 7.75/5.74 ( ( Xa3
% 7.75/5.74 = ( suc @ N2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) ) ) ) )
% 7.75/5.74 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.pelims
% 7.75/5.74 thf(fact_7972_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_p_r_e_d @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [Uu2: $o,Uv2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,Uw2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ! [Va: nat] :
% 7.75/5.74 ( ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B2 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 7.75/5.74 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa3 ) @ one_one_nat
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 7.75/5.74 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ one_one_nat ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.pelims
% 7.75/5.74 thf(fact_7973_pred__empty,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.74 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.74 => ( ( ( vEBT_vebt_pred @ T @ X )
% 7.75/5.74 = none_nat )
% 7.75/5.74 = ( ( collect_nat
% 7.75/5.74 @ ^ [Y6: nat] :
% 7.75/5.74 ( ( vEBT_vebt_member @ T @ Y6 )
% 7.75/5.74 & ( ord_less_nat @ Y6 @ X ) ) )
% 7.75/5.74 = bot_bot_set_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % pred_empty
% 7.75/5.74 thf(fact_7974_buildup__gives__empty,axiom,
% 7.75/5.74 ! [N: nat] :
% 7.75/5.74 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 7.75/5.74 = bot_bot_set_nat ) ).
% 7.75/5.74
% 7.75/5.74 % buildup_gives_empty
% 7.75/5.74 thf(fact_7975_mint__corr__help__empty,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.74 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.74 => ( ( ( vEBT_vebt_mint @ T )
% 7.75/5.74 = none_nat )
% 7.75/5.74 => ( ( vEBT_VEBT_set_vebt @ T )
% 7.75/5.74 = bot_bot_set_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % mint_corr_help_empty
% 7.75/5.74 thf(fact_7976_maxt__corr__help__empty,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT,N: nat] :
% 7.75/5.74 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.74 => ( ( ( vEBT_vebt_maxt @ T )
% 7.75/5.74 = none_nat )
% 7.75/5.74 => ( ( vEBT_VEBT_set_vebt @ T )
% 7.75/5.74 = bot_bot_set_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % maxt_corr_help_empty
% 7.75/5.74 thf(fact_7977_succ__empty,axiom,
% 7.75/5.74 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.74 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.74 => ( ( ( vEBT_vebt_succ @ T @ X )
% 7.75/5.74 = none_nat )
% 7.75/5.74 = ( ( collect_nat
% 7.75/5.74 @ ^ [Y6: nat] :
% 7.75/5.74 ( ( vEBT_vebt_member @ T @ Y6 )
% 7.75/5.74 & ( ord_less_nat @ X @ Y6 ) ) )
% 7.75/5.74 = bot_bot_set_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % succ_empty
% 7.75/5.74 thf(fact_7978_atLeastatMost__empty,axiom,
% 7.75/5.74 ! [B: rat,A: rat] :
% 7.75/5.74 ( ( ord_less_rat @ B @ A )
% 7.75/5.74 => ( ( set_or633870826150836451st_rat @ A @ B )
% 7.75/5.74 = bot_bot_set_rat ) ) ).
% 7.75/5.74
% 7.75/5.74 % atLeastatMost_empty
% 7.75/5.74 thf(fact_7979_atLeastatMost__empty,axiom,
% 7.75/5.74 ! [B: num,A: num] :
% 7.75/5.74 ( ( ord_less_num @ B @ A )
% 7.75/5.74 => ( ( set_or7049704709247886629st_num @ A @ B )
% 7.75/5.74 = bot_bot_set_num ) ) ).
% 7.75/5.74
% 7.75/5.74 % atLeastatMost_empty
% 7.75/5.74 thf(fact_7980_atLeastatMost__empty,axiom,
% 7.75/5.74 ! [B: nat,A: nat] :
% 7.75/5.74 ( ( ord_less_nat @ B @ A )
% 7.75/5.74 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 7.75/5.74 = bot_bot_set_nat ) ) ).
% 7.75/5.74
% 7.75/5.74 % atLeastatMost_empty
% 7.75/5.74 thf(fact_7981_atLeastatMost__empty,axiom,
% 7.75/5.74 ! [B: int,A: int] :
% 7.75/5.74 ( ( ord_less_int @ B @ A )
% 7.75/5.74 => ( ( set_or1266510415728281911st_int @ A @ B )
% 7.75/5.74 = bot_bot_set_int ) ) ).
% 7.75/5.74
% 7.75/5.74 % atLeastatMost_empty
% 7.75/5.74 thf(fact_7982_atLeastatMost__empty,axiom,
% 7.75/5.74 ! [B: code_integer,A: code_integer] :
% 7.75/5.74 ( ( ord_le6747313008572928689nteger @ B @ A )
% 7.75/5.74 => ( ( set_or189985376899183464nteger @ A @ B )
% 7.75/5.74 = bot_bo3990330152332043303nteger ) ) ).
% 7.75/5.74
% 7.75/5.74 % atLeastatMost_empty
% 7.75/5.74 thf(fact_7983_atLeastatMost__empty,axiom,
% 7.75/5.74 ! [B: real,A: real] :
% 7.75/5.74 ( ( ord_less_real @ B @ A )
% 7.75/5.74 => ( ( set_or1222579329274155063t_real @ A @ B )
% 7.75/5.74 = bot_bot_set_real ) ) ).
% 7.75/5.74
% 7.75/5.74 % atLeastatMost_empty
% 7.75/5.74 thf(fact_7984_mod__h__bot__iff_I5_J,axiom,
% 7.75/5.74 ! [P: assn,Q: assn,H2: heap_e7401611519738050253t_unit] :
% 7.75/5.74 ( ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 7.75/5.74 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 7.75/5.74 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % mod_h_bot_iff(5)
% 7.75/5.74 thf(fact_7985_mod__h__bot__iff_I1_J,axiom,
% 7.75/5.74 ! [B: $o,H2: heap_e7401611519738050253t_unit] :
% 7.75/5.74 ( ( rep_assn @ ( pure_assn @ B ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 7.75/5.74 = B ) ).
% 7.75/5.74
% 7.75/5.74 % mod_h_bot_iff(1)
% 7.75/5.74 thf(fact_7986_mod__h__bot__iff_I4_J,axiom,
% 7.75/5.74 ! [Q3: array_VEBT_VEBTi,Y: list_VEBT_VEBTi,H2: heap_e7401611519738050253t_unit] :
% 7.75/5.74 ~ ( rep_assn @ ( snga_assn_VEBT_VEBTi @ Q3 @ Y ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 7.75/5.74
% 7.75/5.74 % mod_h_bot_iff(4)
% 7.75/5.74 thf(fact_7987_set__decode__zero,axiom,
% 7.75/5.74 ( ( nat_set_decode @ zero_zero_nat )
% 7.75/5.74 = bot_bot_set_nat ) ).
% 7.75/5.74
% 7.75/5.74 % set_decode_zero
% 7.75/5.74 thf(fact_7988_set__encode__empty,axiom,
% 7.75/5.74 ( ( nat_set_encode @ bot_bot_set_nat )
% 7.75/5.74 = zero_zero_nat ) ).
% 7.75/5.74
% 7.75/5.74 % set_encode_empty
% 7.75/5.74 thf(fact_7989_mod__h__bot__indep,axiom,
% 7.75/5.74 ! [P: assn,H2: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 7.75/5.74 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 7.75/5.74 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H4 @ bot_bot_set_nat ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % mod_h_bot_indep
% 7.75/5.74 thf(fact_7990_not__psubset__empty,axiom,
% 7.75/5.74 ! [A2: set_real] :
% 7.75/5.74 ~ ( ord_less_set_real @ A2 @ bot_bot_set_real ) ).
% 7.75/5.74
% 7.75/5.74 % not_psubset_empty
% 7.75/5.74 thf(fact_7991_not__psubset__empty,axiom,
% 7.75/5.74 ! [A2: set_nat] :
% 7.75/5.74 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 7.75/5.74
% 7.75/5.74 % not_psubset_empty
% 7.75/5.74 thf(fact_7992_not__psubset__empty,axiom,
% 7.75/5.74 ! [A2: set_int] :
% 7.75/5.74 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 7.75/5.74
% 7.75/5.74 % not_psubset_empty
% 7.75/5.74 thf(fact_7993_ex__min__if__finite,axiom,
% 7.75/5.74 ! [S3: set_Code_integer] :
% 7.75/5.74 ( ( finite6017078050557962740nteger @ S3 )
% 7.75/5.74 => ( ( S3 != bot_bo3990330152332043303nteger )
% 7.75/5.74 => ? [X3: code_integer] :
% 7.75/5.74 ( ( member_Code_integer @ X3 @ S3 )
% 7.75/5.74 & ~ ? [Xa: code_integer] :
% 7.75/5.74 ( ( member_Code_integer @ Xa @ S3 )
% 7.75/5.74 & ( ord_le6747313008572928689nteger @ Xa @ X3 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % ex_min_if_finite
% 7.75/5.74 thf(fact_7994_ex__min__if__finite,axiom,
% 7.75/5.74 ! [S3: set_real] :
% 7.75/5.74 ( ( finite_finite_real @ S3 )
% 7.75/5.74 => ( ( S3 != bot_bot_set_real )
% 7.75/5.74 => ? [X3: real] :
% 7.75/5.74 ( ( member_real @ X3 @ S3 )
% 7.75/5.74 & ~ ? [Xa: real] :
% 7.75/5.74 ( ( member_real @ Xa @ S3 )
% 7.75/5.74 & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % ex_min_if_finite
% 7.75/5.74 thf(fact_7995_ex__min__if__finite,axiom,
% 7.75/5.74 ! [S3: set_rat] :
% 7.75/5.74 ( ( finite_finite_rat @ S3 )
% 7.75/5.74 => ( ( S3 != bot_bot_set_rat )
% 7.75/5.74 => ? [X3: rat] :
% 7.75/5.74 ( ( member_rat @ X3 @ S3 )
% 7.75/5.74 & ~ ? [Xa: rat] :
% 7.75/5.74 ( ( member_rat @ Xa @ S3 )
% 7.75/5.74 & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % ex_min_if_finite
% 7.75/5.74 thf(fact_7996_ex__min__if__finite,axiom,
% 7.75/5.74 ! [S3: set_num] :
% 7.75/5.74 ( ( finite_finite_num @ S3 )
% 7.75/5.74 => ( ( S3 != bot_bot_set_num )
% 7.75/5.74 => ? [X3: num] :
% 7.75/5.74 ( ( member_num @ X3 @ S3 )
% 7.75/5.74 & ~ ? [Xa: num] :
% 7.75/5.74 ( ( member_num @ Xa @ S3 )
% 7.75/5.74 & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % ex_min_if_finite
% 7.75/5.74 thf(fact_7997_ex__min__if__finite,axiom,
% 7.75/5.74 ! [S3: set_nat] :
% 7.75/5.74 ( ( finite_finite_nat @ S3 )
% 7.75/5.74 => ( ( S3 != bot_bot_set_nat )
% 7.75/5.74 => ? [X3: nat] :
% 7.75/5.74 ( ( member_nat @ X3 @ S3 )
% 7.75/5.74 & ~ ? [Xa: nat] :
% 7.75/5.74 ( ( member_nat @ Xa @ S3 )
% 7.75/5.74 & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % ex_min_if_finite
% 7.75/5.74 thf(fact_7998_ex__min__if__finite,axiom,
% 7.75/5.74 ! [S3: set_int] :
% 7.75/5.74 ( ( finite_finite_int @ S3 )
% 7.75/5.74 => ( ( S3 != bot_bot_set_int )
% 7.75/5.74 => ? [X3: int] :
% 7.75/5.74 ( ( member_int @ X3 @ S3 )
% 7.75/5.74 & ~ ? [Xa: int] :
% 7.75/5.74 ( ( member_int @ Xa @ S3 )
% 7.75/5.74 & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % ex_min_if_finite
% 7.75/5.74 thf(fact_7999_infinite__growing,axiom,
% 7.75/5.74 ! [X9: set_Code_integer] :
% 7.75/5.74 ( ( X9 != bot_bo3990330152332043303nteger )
% 7.75/5.74 => ( ! [X3: code_integer] :
% 7.75/5.74 ( ( member_Code_integer @ X3 @ X9 )
% 7.75/5.74 => ? [Xa: code_integer] :
% 7.75/5.74 ( ( member_Code_integer @ Xa @ X9 )
% 7.75/5.74 & ( ord_le6747313008572928689nteger @ X3 @ Xa ) ) )
% 7.75/5.74 => ~ ( finite6017078050557962740nteger @ X9 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % infinite_growing
% 7.75/5.74 thf(fact_8000_infinite__growing,axiom,
% 7.75/5.74 ! [X9: set_real] :
% 7.75/5.74 ( ( X9 != bot_bot_set_real )
% 7.75/5.74 => ( ! [X3: real] :
% 7.75/5.74 ( ( member_real @ X3 @ X9 )
% 7.75/5.74 => ? [Xa: real] :
% 7.75/5.74 ( ( member_real @ Xa @ X9 )
% 7.75/5.74 & ( ord_less_real @ X3 @ Xa ) ) )
% 7.75/5.74 => ~ ( finite_finite_real @ X9 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % infinite_growing
% 7.75/5.74 thf(fact_8001_infinite__growing,axiom,
% 7.75/5.74 ! [X9: set_rat] :
% 7.75/5.74 ( ( X9 != bot_bot_set_rat )
% 7.75/5.74 => ( ! [X3: rat] :
% 7.75/5.74 ( ( member_rat @ X3 @ X9 )
% 7.75/5.74 => ? [Xa: rat] :
% 7.75/5.74 ( ( member_rat @ Xa @ X9 )
% 7.75/5.74 & ( ord_less_rat @ X3 @ Xa ) ) )
% 7.75/5.74 => ~ ( finite_finite_rat @ X9 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % infinite_growing
% 7.75/5.74 thf(fact_8002_infinite__growing,axiom,
% 7.75/5.74 ! [X9: set_num] :
% 7.75/5.74 ( ( X9 != bot_bot_set_num )
% 7.75/5.74 => ( ! [X3: num] :
% 7.75/5.74 ( ( member_num @ X3 @ X9 )
% 7.75/5.74 => ? [Xa: num] :
% 7.75/5.74 ( ( member_num @ Xa @ X9 )
% 7.75/5.74 & ( ord_less_num @ X3 @ Xa ) ) )
% 7.75/5.74 => ~ ( finite_finite_num @ X9 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % infinite_growing
% 7.75/5.74 thf(fact_8003_infinite__growing,axiom,
% 7.75/5.74 ! [X9: set_nat] :
% 7.75/5.74 ( ( X9 != bot_bot_set_nat )
% 7.75/5.74 => ( ! [X3: nat] :
% 7.75/5.74 ( ( member_nat @ X3 @ X9 )
% 7.75/5.74 => ? [Xa: nat] :
% 7.75/5.74 ( ( member_nat @ Xa @ X9 )
% 7.75/5.74 & ( ord_less_nat @ X3 @ Xa ) ) )
% 7.75/5.74 => ~ ( finite_finite_nat @ X9 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % infinite_growing
% 7.75/5.74 thf(fact_8004_infinite__growing,axiom,
% 7.75/5.74 ! [X9: set_int] :
% 7.75/5.74 ( ( X9 != bot_bot_set_int )
% 7.75/5.74 => ( ! [X3: int] :
% 7.75/5.74 ( ( member_int @ X3 @ X9 )
% 7.75/5.74 => ? [Xa: int] :
% 7.75/5.74 ( ( member_int @ Xa @ X9 )
% 7.75/5.74 & ( ord_less_int @ X3 @ Xa ) ) )
% 7.75/5.74 => ~ ( finite_finite_int @ X9 ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % infinite_growing
% 7.75/5.74 thf(fact_8005_mod__emp__simp,axiom,
% 7.75/5.74 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 7.75/5.74
% 7.75/5.74 % mod_emp_simp
% 7.75/5.74 thf(fact_8006_vebt__succ_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: option_nat] :
% 7.75/5.74 ( ( ( vEBT_vebt_succ @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [Uu2: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( ( ( B2
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.74 & ( ~ B2
% 7.75/5.74 => ( Y = none_nat ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 7.75/5.74 => ( ! [Uv2: $o,Uw2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ! [N2: nat] :
% 7.75/5.74 ( ( Xa3
% 7.75/5.74 = ( suc @ N2 ) )
% 7.75/5.74 => ( ( Y = none_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) ) ) ) )
% 7.75/5.74 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( ( Y = none_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) )
% 7.75/5.74 => ( ( Y = none_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 7.75/5.74 => ( ( Y = none_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ Mi ) ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( 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 @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ none_nat
% 7.75/5.74 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ none_nat ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_succ.pelims
% 7.75/5.74 thf(fact_8007_vebt__pred_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: option_nat] :
% 7.75/5.74 ( ( ( vEBT_vebt_pred @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [Uu2: $o,Uv2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( ( Y = none_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,Uw2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( ( ( A5
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.74 & ( ~ A5
% 7.75/5.74 => ( Y = none_nat ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ! [Va: nat] :
% 7.75/5.74 ( ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( ( ( B2
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ one_one_nat ) ) )
% 7.75/5.74 & ( ~ B2
% 7.75/5.74 => ( ( A5
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ zero_zero_nat ) ) )
% 7.75/5.74 & ( ~ A5
% 7.75/5.74 => ( Y = none_nat ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 7.75/5.74 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 7.75/5.74 => ( ( Y = none_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 7.75/5.74 => ( ( Y = none_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 7.75/5.74 => ( ( Y = none_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( ( ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( some_nat @ Ma2 ) ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( 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 @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( if_option_nat
% 7.75/5.74 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( if_option_nat @ ( ord_less_nat @ Mi @ Xa3 ) @ ( some_nat @ Mi ) @ none_nat )
% 7.75/5.74 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ none_nat ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_pred.pelims
% 7.75/5.74 thf(fact_8008_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_V1232361888498592333_e_t_e @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ! [N2: nat] :
% 7.75/5.74 ( ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ N2 ) ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 7.75/5.74 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( ( ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 => ( Y = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 => ( ( ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 => ( Y = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.pelims
% 7.75/5.74 thf(fact_8009_vebt__delete_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: vEBT_VEBT] :
% 7.75/5.74 ( ( ( vEBT_vebt_delete @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( vEBT_Leaf @ $false @ B2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ $false ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ! [N2: nat] :
% 7.75/5.74 ( ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ N2 ) ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 7.75/5.74 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Mi: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( ( ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 7.75/5.74 & ( ~ ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 | ( ord_less_nat @ Ma2 @ Xa3 ) )
% 7.75/5.74 => ( ( ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 7.75/5.74 & ( ~ ( ( Xa3 = Mi )
% 7.75/5.74 & ( Xa3 = Ma2 ) )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa3 = Mi ) @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ Mi )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( Xa3 = Mi )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 7.75/5.74 = Ma2 ) )
% 7.75/5.74 & ( ( Xa3 != Mi )
% 7.75/5.74 => ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 = none_nat )
% 7.75/5.74 @ ( if_nat @ ( Xa3 = Mi ) @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ Mi )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma2 ) ) )
% 7.75/5.74 @ ( suc @ ( suc @ Va ) )
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( vEBT_Node
% 7.75/5.74 @ ( some_P7363390416028606310at_nat
% 7.75/5.74 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa3 = Mi ) @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ Mi )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( Xa3 = Mi )
% 7.75/5.74 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 7.75/5.74 = Ma2 ) )
% 7.75/5.74 & ( ( Xa3 != Mi )
% 7.75/5.74 => ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ Ma2 ) ) )
% 7.75/5.74 @ ( suc @ ( suc @ Va ) )
% 7.75/5.74 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa3 = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ Summary2 ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_delete.pelims
% 7.75/5.74 thf(fact_8010_one__assn__raw_Ocases,axiom,
% 7.75/5.74 ! [X: produc3658429121746597890et_nat] :
% 7.75/5.74 ~ ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 7.75/5.74 ( X
% 7.75/5.74 != ( produc7507926704131184380et_nat @ H3 @ As ) ) ).
% 7.75/5.74
% 7.75/5.74 % one_assn_raw.cases
% 7.75/5.74 thf(fact_8011_times__assn__raw_Ocases,axiom,
% 7.75/5.74 ! [X: produc2732055786443039994et_nat] :
% 7.75/5.74 ~ ! [P7: produc3658429121746597890et_nat > $o,Q8: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 7.75/5.74 ( X
% 7.75/5.74 != ( produc2245416461498447860et_nat @ P7 @ ( produc5001842942810119800et_nat @ Q8 @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % times_assn_raw.cases
% 7.75/5.74 thf(fact_8012_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [Uu2: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ B2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B2 ) @ zero_zero_nat ) ) ) ) )
% 7.75/5.74 => ( ! [Uv2: $o,Uw2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ! [N2: nat] :
% 7.75/5.74 ( ( Xa3
% 7.75/5.74 = ( suc @ N2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N2 ) ) ) ) ) )
% 7.75/5.74 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( ( ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( Y = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.pelims
% 7.75/5.74 thf(fact_8013_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,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa3 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 & ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.pelims
% 7.75/5.74 thf(fact_8014_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [Uu2: $o,Uv2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.74 => ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,Uw2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 7.75/5.74 => ( ( Xa3
% 7.75/5.74 = ( suc @ zero_zero_nat ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ! [Va: nat] :
% 7.75/5.74 ( ( Xa3
% 7.75/5.74 = ( suc @ ( suc @ Va ) ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 7.75/5.74 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( ( ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( Y = one_one_nat ) )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 != none_nat )
% 7.75/5.74 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.pelims
% 7.75/5.74 thf(fact_8015_vebt__insert_Opelims,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: vEBT_VEBT] :
% 7.75/5.74 ( ( ( vEBT_vebt_insert @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Leaf @ $true @ B2 ) ) )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 7.75/5.74 & ( ( Xa3 != one_one_nat )
% 7.75/5.74 => ( Y
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa3 @ Xa3 ) ) @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( if_VEBT_VEBT
% 7.75/5.74 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 & ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Xa3 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 7.75/5.74 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_insert.pelims
% 7.75/5.74 thf(fact_8016_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,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V3 ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 & ~ ( ( Xa3 = Mi )
% 7.75/5.74 | ( Xa3 = Ma2 ) ) )
% 7.75/5.74 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ Mi @ Xa3 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 7.75/5.74 @ one_one_nat ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.pelims
% 7.75/5.74 thf(fact_8017_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,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa3 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa3 = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa3 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa3 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.pelims
% 7.75/5.74 thf(fact_8018_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,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: nat] :
% 7.75/5.74 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) )
% 7.75/5.74 => ( ( Y = one_one_nat )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( plus_plus_nat @ one_one_nat
% 7.75/5.74 @ ( if_nat @ ( Xa3 = Mi ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat @ ( Xa3 = Ma2 ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Xa3 @ Mi ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa3 ) @ zero_zero_nat
% 7.75/5.74 @ ( if_nat
% 7.75/5.74 @ ( ( ord_less_nat @ Mi @ Xa3 )
% 7.75/5.74 & ( ord_less_nat @ Xa3 @ Ma2 ) )
% 7.75/5.74 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 7.75/5.74 @ zero_zero_nat ) ) ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.pelims
% 7.75/5.74 thf(fact_8019_vebt__member_Opelims_I3_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.74 ( ~ ( vEBT_vebt_member @ X @ Xa3 )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) )
% 7.75/5.74 => ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) ) )
% 7.75/5.74 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa3 ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa3 ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ Xa3 ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) )
% 7.75/5.74 => ( ( Xa3 != Mi )
% 7.75/5.74 => ( ( Xa3 != Ma2 )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_member.pelims(3)
% 7.75/5.74 thf(fact_8020_vebt__member_Opelims_I2_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.74 ( ( vEBT_vebt_member @ X @ Xa3 )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) )
% 7.75/5.74 => ~ ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) )
% 7.75/5.74 => ~ ( ( Xa3 != Mi )
% 7.75/5.74 => ( ( Xa3 != Ma2 )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_member.pelims(2)
% 7.75/5.74 thf(fact_8021_vebt__member_Opelims_I1_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat,Y: $o] :
% 7.75/5.74 ( ( ( vEBT_vebt_member @ X @ Xa3 )
% 7.75/5.74 = Y )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ( ~ Y
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 7.75/5.74 => ( ~ Y
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa3 ) ) ) )
% 7.75/5.74 => ( ! [V3: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) )
% 7.75/5.74 => ( ~ Y
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V3 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc ) @ Xa3 ) ) ) )
% 7.75/5.74 => ~ ! [Mi: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 7.75/5.74 => ( ( Y
% 7.75/5.74 = ( ( Xa3 != Mi )
% 7.75/5.74 => ( ( Xa3 != Ma2 )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Xa3 @ Mi )
% 7.75/5.74 => ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 & ( ~ ( ord_less_nat @ Ma2 @ Xa3 )
% 7.75/5.74 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.74 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.74 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.74
% 7.75/5.74 % vebt_member.pelims(1)
% 7.75/5.74 thf(fact_8022_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 7.75/5.74 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.74 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa3 )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.74 => ( ! [A5: $o,B2: $o] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.74 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) )
% 7.75/5.74 => ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.74 => A5 )
% 7.75/5.74 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.74 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.74 => B2 )
% 7.75/5.74 & ( Xa3 = one_one_nat ) ) ) ) ) )
% 7.75/5.74 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 7.75/5.74 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa3 ) ) )
% 7.75/5.74 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.74 ( ( X
% 7.75/5.74 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) @ Xa3 ) )
% 7.75/5.75 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.75 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.75 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % VEBT_internal.naive_member.pelims(3)
% 7.75/5.75 thf(fact_8023_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 7.75/5.75 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.75 ( ( vEBT_V5719532721284313246member @ X @ Xa3 )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.75 => ( ! [A5: $o,B2: $o] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) )
% 7.75/5.75 => ~ ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.75 => A5 )
% 7.75/5.75 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.75 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.75 => B2 )
% 7.75/5.75 & ( Xa3 = one_one_nat ) ) ) ) ) )
% 7.75/5.75 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) @ Xa3 ) )
% 7.75/5.75 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.75 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.75 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % VEBT_internal.naive_member.pelims(2)
% 7.75/5.75 thf(fact_8024_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 7.75/5.75 ! [X: vEBT_VEBT,Xa3: nat,Y: $o] :
% 7.75/5.75 ( ( ( vEBT_V5719532721284313246member @ X @ Xa3 )
% 7.75/5.75 = Y )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.75 => ( ! [A5: $o,B2: $o] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.75/5.75 => ( ( Y
% 7.75/5.75 = ( ( ( Xa3 = zero_zero_nat )
% 7.75/5.75 => A5 )
% 7.75/5.75 & ( ( Xa3 != zero_zero_nat )
% 7.75/5.75 => ( ( ( Xa3 = one_one_nat )
% 7.75/5.75 => B2 )
% 7.75/5.75 & ( Xa3 = one_one_nat ) ) ) ) )
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B2 ) @ Xa3 ) ) ) )
% 7.75/5.75 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 7.75/5.75 => ( ~ Y
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa3 ) ) ) )
% 7.75/5.75 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) )
% 7.75/5.75 => ( ( Y
% 7.75/5.75 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.75 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.75 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S2 ) @ Xa3 ) ) ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % VEBT_internal.naive_member.pelims(1)
% 7.75/5.75 thf(fact_8025_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 7.75/5.75 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.75 ( ~ ( vEBT_VEBT_membermima @ X @ Xa3 )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.75 => ( ! [Uu2: $o,Uv2: $o] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa3 ) ) )
% 7.75/5.75 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa3 ) ) )
% 7.75/5.75 => ( ! [Mi: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa3 ) )
% 7.75/5.75 => ( ( Xa3 = Mi )
% 7.75/5.75 | ( Xa3 = Ma2 ) ) ) )
% 7.75/5.75 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) @ Xa3 ) )
% 7.75/5.75 => ( ( Xa3 = Mi )
% 7.75/5.75 | ( Xa3 = Ma2 )
% 7.75/5.75 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.75 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.75 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 7.75/5.75 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) @ Xa3 ) )
% 7.75/5.75 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.75 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.75 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % VEBT_internal.membermima.pelims(3)
% 7.75/5.75 thf(fact_8026_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 7.75/5.75 ! [X: vEBT_VEBT,Xa3: nat] :
% 7.75/5.75 ( ( vEBT_VEBT_membermima @ X @ Xa3 )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.75 => ( ! [Mi: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa3 ) )
% 7.75/5.75 => ~ ( ( Xa3 = Mi )
% 7.75/5.75 | ( Xa3 = Ma2 ) ) ) )
% 7.75/5.75 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) @ Xa3 ) )
% 7.75/5.75 => ~ ( ( Xa3 = Mi )
% 7.75/5.75 | ( Xa3 = Ma2 )
% 7.75/5.75 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.75 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.75 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 7.75/5.75 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) @ Xa3 ) )
% 7.75/5.75 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.75 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.75 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % VEBT_internal.membermima.pelims(2)
% 7.75/5.75 thf(fact_8027_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 7.75/5.75 ! [X: vEBT_VEBT,Xa3: nat,Y: $o] :
% 7.75/5.75 ( ( ( vEBT_VEBT_membermima @ X @ Xa3 )
% 7.75/5.75 = Y )
% 7.75/5.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 7.75/5.75 => ( ! [Uu2: $o,Uv2: $o] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 7.75/5.75 => ( ~ Y
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa3 ) ) ) )
% 7.75/5.75 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 7.75/5.75 => ( ~ Y
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa3 ) ) ) )
% 7.75/5.75 => ( ! [Mi: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 7.75/5.75 => ( ( Y
% 7.75/5.75 = ( ( Xa3 = Mi )
% 7.75/5.75 | ( Xa3 = Ma2 ) ) )
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa3 ) ) ) )
% 7.75/5.75 => ( ! [Mi: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 7.75/5.75 => ( ( Y
% 7.75/5.75 = ( ( Xa3 = Mi )
% 7.75/5.75 | ( Xa3 = Ma2 )
% 7.75/5.75 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.75 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.75 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) @ Xa3 ) ) ) )
% 7.75/5.75 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 7.75/5.75 ( ( X
% 7.75/5.75 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) )
% 7.75/5.75 => ( ( Y
% 7.75/5.75 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 7.75/5.75 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 7.75/5.75 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa3 @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 7.75/5.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd2 ) @ Xa3 ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % VEBT_internal.membermima.pelims(1)
% 7.75/5.75 thf(fact_8028_monoseq__arctan__series,axiom,
% 7.75/5.75 ! [X: real] :
% 7.75/5.75 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.75/5.75 => ( topolo6980174941875973593q_real
% 7.75/5.75 @ ^ [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 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % monoseq_arctan_series
% 7.75/5.75 thf(fact_8029_delete__correct,axiom,
% 7.75/5.75 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.75 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.75 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 7.75/5.75 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % delete_correct
% 7.75/5.75 thf(fact_8030_foldr__zero,axiom,
% 7.75/5.75 ! [Xs2: list_nat,D2: nat] :
% 7.75/5.75 ( ! [I3: nat] :
% 7.75/5.75 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.75 => ( ord_less_nat @ zero_zero_nat @ ( nth_nat @ Xs2 @ I3 ) ) )
% 7.75/5.75 => ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ ( minus_minus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs2 @ D2 ) @ D2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_zero
% 7.75/5.75 thf(fact_8031_foldr__one,axiom,
% 7.75/5.75 ! [D2: nat,Ys: list_nat] : ( ord_less_eq_nat @ D2 @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D2 ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_one
% 7.75/5.75 thf(fact_8032_foldr__same__int,axiom,
% 7.75/5.75 ! [Xs2: list_nat,Y: nat] :
% 7.75/5.75 ( ! [X3: nat,Y3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.75/5.75 => ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 7.75/5.75 => ( X3 = Y3 ) ) )
% 7.75/5.75 => ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.75/5.75 => ( X3 = Y ) )
% 7.75/5.75 => ( ( foldr_nat_nat @ plus_plus_nat @ Xs2 @ zero_zero_nat )
% 7.75/5.75 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ Y ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_same_int
% 7.75/5.75 thf(fact_8033_delete__correct_H,axiom,
% 7.75/5.75 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 7.75/5.75 ( ( vEBT_invar_vebt @ T @ N )
% 7.75/5.75 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 7.75/5.75 = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % delete_correct'
% 7.75/5.75 thf(fact_8034_foldr__mono,axiom,
% 7.75/5.75 ! [Xs2: list_nat,Ys: list_nat,C: nat,D2: nat] :
% 7.75/5.75 ( ( ( size_size_list_nat @ Xs2 )
% 7.75/5.75 = ( size_size_list_nat @ Ys ) )
% 7.75/5.75 => ( ! [I3: nat] :
% 7.75/5.75 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 7.75/5.75 => ( ord_less_nat @ ( nth_nat @ Xs2 @ I3 ) @ ( nth_nat @ Ys @ I3 ) ) )
% 7.75/5.75 => ( ( ord_less_eq_nat @ C @ D2 )
% 7.75/5.75 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs2 @ C ) @ ( size_size_list_nat @ Ys ) ) @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_mono
% 7.75/5.75 thf(fact_8035_foldr__length,axiom,
% 7.75/5.75 ! [L: list_real] :
% 7.75/5.75 ( ( foldr_real_nat
% 7.75/5.75 @ ^ [X2: real] : suc
% 7.75/5.75 @ L
% 7.75/5.75 @ zero_zero_nat )
% 7.75/5.75 = ( size_size_list_real @ L ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_length
% 7.75/5.75 thf(fact_8036_foldr__length,axiom,
% 7.75/5.75 ! [L: list_o] :
% 7.75/5.75 ( ( foldr_o_nat
% 7.75/5.75 @ ^ [X2: $o] : suc
% 7.75/5.75 @ L
% 7.75/5.75 @ zero_zero_nat )
% 7.75/5.75 = ( size_size_list_o @ L ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_length
% 7.75/5.75 thf(fact_8037_foldr__length,axiom,
% 7.75/5.75 ! [L: list_nat] :
% 7.75/5.75 ( ( foldr_nat_nat
% 7.75/5.75 @ ^ [X2: nat] : suc
% 7.75/5.75 @ L
% 7.75/5.75 @ zero_zero_nat )
% 7.75/5.75 = ( size_size_list_nat @ L ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_length
% 7.75/5.75 thf(fact_8038_foldr__length,axiom,
% 7.75/5.75 ! [L: list_int] :
% 7.75/5.75 ( ( foldr_int_nat
% 7.75/5.75 @ ^ [X2: int] : suc
% 7.75/5.75 @ L
% 7.75/5.75 @ zero_zero_nat )
% 7.75/5.75 = ( size_size_list_int @ L ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_length
% 7.75/5.75 thf(fact_8039_set__replicate,axiom,
% 7.75/5.75 ! [N: nat,X: vEBT_VEBT] :
% 7.75/5.75 ( ( N != zero_zero_nat )
% 7.75/5.75 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 7.75/5.75 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate
% 7.75/5.75 thf(fact_8040_set__replicate,axiom,
% 7.75/5.75 ! [N: nat,X: real] :
% 7.75/5.75 ( ( N != zero_zero_nat )
% 7.75/5.75 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 7.75/5.75 = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate
% 7.75/5.75 thf(fact_8041_set__replicate,axiom,
% 7.75/5.75 ! [N: nat,X: nat] :
% 7.75/5.75 ( ( N != zero_zero_nat )
% 7.75/5.75 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 7.75/5.75 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate
% 7.75/5.75 thf(fact_8042_set__replicate,axiom,
% 7.75/5.75 ! [N: nat,X: int] :
% 7.75/5.75 ( ( N != zero_zero_nat )
% 7.75/5.75 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 7.75/5.75 = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate
% 7.75/5.75 thf(fact_8043_set__encode__insert,axiom,
% 7.75/5.75 ! [A2: set_nat,N: nat] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ~ ( member_nat @ N @ A2 )
% 7.75/5.75 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 7.75/5.75 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_encode_insert
% 7.75/5.75 thf(fact_8044_foldr__cong,axiom,
% 7.75/5.75 ! [A: nat,B: nat,L: list_o,K: list_o,F: $o > nat > nat,G: $o > nat > nat] :
% 7.75/5.75 ( ( A = B )
% 7.75/5.75 => ( ( L = K )
% 7.75/5.75 => ( ! [A5: nat,X3: $o] :
% 7.75/5.75 ( ( member_o @ X3 @ ( set_o2 @ L ) )
% 7.75/5.75 => ( ( F @ X3 @ A5 )
% 7.75/5.75 = ( G @ X3 @ A5 ) ) )
% 7.75/5.75 => ( ( foldr_o_nat @ F @ L @ A )
% 7.75/5.75 = ( foldr_o_nat @ G @ K @ B ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_cong
% 7.75/5.75 thf(fact_8045_foldr__cong,axiom,
% 7.75/5.75 ! [A: nat,B: nat,L: list_nat,K: list_nat,F: nat > nat > nat,G: nat > nat > nat] :
% 7.75/5.75 ( ( A = B )
% 7.75/5.75 => ( ( L = K )
% 7.75/5.75 => ( ! [A5: nat,X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ ( set_nat2 @ L ) )
% 7.75/5.75 => ( ( F @ X3 @ A5 )
% 7.75/5.75 = ( G @ X3 @ A5 ) ) )
% 7.75/5.75 => ( ( foldr_nat_nat @ F @ L @ A )
% 7.75/5.75 = ( foldr_nat_nat @ G @ K @ B ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_cong
% 7.75/5.75 thf(fact_8046_foldr__cong,axiom,
% 7.75/5.75 ! [A: real,B: real,L: list_real,K: list_real,F: real > real > real,G: real > real > real] :
% 7.75/5.75 ( ( A = B )
% 7.75/5.75 => ( ( L = K )
% 7.75/5.75 => ( ! [A5: real,X3: real] :
% 7.75/5.75 ( ( member_real @ X3 @ ( set_real2 @ L ) )
% 7.75/5.75 => ( ( F @ X3 @ A5 )
% 7.75/5.75 = ( G @ X3 @ A5 ) ) )
% 7.75/5.75 => ( ( foldr_real_real @ F @ L @ A )
% 7.75/5.75 = ( foldr_real_real @ G @ K @ B ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_cong
% 7.75/5.75 thf(fact_8047_finite__linorder__min__induct,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,P: set_Code_integer > $o] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( P @ bot_bo3990330152332043303nteger )
% 7.75/5.75 => ( ! [B2: code_integer,A8: set_Code_integer] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A8 )
% 7.75/5.75 => ( ! [X5: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X5 @ A8 )
% 7.75/5.75 => ( ord_le6747313008572928689nteger @ B2 @ X5 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_Code_integer @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_min_induct
% 7.75/5.75 thf(fact_8048_finite__linorder__min__induct,axiom,
% 7.75/5.75 ! [A2: set_real,P: set_real > $o] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_real )
% 7.75/5.75 => ( ! [B2: real,A8: set_real] :
% 7.75/5.75 ( ( finite_finite_real @ A8 )
% 7.75/5.75 => ( ! [X5: real] :
% 7.75/5.75 ( ( member_real @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_real @ B2 @ X5 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_real @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_min_induct
% 7.75/5.75 thf(fact_8049_finite__linorder__min__induct,axiom,
% 7.75/5.75 ! [A2: set_rat,P: set_rat > $o] :
% 7.75/5.75 ( ( finite_finite_rat @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_rat )
% 7.75/5.75 => ( ! [B2: rat,A8: set_rat] :
% 7.75/5.75 ( ( finite_finite_rat @ A8 )
% 7.75/5.75 => ( ! [X5: rat] :
% 7.75/5.75 ( ( member_rat @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_rat @ B2 @ X5 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_rat @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_min_induct
% 7.75/5.75 thf(fact_8050_finite__linorder__min__induct,axiom,
% 7.75/5.75 ! [A2: set_num,P: set_num > $o] :
% 7.75/5.75 ( ( finite_finite_num @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_num )
% 7.75/5.75 => ( ! [B2: num,A8: set_num] :
% 7.75/5.75 ( ( finite_finite_num @ A8 )
% 7.75/5.75 => ( ! [X5: num] :
% 7.75/5.75 ( ( member_num @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_num @ B2 @ X5 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_num @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_min_induct
% 7.75/5.75 thf(fact_8051_finite__linorder__min__induct,axiom,
% 7.75/5.75 ! [A2: set_nat,P: set_nat > $o] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_nat )
% 7.75/5.75 => ( ! [B2: nat,A8: set_nat] :
% 7.75/5.75 ( ( finite_finite_nat @ A8 )
% 7.75/5.75 => ( ! [X5: nat] :
% 7.75/5.75 ( ( member_nat @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_nat @ B2 @ X5 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_nat @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_min_induct
% 7.75/5.75 thf(fact_8052_finite__linorder__min__induct,axiom,
% 7.75/5.75 ! [A2: set_int,P: set_int > $o] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_int )
% 7.75/5.75 => ( ! [B2: int,A8: set_int] :
% 7.75/5.75 ( ( finite_finite_int @ A8 )
% 7.75/5.75 => ( ! [X5: int] :
% 7.75/5.75 ( ( member_int @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_int @ B2 @ X5 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_int @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_min_induct
% 7.75/5.75 thf(fact_8053_finite__linorder__max__induct,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,P: set_Code_integer > $o] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( P @ bot_bo3990330152332043303nteger )
% 7.75/5.75 => ( ! [B2: code_integer,A8: set_Code_integer] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A8 )
% 7.75/5.75 => ( ! [X5: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X5 @ A8 )
% 7.75/5.75 => ( ord_le6747313008572928689nteger @ X5 @ B2 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_Code_integer @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_max_induct
% 7.75/5.75 thf(fact_8054_finite__linorder__max__induct,axiom,
% 7.75/5.75 ! [A2: set_real,P: set_real > $o] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_real )
% 7.75/5.75 => ( ! [B2: real,A8: set_real] :
% 7.75/5.75 ( ( finite_finite_real @ A8 )
% 7.75/5.75 => ( ! [X5: real] :
% 7.75/5.75 ( ( member_real @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_real @ X5 @ B2 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_real @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_max_induct
% 7.75/5.75 thf(fact_8055_finite__linorder__max__induct,axiom,
% 7.75/5.75 ! [A2: set_rat,P: set_rat > $o] :
% 7.75/5.75 ( ( finite_finite_rat @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_rat )
% 7.75/5.75 => ( ! [B2: rat,A8: set_rat] :
% 7.75/5.75 ( ( finite_finite_rat @ A8 )
% 7.75/5.75 => ( ! [X5: rat] :
% 7.75/5.75 ( ( member_rat @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_rat @ X5 @ B2 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_rat @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_max_induct
% 7.75/5.75 thf(fact_8056_finite__linorder__max__induct,axiom,
% 7.75/5.75 ! [A2: set_num,P: set_num > $o] :
% 7.75/5.75 ( ( finite_finite_num @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_num )
% 7.75/5.75 => ( ! [B2: num,A8: set_num] :
% 7.75/5.75 ( ( finite_finite_num @ A8 )
% 7.75/5.75 => ( ! [X5: num] :
% 7.75/5.75 ( ( member_num @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_num @ X5 @ B2 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_num @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_max_induct
% 7.75/5.75 thf(fact_8057_finite__linorder__max__induct,axiom,
% 7.75/5.75 ! [A2: set_nat,P: set_nat > $o] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_nat )
% 7.75/5.75 => ( ! [B2: nat,A8: set_nat] :
% 7.75/5.75 ( ( finite_finite_nat @ A8 )
% 7.75/5.75 => ( ! [X5: nat] :
% 7.75/5.75 ( ( member_nat @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_nat @ X5 @ B2 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_nat @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_max_induct
% 7.75/5.75 thf(fact_8058_finite__linorder__max__induct,axiom,
% 7.75/5.75 ! [A2: set_int,P: set_int > $o] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( P @ bot_bot_set_int )
% 7.75/5.75 => ( ! [B2: int,A8: set_int] :
% 7.75/5.75 ( ( finite_finite_int @ A8 )
% 7.75/5.75 => ( ! [X5: int] :
% 7.75/5.75 ( ( member_int @ X5 @ A8 )
% 7.75/5.75 => ( ord_less_int @ X5 @ B2 ) )
% 7.75/5.75 => ( ( P @ A8 )
% 7.75/5.75 => ( P @ ( insert_int @ B2 @ A8 ) ) ) ) )
% 7.75/5.75 => ( P @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_linorder_max_induct
% 7.75/5.75 thf(fact_8059_atLeast0__atMost__Suc,axiom,
% 7.75/5.75 ! [N: nat] :
% 7.75/5.75 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 7.75/5.75 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % atLeast0_atMost_Suc
% 7.75/5.75 thf(fact_8060_atLeastAtMost__insertL,axiom,
% 7.75/5.75 ! [M: nat,N: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 7.75/5.75 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % atLeastAtMost_insertL
% 7.75/5.75 thf(fact_8061_atLeastAtMostSuc__conv,axiom,
% 7.75/5.75 ! [M: nat,N: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.75 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 7.75/5.75 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % atLeastAtMostSuc_conv
% 7.75/5.75 thf(fact_8062_Icc__eq__insert__lb__nat,axiom,
% 7.75/5.75 ! [M: nat,N: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 7.75/5.75 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % Icc_eq_insert_lb_nat
% 7.75/5.75 thf(fact_8063_remove__subset,axiom,
% 7.75/5.75 ! [X: vEBT_VEBT,S3: set_VEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ X @ S3 )
% 7.75/5.75 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ S3 ) ) ).
% 7.75/5.75
% 7.75/5.75 % remove_subset
% 7.75/5.75 thf(fact_8064_remove__subset,axiom,
% 7.75/5.75 ! [X: complex,S3: set_complex] :
% 7.75/5.75 ( ( member_complex @ X @ S3 )
% 7.75/5.75 => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ S3 ) ) ).
% 7.75/5.75
% 7.75/5.75 % remove_subset
% 7.75/5.75 thf(fact_8065_remove__subset,axiom,
% 7.75/5.75 ! [X: real,S3: set_real] :
% 7.75/5.75 ( ( member_real @ X @ S3 )
% 7.75/5.75 => ( ord_less_set_real @ ( minus_minus_set_real @ S3 @ ( insert_real @ X @ bot_bot_set_real ) ) @ S3 ) ) ).
% 7.75/5.75
% 7.75/5.75 % remove_subset
% 7.75/5.75 thf(fact_8066_remove__subset,axiom,
% 7.75/5.75 ! [X: int,S3: set_int] :
% 7.75/5.75 ( ( member_int @ X @ S3 )
% 7.75/5.75 => ( ord_less_set_int @ ( minus_minus_set_int @ S3 @ ( insert_int @ X @ bot_bot_set_int ) ) @ S3 ) ) ).
% 7.75/5.75
% 7.75/5.75 % remove_subset
% 7.75/5.75 thf(fact_8067_remove__subset,axiom,
% 7.75/5.75 ! [X: nat,S3: set_nat] :
% 7.75/5.75 ( ( member_nat @ X @ S3 )
% 7.75/5.75 => ( ord_less_set_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ S3 ) ) ).
% 7.75/5.75
% 7.75/5.75 % remove_subset
% 7.75/5.75 thf(fact_8068_set__update__subset__insert,axiom,
% 7.75/5.75 ! [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 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_update_subset_insert
% 7.75/5.75 thf(fact_8069_set__update__subset__insert,axiom,
% 7.75/5.75 ! [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 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_update_subset_insert
% 7.75/5.75 thf(fact_8070_set__update__subset__insert,axiom,
% 7.75/5.75 ! [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 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_update_subset_insert
% 7.75/5.75 thf(fact_8071_set__update__subset__insert,axiom,
% 7.75/5.75 ! [Xs2: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] : ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs2 @ I @ X ) ) @ ( insert_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_update_subset_insert
% 7.75/5.75 thf(fact_8072_set__update__subset__insert,axiom,
% 7.75/5.75 ! [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 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_update_subset_insert
% 7.75/5.75 thf(fact_8073_foldr__length__aux,axiom,
% 7.75/5.75 ! [L: list_real,A: nat] :
% 7.75/5.75 ( ( foldr_real_nat
% 7.75/5.75 @ ^ [X2: real] : suc
% 7.75/5.75 @ L
% 7.75/5.75 @ A )
% 7.75/5.75 = ( plus_plus_nat @ A @ ( size_size_list_real @ L ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_length_aux
% 7.75/5.75 thf(fact_8074_foldr__length__aux,axiom,
% 7.75/5.75 ! [L: list_o,A: nat] :
% 7.75/5.75 ( ( foldr_o_nat
% 7.75/5.75 @ ^ [X2: $o] : suc
% 7.75/5.75 @ L
% 7.75/5.75 @ A )
% 7.75/5.75 = ( plus_plus_nat @ A @ ( size_size_list_o @ L ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_length_aux
% 7.75/5.75 thf(fact_8075_foldr__length__aux,axiom,
% 7.75/5.75 ! [L: list_nat,A: nat] :
% 7.75/5.75 ( ( foldr_nat_nat
% 7.75/5.75 @ ^ [X2: nat] : suc
% 7.75/5.75 @ L
% 7.75/5.75 @ A )
% 7.75/5.75 = ( plus_plus_nat @ A @ ( size_size_list_nat @ L ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_length_aux
% 7.75/5.75 thf(fact_8076_foldr__length__aux,axiom,
% 7.75/5.75 ! [L: list_int,A: nat] :
% 7.75/5.75 ( ( foldr_int_nat
% 7.75/5.75 @ ^ [X2: int] : suc
% 7.75/5.75 @ L
% 7.75/5.75 @ A )
% 7.75/5.75 = ( plus_plus_nat @ A @ ( size_size_list_int @ L ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_length_aux
% 7.75/5.75 thf(fact_8077_finite__induct__select,axiom,
% 7.75/5.75 ! [S3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ S3 )
% 7.75/5.75 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 7.75/5.75 => ( ! [T3: set_VEBT_VEBT] :
% 7.75/5.75 ( ( ord_le3480810397992357184T_VEBT @ T3 @ S3 )
% 7.75/5.75 => ( ( P @ T3 )
% 7.75/5.75 => ? [X5: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ X5 @ ( minus_5127226145743854075T_VEBT @ S3 @ T3 ) )
% 7.75/5.75 & ( P @ ( insert_VEBT_VEBT @ X5 @ T3 ) ) ) ) )
% 7.75/5.75 => ( P @ S3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_induct_select
% 7.75/5.75 thf(fact_8078_finite__induct__select,axiom,
% 7.75/5.75 ! [S3: set_complex,P: set_complex > $o] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ S3 )
% 7.75/5.75 => ( ( P @ bot_bot_set_complex )
% 7.75/5.75 => ( ! [T3: set_complex] :
% 7.75/5.75 ( ( ord_less_set_complex @ T3 @ S3 )
% 7.75/5.75 => ( ( P @ T3 )
% 7.75/5.75 => ? [X5: complex] :
% 7.75/5.75 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ S3 @ T3 ) )
% 7.75/5.75 & ( P @ ( insert_complex @ X5 @ T3 ) ) ) ) )
% 7.75/5.75 => ( P @ S3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_induct_select
% 7.75/5.75 thf(fact_8079_finite__induct__select,axiom,
% 7.75/5.75 ! [S3: set_Code_integer,P: set_Code_integer > $o] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ S3 )
% 7.75/5.75 => ( ( P @ bot_bo3990330152332043303nteger )
% 7.75/5.75 => ( ! [T3: set_Code_integer] :
% 7.75/5.75 ( ( ord_le1307284697595431911nteger @ T3 @ S3 )
% 7.75/5.75 => ( ( P @ T3 )
% 7.75/5.75 => ? [X5: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X5 @ ( minus_2355218937544613996nteger @ S3 @ T3 ) )
% 7.75/5.75 & ( P @ ( insert_Code_integer @ X5 @ T3 ) ) ) ) )
% 7.75/5.75 => ( P @ S3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_induct_select
% 7.75/5.75 thf(fact_8080_finite__induct__select,axiom,
% 7.75/5.75 ! [S3: set_real,P: set_real > $o] :
% 7.75/5.75 ( ( finite_finite_real @ S3 )
% 7.75/5.75 => ( ( P @ bot_bot_set_real )
% 7.75/5.75 => ( ! [T3: set_real] :
% 7.75/5.75 ( ( ord_less_set_real @ T3 @ S3 )
% 7.75/5.75 => ( ( P @ T3 )
% 7.75/5.75 => ? [X5: real] :
% 7.75/5.75 ( ( member_real @ X5 @ ( minus_minus_set_real @ S3 @ T3 ) )
% 7.75/5.75 & ( P @ ( insert_real @ X5 @ T3 ) ) ) ) )
% 7.75/5.75 => ( P @ S3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_induct_select
% 7.75/5.75 thf(fact_8081_finite__induct__select,axiom,
% 7.75/5.75 ! [S3: set_int,P: set_int > $o] :
% 7.75/5.75 ( ( finite_finite_int @ S3 )
% 7.75/5.75 => ( ( P @ bot_bot_set_int )
% 7.75/5.75 => ( ! [T3: set_int] :
% 7.75/5.75 ( ( ord_less_set_int @ T3 @ S3 )
% 7.75/5.75 => ( ( P @ T3 )
% 7.75/5.75 => ? [X5: int] :
% 7.75/5.75 ( ( member_int @ X5 @ ( minus_minus_set_int @ S3 @ T3 ) )
% 7.75/5.75 & ( P @ ( insert_int @ X5 @ T3 ) ) ) ) )
% 7.75/5.75 => ( P @ S3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_induct_select
% 7.75/5.75 thf(fact_8082_finite__induct__select,axiom,
% 7.75/5.75 ! [S3: set_nat,P: set_nat > $o] :
% 7.75/5.75 ( ( finite_finite_nat @ S3 )
% 7.75/5.75 => ( ( P @ bot_bot_set_nat )
% 7.75/5.75 => ( ! [T3: set_nat] :
% 7.75/5.75 ( ( ord_less_set_nat @ T3 @ S3 )
% 7.75/5.75 => ( ( P @ T3 )
% 7.75/5.75 => ? [X5: nat] :
% 7.75/5.75 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ S3 @ T3 ) )
% 7.75/5.75 & ( P @ ( insert_nat @ X5 @ T3 ) ) ) ) )
% 7.75/5.75 => ( P @ S3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % finite_induct_select
% 7.75/5.75 thf(fact_8083_set__replicate__Suc,axiom,
% 7.75/5.75 ! [N: nat,X: vEBT_VEBT] :
% 7.75/5.75 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 7.75/5.75 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate_Suc
% 7.75/5.75 thf(fact_8084_set__replicate__Suc,axiom,
% 7.75/5.75 ! [N: nat,X: real] :
% 7.75/5.75 ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X ) )
% 7.75/5.75 = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate_Suc
% 7.75/5.75 thf(fact_8085_set__replicate__Suc,axiom,
% 7.75/5.75 ! [N: nat,X: nat] :
% 7.75/5.75 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 7.75/5.75 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate_Suc
% 7.75/5.75 thf(fact_8086_set__replicate__Suc,axiom,
% 7.75/5.75 ! [N: nat,X: int] :
% 7.75/5.75 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 7.75/5.75 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate_Suc
% 7.75/5.75 thf(fact_8087_psubset__insert__iff,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,B3: set_VEBT_VEBT] :
% 7.75/5.75 ( ( ord_le3480810397992357184T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ B3 ) )
% 7.75/5.75 = ( ( ( member_VEBT_VEBT @ X @ B3 )
% 7.75/5.75 => ( ord_le3480810397992357184T_VEBT @ A2 @ B3 ) )
% 7.75/5.75 & ( ~ ( member_VEBT_VEBT @ X @ B3 )
% 7.75/5.75 => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 7.75/5.75 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B3 ) )
% 7.75/5.75 & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 7.75/5.75 => ( ord_le4337996190870823476T_VEBT @ A2 @ B3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % psubset_insert_iff
% 7.75/5.75 thf(fact_8088_psubset__insert__iff,axiom,
% 7.75/5.75 ! [A2: set_complex,X: complex,B3: set_complex] :
% 7.75/5.75 ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X @ B3 ) )
% 7.75/5.75 = ( ( ( member_complex @ X @ B3 )
% 7.75/5.75 => ( ord_less_set_complex @ A2 @ B3 ) )
% 7.75/5.75 & ( ~ ( member_complex @ X @ B3 )
% 7.75/5.75 => ( ( ( member_complex @ X @ A2 )
% 7.75/5.75 => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B3 ) )
% 7.75/5.75 & ( ~ ( member_complex @ X @ A2 )
% 7.75/5.75 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % psubset_insert_iff
% 7.75/5.75 thf(fact_8089_psubset__insert__iff,axiom,
% 7.75/5.75 ! [A2: set_real,X: real,B3: set_real] :
% 7.75/5.75 ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 7.75/5.75 = ( ( ( member_real @ X @ B3 )
% 7.75/5.75 => ( ord_less_set_real @ A2 @ B3 ) )
% 7.75/5.75 & ( ~ ( member_real @ X @ B3 )
% 7.75/5.75 => ( ( ( member_real @ X @ A2 )
% 7.75/5.75 => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 ) )
% 7.75/5.75 & ( ~ ( member_real @ X @ A2 )
% 7.75/5.75 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % psubset_insert_iff
% 7.75/5.75 thf(fact_8090_psubset__insert__iff,axiom,
% 7.75/5.75 ! [A2: set_int,X: int,B3: set_int] :
% 7.75/5.75 ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 7.75/5.75 = ( ( ( member_int @ X @ B3 )
% 7.75/5.75 => ( ord_less_set_int @ A2 @ B3 ) )
% 7.75/5.75 & ( ~ ( member_int @ X @ B3 )
% 7.75/5.75 => ( ( ( member_int @ X @ A2 )
% 7.75/5.75 => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 ) )
% 7.75/5.75 & ( ~ ( member_int @ X @ A2 )
% 7.75/5.75 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % psubset_insert_iff
% 7.75/5.75 thf(fact_8091_psubset__insert__iff,axiom,
% 7.75/5.75 ! [A2: set_nat,X: nat,B3: set_nat] :
% 7.75/5.75 ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 7.75/5.75 = ( ( ( member_nat @ X @ B3 )
% 7.75/5.75 => ( ord_less_set_nat @ A2 @ B3 ) )
% 7.75/5.75 & ( ~ ( member_nat @ X @ B3 )
% 7.75/5.75 => ( ( ( member_nat @ X @ A2 )
% 7.75/5.75 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 ) )
% 7.75/5.75 & ( ~ ( member_nat @ X @ A2 )
% 7.75/5.75 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % psubset_insert_iff
% 7.75/5.75 thf(fact_8092_set__replicate__conv__if,axiom,
% 7.75/5.75 ! [N: nat,X: vEBT_VEBT] :
% 7.75/5.75 ( ( ( N = zero_zero_nat )
% 7.75/5.75 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 7.75/5.75 = bot_bo8194388402131092736T_VEBT ) )
% 7.75/5.75 & ( ( N != zero_zero_nat )
% 7.75/5.75 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 7.75/5.75 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate_conv_if
% 7.75/5.75 thf(fact_8093_set__replicate__conv__if,axiom,
% 7.75/5.75 ! [N: nat,X: real] :
% 7.75/5.75 ( ( ( N = zero_zero_nat )
% 7.75/5.75 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 7.75/5.75 = bot_bot_set_real ) )
% 7.75/5.75 & ( ( N != zero_zero_nat )
% 7.75/5.75 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 7.75/5.75 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate_conv_if
% 7.75/5.75 thf(fact_8094_set__replicate__conv__if,axiom,
% 7.75/5.75 ! [N: nat,X: nat] :
% 7.75/5.75 ( ( ( N = zero_zero_nat )
% 7.75/5.75 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 7.75/5.75 = bot_bot_set_nat ) )
% 7.75/5.75 & ( ( N != zero_zero_nat )
% 7.75/5.75 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 7.75/5.75 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate_conv_if
% 7.75/5.75 thf(fact_8095_set__replicate__conv__if,axiom,
% 7.75/5.75 ! [N: nat,X: int] :
% 7.75/5.75 ( ( ( N = zero_zero_nat )
% 7.75/5.75 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 7.75/5.75 = bot_bot_set_int ) )
% 7.75/5.75 & ( ( N != zero_zero_nat )
% 7.75/5.75 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 7.75/5.75 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_replicate_conv_if
% 7.75/5.75 thf(fact_8096_insert__swap__set__eq,axiom,
% 7.75/5.75 ! [I: nat,L: list_VEBT_VEBT,X: vEBT_VEBT] :
% 7.75/5.75 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 7.75/5.75 => ( ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ L @ I ) @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) ) )
% 7.75/5.75 = ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ L ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % insert_swap_set_eq
% 7.75/5.75 thf(fact_8097_insert__swap__set__eq,axiom,
% 7.75/5.75 ! [I: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 7.75/5.75 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 7.75/5.75 => ( ( insert_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ L @ I ) @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) ) )
% 7.75/5.75 = ( insert_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ L ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % insert_swap_set_eq
% 7.75/5.75 thf(fact_8098_insert__swap__set__eq,axiom,
% 7.75/5.75 ! [I: nat,L: list_real,X: real] :
% 7.75/5.75 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 7.75/5.75 => ( ( insert_real @ ( nth_real @ L @ I ) @ ( set_real2 @ ( list_update_real @ L @ I @ X ) ) )
% 7.75/5.75 = ( insert_real @ X @ ( set_real2 @ L ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % insert_swap_set_eq
% 7.75/5.75 thf(fact_8099_insert__swap__set__eq,axiom,
% 7.75/5.75 ! [I: nat,L: list_o,X: $o] :
% 7.75/5.75 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 7.75/5.75 => ( ( insert_o @ ( nth_o @ L @ I ) @ ( set_o2 @ ( list_update_o @ L @ I @ X ) ) )
% 7.75/5.75 = ( insert_o @ X @ ( set_o2 @ L ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % insert_swap_set_eq
% 7.75/5.75 thf(fact_8100_insert__swap__set__eq,axiom,
% 7.75/5.75 ! [I: nat,L: list_nat,X: nat] :
% 7.75/5.75 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 7.75/5.75 => ( ( insert_nat @ ( nth_nat @ L @ I ) @ ( set_nat2 @ ( list_update_nat @ L @ I @ X ) ) )
% 7.75/5.75 = ( insert_nat @ X @ ( set_nat2 @ L ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % insert_swap_set_eq
% 7.75/5.75 thf(fact_8101_insert__swap__set__eq,axiom,
% 7.75/5.75 ! [I: nat,L: list_int,X: int] :
% 7.75/5.75 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 7.75/5.75 => ( ( insert_int @ ( nth_int @ L @ I ) @ ( set_int2 @ ( list_update_int @ L @ I @ X ) ) )
% 7.75/5.75 = ( insert_int @ X @ ( set_int2 @ L ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % insert_swap_set_eq
% 7.75/5.75 thf(fact_8102_monoseq__realpow,axiom,
% 7.75/5.75 ! [X: real] :
% 7.75/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.75/5.75 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.75/5.75 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % monoseq_realpow
% 7.75/5.75 thf(fact_8103_set__decode__plus__power__2,axiom,
% 7.75/5.75 ! [N: nat,Z: nat] :
% 7.75/5.75 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 7.75/5.75 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 7.75/5.75 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % set_decode_plus_power_2
% 7.75/5.75 thf(fact_8104_foldr__same,axiom,
% 7.75/5.75 ! [Xs2: list_real,Y: real] :
% 7.75/5.75 ( ! [X3: real,Y3: real] :
% 7.75/5.75 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.75/5.75 => ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 7.75/5.75 => ( X3 = Y3 ) ) )
% 7.75/5.75 => ( ! [X3: real] :
% 7.75/5.75 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.75/5.75 => ( X3 = Y ) )
% 7.75/5.75 => ( ( foldr_real_real @ plus_plus_real @ Xs2 @ zero_zero_real )
% 7.75/5.75 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_real @ Xs2 ) ) @ Y ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr_same
% 7.75/5.75 thf(fact_8105_diff__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: set_nat > nat,N4: set_nat > nat] :
% 7.75/5.75 ( ( finite1152437895449049373et_nat
% 7.75/5.75 @ ( collect_set_nat
% 7.75/5.75 @ ^ [X2: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite1152437895449049373et_nat
% 7.75/5.75 @ ( collect_set_nat
% 7.75/5.75 @ ^ [X2: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X2 ) @ ( N4 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % diff_preserves_multiset
% 7.75/5.75 thf(fact_8106_diff__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: nat > nat,N4: nat > nat] :
% 7.75/5.75 ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [X2: nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [X2: nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X2 ) @ ( N4 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % diff_preserves_multiset
% 7.75/5.75 thf(fact_8107_diff__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: int > nat,N4: int > nat] :
% 7.75/5.75 ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [X2: int] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [X2: int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X2 ) @ ( N4 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % diff_preserves_multiset
% 7.75/5.75 thf(fact_8108_diff__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: complex > nat,N4: complex > nat] :
% 7.75/5.75 ( ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [X2: complex] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [X2: complex] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X2 ) @ ( N4 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % diff_preserves_multiset
% 7.75/5.75 thf(fact_8109_diff__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: code_integer > nat,N4: code_integer > nat] :
% 7.75/5.75 ( ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [X2: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [X2: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X2 ) @ ( N4 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % diff_preserves_multiset
% 7.75/5.75 thf(fact_8110_add__mset__in__multiset,axiom,
% 7.75/5.75 ! [M7: set_nat > nat,A: set_nat] :
% 7.75/5.75 ( ( finite1152437895449049373et_nat
% 7.75/5.75 @ ( collect_set_nat
% 7.75/5.75 @ ^ [X2: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite1152437895449049373et_nat
% 7.75/5.75 @ ( collect_set_nat
% 7.75/5.75 @ ^ [X2: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X2 = A ) @ ( suc @ ( M7 @ X2 ) ) @ ( M7 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % add_mset_in_multiset
% 7.75/5.75 thf(fact_8111_add__mset__in__multiset,axiom,
% 7.75/5.75 ! [M7: nat > nat,A: nat] :
% 7.75/5.75 ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [X2: nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [X2: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X2 = A ) @ ( suc @ ( M7 @ X2 ) ) @ ( M7 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % add_mset_in_multiset
% 7.75/5.75 thf(fact_8112_add__mset__in__multiset,axiom,
% 7.75/5.75 ! [M7: int > nat,A: int] :
% 7.75/5.75 ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [X2: int] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [X2: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X2 = A ) @ ( suc @ ( M7 @ X2 ) ) @ ( M7 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % add_mset_in_multiset
% 7.75/5.75 thf(fact_8113_add__mset__in__multiset,axiom,
% 7.75/5.75 ! [M7: complex > nat,A: complex] :
% 7.75/5.75 ( ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [X2: complex] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [X2: complex] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X2 = A ) @ ( suc @ ( M7 @ X2 ) ) @ ( M7 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % add_mset_in_multiset
% 7.75/5.75 thf(fact_8114_add__mset__in__multiset,axiom,
% 7.75/5.75 ! [M7: code_integer > nat,A: code_integer] :
% 7.75/5.75 ( ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [X2: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [X2: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X2 = A ) @ ( suc @ ( M7 @ X2 ) ) @ ( M7 @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % add_mset_in_multiset
% 7.75/5.75 thf(fact_8115_pochhammer__times__pochhammer__half,axiom,
% 7.75/5.75 ! [Z: rat,N: nat] :
% 7.75/5.75 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 7.75/5.75 = ( groups73079841787564623at_rat
% 7.75/5.75 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_times_pochhammer_half
% 7.75/5.75 thf(fact_8116_pochhammer__times__pochhammer__half,axiom,
% 7.75/5.75 ! [Z: real,N: nat] :
% 7.75/5.75 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 7.75/5.75 = ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_times_pochhammer_half
% 7.75/5.75 thf(fact_8117_pochhammer__times__pochhammer__half,axiom,
% 7.75/5.75 ! [Z: complex,N: nat] :
% 7.75/5.75 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 7.75/5.75 = ( groups6464643781859351333omplex
% 7.75/5.75 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_times_pochhammer_half
% 7.75/5.75 thf(fact_8118_foldr0,axiom,
% 7.75/5.75 ! [Xs2: list_real,C: real,D2: real] :
% 7.75/5.75 ( ( foldr_real_real @ plus_plus_real @ Xs2 @ ( plus_plus_real @ C @ D2 ) )
% 7.75/5.75 = ( plus_plus_real @ ( foldr_real_real @ plus_plus_real @ Xs2 @ D2 ) @ C ) ) ).
% 7.75/5.75
% 7.75/5.75 % foldr0
% 7.75/5.75 thf(fact_8119_prod_Ocl__ivl__Suc,axiom,
% 7.75/5.75 ! [N: nat,M: nat,G: nat > rat] :
% 7.75/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = one_one_rat ) )
% 7.75/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.cl_ivl_Suc
% 7.75/5.75 thf(fact_8120_prod_Ocl__ivl__Suc,axiom,
% 7.75/5.75 ! [N: nat,M: nat,G: nat > assn] :
% 7.75/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = one_one_assn ) )
% 7.75/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.cl_ivl_Suc
% 7.75/5.75 thf(fact_8121_prod_Ocl__ivl__Suc,axiom,
% 7.75/5.75 ! [N: nat,M: nat,G: nat > real] :
% 7.75/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = one_one_real ) )
% 7.75/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.cl_ivl_Suc
% 7.75/5.75 thf(fact_8122_prod_Ocl__ivl__Suc,axiom,
% 7.75/5.75 ! [N: nat,M: nat,G: nat > code_integer] :
% 7.75/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = one_one_Code_integer ) )
% 7.75/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.cl_ivl_Suc
% 7.75/5.75 thf(fact_8123_prod_Ocl__ivl__Suc,axiom,
% 7.75/5.75 ! [N: nat,M: nat,G: nat > complex] :
% 7.75/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = one_one_complex ) )
% 7.75/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.cl_ivl_Suc
% 7.75/5.75 thf(fact_8124_prod_Ocl__ivl__Suc,axiom,
% 7.75/5.75 ! [N: nat,M: nat,G: nat > nat] :
% 7.75/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = one_one_nat ) )
% 7.75/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.cl_ivl_Suc
% 7.75/5.75 thf(fact_8125_prod_Ocl__ivl__Suc,axiom,
% 7.75/5.75 ! [N: nat,M: nat,G: nat > int] :
% 7.75/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = one_one_int ) )
% 7.75/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 7.75/5.75 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.cl_ivl_Suc
% 7.75/5.75 thf(fact_8126_mod__prod__eq,axiom,
% 7.75/5.75 ! [F: nat > nat,A: nat,A2: set_nat] :
% 7.75/5.75 ( ( modulo_modulo_nat
% 7.75/5.75 @ ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [I2: nat] : ( modulo_modulo_nat @ ( F @ I2 ) @ A )
% 7.75/5.75 @ A2 )
% 7.75/5.75 @ A )
% 7.75/5.75 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 7.75/5.75
% 7.75/5.75 % mod_prod_eq
% 7.75/5.75 thf(fact_8127_mod__prod__eq,axiom,
% 7.75/5.75 ! [F: nat > int,A: int,A2: set_nat] :
% 7.75/5.75 ( ( modulo_modulo_int
% 7.75/5.75 @ ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [I2: nat] : ( modulo_modulo_int @ ( F @ I2 ) @ A )
% 7.75/5.75 @ A2 )
% 7.75/5.75 @ A )
% 7.75/5.75 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 7.75/5.75
% 7.75/5.75 % mod_prod_eq
% 7.75/5.75 thf(fact_8128_mod__prod__eq,axiom,
% 7.75/5.75 ! [F: int > int,A: int,A2: set_int] :
% 7.75/5.75 ( ( modulo_modulo_int
% 7.75/5.75 @ ( groups1705073143266064639nt_int
% 7.75/5.75 @ ^ [I2: int] : ( modulo_modulo_int @ ( F @ I2 ) @ A )
% 7.75/5.75 @ A2 )
% 7.75/5.75 @ A )
% 7.75/5.75 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 7.75/5.75
% 7.75/5.75 % mod_prod_eq
% 7.75/5.75 thf(fact_8129_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 7.75/5.75 ! [G: nat > nat,M: nat,N: nat] :
% 7.75/5.75 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 7.75/5.75 = ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.shift_bounds_cl_Suc_ivl
% 7.75/5.75 thf(fact_8130_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 7.75/5.75 ! [G: nat > int,M: nat,N: nat] :
% 7.75/5.75 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 7.75/5.75 = ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.shift_bounds_cl_Suc_ivl
% 7.75/5.75 thf(fact_8131_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 7.75/5.75 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 7.75/5.75 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 7.75/5.75 = ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ I2 @ K ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.shift_bounds_cl_nat_ivl
% 7.75/5.75 thf(fact_8132_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 7.75/5.75 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 7.75/5.75 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 7.75/5.75 = ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ I2 @ K ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.shift_bounds_cl_nat_ivl
% 7.75/5.75 thf(fact_8133_prod_OatLeastAtMost__rev,axiom,
% 7.75/5.75 ! [G: nat > nat,N: nat,M: nat] :
% 7.75/5.75 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 7.75/5.75 = ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeastAtMost_rev
% 7.75/5.75 thf(fact_8134_prod_OatLeastAtMost__rev,axiom,
% 7.75/5.75 ! [G: nat > int,N: nat,M: nat] :
% 7.75/5.75 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 7.75/5.75 = ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeastAtMost_rev
% 7.75/5.75 thf(fact_8135_prod_OatLeast0__atMost__Suc,axiom,
% 7.75/5.75 ! [G: nat > assn,N: nat] :
% 7.75/5.75 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast0_atMost_Suc
% 7.75/5.75 thf(fact_8136_prod_OatLeast0__atMost__Suc,axiom,
% 7.75/5.75 ! [G: nat > real,N: nat] :
% 7.75/5.75 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast0_atMost_Suc
% 7.75/5.75 thf(fact_8137_prod_OatLeast0__atMost__Suc,axiom,
% 7.75/5.75 ! [G: nat > code_integer,N: nat] :
% 7.75/5.75 ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast0_atMost_Suc
% 7.75/5.75 thf(fact_8138_prod_OatLeast0__atMost__Suc,axiom,
% 7.75/5.75 ! [G: nat > complex,N: nat] :
% 7.75/5.75 ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast0_atMost_Suc
% 7.75/5.75 thf(fact_8139_prod_OatLeast0__atMost__Suc,axiom,
% 7.75/5.75 ! [G: nat > nat,N: nat] :
% 7.75/5.75 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast0_atMost_Suc
% 7.75/5.75 thf(fact_8140_prod_OatLeast0__atMost__Suc,axiom,
% 7.75/5.75 ! [G: nat > int,N: nat] :
% 7.75/5.75 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast0_atMost_Suc
% 7.75/5.75 thf(fact_8141_prod_Onat__ivl__Suc_H,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > assn] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_assn @ ( G @ ( suc @ N ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.nat_ivl_Suc'
% 7.75/5.75 thf(fact_8142_prod_Onat__ivl__Suc_H,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > real] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.75 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_real @ ( G @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.nat_ivl_Suc'
% 7.75/5.75 thf(fact_8143_prod_Onat__ivl__Suc_H,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > code_integer] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.75 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_3573771949741848930nteger @ ( G @ ( suc @ N ) ) @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.nat_ivl_Suc'
% 7.75/5.75 thf(fact_8144_prod_Onat__ivl__Suc_H,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > complex] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.75 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_complex @ ( G @ ( suc @ N ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.nat_ivl_Suc'
% 7.75/5.75 thf(fact_8145_prod_Onat__ivl__Suc_H,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.75 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_nat @ ( G @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.nat_ivl_Suc'
% 7.75/5.75 thf(fact_8146_prod_Onat__ivl__Suc_H,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > int] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 7.75/5.75 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_int @ ( G @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.nat_ivl_Suc'
% 7.75/5.75 thf(fact_8147_prod_OatLeast__Suc__atMost,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > assn] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 7.75/5.75 = ( times_times_assn @ ( G @ M ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast_Suc_atMost
% 7.75/5.75 thf(fact_8148_prod_OatLeast__Suc__atMost,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > real] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 7.75/5.75 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast_Suc_atMost
% 7.75/5.75 thf(fact_8149_prod_OatLeast__Suc__atMost,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > code_integer] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 7.75/5.75 = ( times_3573771949741848930nteger @ ( G @ M ) @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast_Suc_atMost
% 7.75/5.75 thf(fact_8150_prod_OatLeast__Suc__atMost,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > complex] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 7.75/5.75 = ( times_times_complex @ ( G @ M ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast_Suc_atMost
% 7.75/5.75 thf(fact_8151_prod_OatLeast__Suc__atMost,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 7.75/5.75 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast_Suc_atMost
% 7.75/5.75 thf(fact_8152_prod_OatLeast__Suc__atMost,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > int] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 7.75/5.75 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.atLeast_Suc_atMost
% 7.75/5.75 thf(fact_8153_prod_OSuc__reindex__ivl,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > assn] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_assn @ ( G @ M )
% 7.75/5.75 @ ( groups6906906614972039071t_assn
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.Suc_reindex_ivl
% 7.75/5.75 thf(fact_8154_prod_OSuc__reindex__ivl,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > real] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_real @ ( G @ M )
% 7.75/5.75 @ ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.Suc_reindex_ivl
% 7.75/5.75 thf(fact_8155_prod_OSuc__reindex__ivl,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > code_integer] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_3573771949741848930nteger @ ( G @ M )
% 7.75/5.75 @ ( groups3455450783089532116nteger
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.Suc_reindex_ivl
% 7.75/5.75 thf(fact_8156_prod_OSuc__reindex__ivl,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > complex] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_complex @ ( G @ M )
% 7.75/5.75 @ ( groups6464643781859351333omplex
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.Suc_reindex_ivl
% 7.75/5.75 thf(fact_8157_prod_OSuc__reindex__ivl,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_nat @ ( G @ M )
% 7.75/5.75 @ ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.Suc_reindex_ivl
% 7.75/5.75 thf(fact_8158_prod_OSuc__reindex__ivl,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > int] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ N )
% 7.75/5.75 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 7.75/5.75 = ( times_times_int @ ( G @ M )
% 7.75/5.75 @ ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.Suc_reindex_ivl
% 7.75/5.75 thf(fact_8159_fact__prod,axiom,
% 7.75/5.75 ( semiri1406184849735516958ct_int
% 7.75/5.75 = ( ^ [N3: nat] :
% 7.75/5.75 ( semiri1314217659103216013at_int
% 7.75/5.75 @ ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [X2: nat] : X2
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % fact_prod
% 7.75/5.75 thf(fact_8160_fact__prod,axiom,
% 7.75/5.75 ( semiri1408675320244567234ct_nat
% 7.75/5.75 = ( ^ [N3: nat] :
% 7.75/5.75 ( semiri1316708129612266289at_nat
% 7.75/5.75 @ ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [X2: nat] : X2
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % fact_prod
% 7.75/5.75 thf(fact_8161_fact__prod,axiom,
% 7.75/5.75 ( semiri2265585572941072030t_real
% 7.75/5.75 = ( ^ [N3: nat] :
% 7.75/5.75 ( semiri5074537144036343181t_real
% 7.75/5.75 @ ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [X2: nat] : X2
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % fact_prod
% 7.75/5.75 thf(fact_8162_fact__prod,axiom,
% 7.75/5.75 ( semiri5044797733671781792omplex
% 7.75/5.75 = ( ^ [N3: nat] :
% 7.75/5.75 ( semiri8010041392384452111omplex
% 7.75/5.75 @ ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [X2: nat] : X2
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % fact_prod
% 7.75/5.75 thf(fact_8163_atLeastAtMostPlus1__int__conv,axiom,
% 7.75/5.75 ! [M: int,N: int] :
% 7.75/5.75 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 7.75/5.75 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 7.75/5.75 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % atLeastAtMostPlus1_int_conv
% 7.75/5.75 thf(fact_8164_simp__from__to,axiom,
% 7.75/5.75 ( set_or1266510415728281911st_int
% 7.75/5.75 = ( ^ [I2: int,J2: int] : ( if_set_int @ ( ord_less_int @ J2 @ I2 ) @ bot_bot_set_int @ ( insert_int @ I2 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % simp_from_to
% 7.75/5.75 thf(fact_8165_prod__atLeastAtMost__code,axiom,
% 7.75/5.75 ! [F: nat > rat,A: nat,B: nat] :
% 7.75/5.75 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 7.75/5.75 = ( set_fo1949268297981939178at_rat
% 7.75/5.75 @ ^ [A3: nat] : ( times_times_rat @ ( F @ A3 ) )
% 7.75/5.75 @ A
% 7.75/5.75 @ B
% 7.75/5.75 @ one_one_rat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_atLeastAtMost_code
% 7.75/5.75 thf(fact_8166_prod__atLeastAtMost__code,axiom,
% 7.75/5.75 ! [F: nat > assn,A: nat,B: nat] :
% 7.75/5.75 ( ( groups6906906614972039071t_assn @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 7.75/5.75 = ( set_fo1959793692361082170t_assn
% 7.75/5.75 @ ^ [A3: nat] : ( times_times_assn @ ( F @ A3 ) )
% 7.75/5.75 @ A
% 7.75/5.75 @ B
% 7.75/5.75 @ one_one_assn ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_atLeastAtMost_code
% 7.75/5.75 thf(fact_8167_prod__atLeastAtMost__code,axiom,
% 7.75/5.75 ! [F: nat > real,A: nat,B: nat] :
% 7.75/5.75 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 7.75/5.75 = ( set_fo3111899725591712190t_real
% 7.75/5.75 @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 7.75/5.75 @ A
% 7.75/5.75 @ B
% 7.75/5.75 @ one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_atLeastAtMost_code
% 7.75/5.75 thf(fact_8168_prod__atLeastAtMost__code,axiom,
% 7.75/5.75 ! [F: nat > code_integer,A: nat,B: nat] :
% 7.75/5.75 ( ( groups3455450783089532116nteger @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 7.75/5.75 = ( set_fo1084959871951514735nteger
% 7.75/5.75 @ ^ [A3: nat] : ( times_3573771949741848930nteger @ ( F @ A3 ) )
% 7.75/5.75 @ A
% 7.75/5.75 @ B
% 7.75/5.75 @ one_one_Code_integer ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_atLeastAtMost_code
% 7.75/5.75 thf(fact_8169_prod__atLeastAtMost__code,axiom,
% 7.75/5.75 ! [F: nat > complex,A: nat,B: nat] :
% 7.75/5.75 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 7.75/5.75 = ( set_fo1517530859248394432omplex
% 7.75/5.75 @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 7.75/5.75 @ A
% 7.75/5.75 @ B
% 7.75/5.75 @ one_one_complex ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_atLeastAtMost_code
% 7.75/5.75 thf(fact_8170_prod__atLeastAtMost__code,axiom,
% 7.75/5.75 ! [F: nat > nat,A: nat,B: nat] :
% 7.75/5.75 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 7.75/5.75 = ( set_fo2584398358068434914at_nat
% 7.75/5.75 @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 7.75/5.75 @ A
% 7.75/5.75 @ B
% 7.75/5.75 @ one_one_nat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_atLeastAtMost_code
% 7.75/5.75 thf(fact_8171_prod__atLeastAtMost__code,axiom,
% 7.75/5.75 ! [F: nat > int,A: nat,B: nat] :
% 7.75/5.75 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 7.75/5.75 = ( set_fo2581907887559384638at_int
% 7.75/5.75 @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 7.75/5.75 @ A
% 7.75/5.75 @ B
% 7.75/5.75 @ one_one_int ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_atLeastAtMost_code
% 7.75/5.75 thf(fact_8172_even__prod__iff,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > nat] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 7.75/5.75 = ( ? [X2: int] :
% 7.75/5.75 ( ( member_int @ X2 @ A2 )
% 7.75/5.75 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % even_prod_iff
% 7.75/5.75 thf(fact_8173_even__prod__iff,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > nat] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 7.75/5.75 = ( ? [X2: complex] :
% 7.75/5.75 ( ( member_complex @ X2 @ A2 )
% 7.75/5.75 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % even_prod_iff
% 7.75/5.75 thf(fact_8174_even__prod__iff,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,F: code_integer > nat] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3190895334310489300er_nat @ F @ A2 ) )
% 7.75/5.75 = ( ? [X2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X2 @ A2 )
% 7.75/5.75 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % even_prod_iff
% 7.75/5.75 thf(fact_8175_even__prod__iff,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > int] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups858564598930262913ex_int @ F @ A2 ) )
% 7.75/5.75 = ( ? [X2: complex] :
% 7.75/5.75 ( ( member_complex @ X2 @ A2 )
% 7.75/5.75 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % even_prod_iff
% 7.75/5.75 thf(fact_8176_even__prod__iff,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,F: code_integer > int] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3188404863801439024er_int @ F @ A2 ) )
% 7.75/5.75 = ( ? [X2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X2 @ A2 )
% 7.75/5.75 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % even_prod_iff
% 7.75/5.75 thf(fact_8177_even__prod__iff,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > nat] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 7.75/5.75 = ( ? [X2: nat] :
% 7.75/5.75 ( ( member_nat @ X2 @ A2 )
% 7.75/5.75 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % even_prod_iff
% 7.75/5.75 thf(fact_8178_even__prod__iff,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > int] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups705719431365010083at_int @ F @ A2 ) )
% 7.75/5.75 = ( ? [X2: nat] :
% 7.75/5.75 ( ( member_nat @ X2 @ A2 )
% 7.75/5.75 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % even_prod_iff
% 7.75/5.75 thf(fact_8179_even__prod__iff,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > int] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups1705073143266064639nt_int @ F @ A2 ) )
% 7.75/5.75 = ( ? [X2: int] :
% 7.75/5.75 ( ( member_int @ X2 @ A2 )
% 7.75/5.75 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % even_prod_iff
% 7.75/5.75 thf(fact_8180_prod_Oub__add__nat,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > assn,P4: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 7.75/5.75 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.ub_add_nat
% 7.75/5.75 thf(fact_8181_prod_Oub__add__nat,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > real,P4: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 7.75/5.75 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 7.75/5.75 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.ub_add_nat
% 7.75/5.75 thf(fact_8182_prod_Oub__add__nat,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > code_integer,P4: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 7.75/5.75 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 7.75/5.75 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.ub_add_nat
% 7.75/5.75 thf(fact_8183_prod_Oub__add__nat,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > complex,P4: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 7.75/5.75 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 7.75/5.75 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.ub_add_nat
% 7.75/5.75 thf(fact_8184_prod_Oub__add__nat,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > nat,P4: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 7.75/5.75 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 7.75/5.75 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.ub_add_nat
% 7.75/5.75 thf(fact_8185_prod_Oub__add__nat,axiom,
% 7.75/5.75 ! [M: nat,N: nat,G: nat > int,P4: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 7.75/5.75 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 7.75/5.75 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.ub_add_nat
% 7.75/5.75 thf(fact_8186_fact__eq__fact__times,axiom,
% 7.75/5.75 ! [N: nat,M: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.75 => ( ( semiri1408675320244567234ct_nat @ M )
% 7.75/5.75 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 7.75/5.75 @ ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [X2: nat] : X2
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % fact_eq_fact_times
% 7.75/5.75 thf(fact_8187_pochhammer__Suc__prod,axiom,
% 7.75/5.75 ! [A: rat,N: nat] :
% 7.75/5.75 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups73079841787564623at_rat
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod
% 7.75/5.75 thf(fact_8188_pochhammer__Suc__prod,axiom,
% 7.75/5.75 ! [A: real,N: nat] :
% 7.75/5.75 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod
% 7.75/5.75 thf(fact_8189_pochhammer__Suc__prod,axiom,
% 7.75/5.75 ! [A: complex,N: nat] :
% 7.75/5.75 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups6464643781859351333omplex
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod
% 7.75/5.75 thf(fact_8190_pochhammer__Suc__prod,axiom,
% 7.75/5.75 ! [A: nat,N: nat] :
% 7.75/5.75 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod
% 7.75/5.75 thf(fact_8191_pochhammer__Suc__prod,axiom,
% 7.75/5.75 ! [A: int,N: nat] :
% 7.75/5.75 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I2 ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod
% 7.75/5.75 thf(fact_8192_pochhammer__prod__rev,axiom,
% 7.75/5.75 ( comm_s4028243227959126397er_rat
% 7.75/5.75 = ( ^ [A3: rat,N3: nat] :
% 7.75/5.75 ( groups73079841787564623at_rat
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N3 @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_prod_rev
% 7.75/5.75 thf(fact_8193_pochhammer__prod__rev,axiom,
% 7.75/5.75 ( comm_s7457072308508201937r_real
% 7.75/5.75 = ( ^ [A3: real,N3: nat] :
% 7.75/5.75 ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N3 @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_prod_rev
% 7.75/5.75 thf(fact_8194_pochhammer__prod__rev,axiom,
% 7.75/5.75 ( comm_s2602460028002588243omplex
% 7.75/5.75 = ( ^ [A3: complex,N3: nat] :
% 7.75/5.75 ( groups6464643781859351333omplex
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N3 @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_prod_rev
% 7.75/5.75 thf(fact_8195_pochhammer__prod__rev,axiom,
% 7.75/5.75 ( comm_s4663373288045622133er_nat
% 7.75/5.75 = ( ^ [A3: nat,N3: nat] :
% 7.75/5.75 ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N3 @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_prod_rev
% 7.75/5.75 thf(fact_8196_pochhammer__prod__rev,axiom,
% 7.75/5.75 ( comm_s4660882817536571857er_int
% 7.75/5.75 = ( ^ [A3: int,N3: nat] :
% 7.75/5.75 ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N3 @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_prod_rev
% 7.75/5.75 thf(fact_8197_fact__div__fact,axiom,
% 7.75/5.75 ! [N: nat,M: nat] :
% 7.75/5.75 ( ( ord_less_eq_nat @ N @ M )
% 7.75/5.75 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 7.75/5.75 = ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [X2: nat] : X2
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % fact_div_fact
% 7.75/5.75 thf(fact_8198_prod_Oin__pairs,axiom,
% 7.75/5.75 ! [G: nat > assn,M: nat,N: nat] :
% 7.75/5.75 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.75 = ( groups6906906614972039071t_assn
% 7.75/5.75 @ ^ [I2: nat] : ( times_times_assn @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.in_pairs
% 7.75/5.75 thf(fact_8199_prod_Oin__pairs,axiom,
% 7.75/5.75 ! [G: nat > real,M: nat,N: nat] :
% 7.75/5.75 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.75 = ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [I2: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.in_pairs
% 7.75/5.75 thf(fact_8200_prod_Oin__pairs,axiom,
% 7.75/5.75 ! [G: nat > code_integer,M: nat,N: nat] :
% 7.75/5.75 ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.75 = ( groups3455450783089532116nteger
% 7.75/5.75 @ ^ [I2: nat] : ( times_3573771949741848930nteger @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.in_pairs
% 7.75/5.75 thf(fact_8201_prod_Oin__pairs,axiom,
% 7.75/5.75 ! [G: nat > complex,M: nat,N: nat] :
% 7.75/5.75 ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.75 = ( groups6464643781859351333omplex
% 7.75/5.75 @ ^ [I2: nat] : ( times_times_complex @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.in_pairs
% 7.75/5.75 thf(fact_8202_prod_Oin__pairs,axiom,
% 7.75/5.75 ! [G: nat > nat,M: nat,N: nat] :
% 7.75/5.75 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.75 = ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [I2: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.in_pairs
% 7.75/5.75 thf(fact_8203_prod_Oin__pairs,axiom,
% 7.75/5.75 ! [G: nat > int,M: nat,N: nat] :
% 7.75/5.75 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 7.75/5.75 = ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [I2: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.in_pairs
% 7.75/5.75 thf(fact_8204_pochhammer__Suc__prod__rev,axiom,
% 7.75/5.75 ! [A: rat,N: nat] :
% 7.75/5.75 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups73079841787564623at_rat
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod_rev
% 7.75/5.75 thf(fact_8205_pochhammer__Suc__prod__rev,axiom,
% 7.75/5.75 ! [A: real,N: nat] :
% 7.75/5.75 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod_rev
% 7.75/5.75 thf(fact_8206_pochhammer__Suc__prod__rev,axiom,
% 7.75/5.75 ! [A: complex,N: nat] :
% 7.75/5.75 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups6464643781859351333omplex
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ ( minus_minus_nat @ N @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod_rev
% 7.75/5.75 thf(fact_8207_pochhammer__Suc__prod__rev,axiom,
% 7.75/5.75 ! [A: nat,N: nat] :
% 7.75/5.75 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod_rev
% 7.75/5.75 thf(fact_8208_pochhammer__Suc__prod__rev,axiom,
% 7.75/5.75 ! [A: int,N: nat] :
% 7.75/5.75 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 7.75/5.75 = ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [I2: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I2 ) ) )
% 7.75/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % pochhammer_Suc_prod_rev
% 7.75/5.75 thf(fact_8209_filter__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: set_nat > nat,P: set_nat > $o] :
% 7.75/5.75 ( ( finite1152437895449049373et_nat
% 7.75/5.75 @ ( collect_set_nat
% 7.75/5.75 @ ^ [X2: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite1152437895449049373et_nat
% 7.75/5.75 @ ( collect_set_nat
% 7.75/5.75 @ ^ [X2: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X2 ) @ ( M7 @ X2 ) @ zero_zero_nat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % filter_preserves_multiset
% 7.75/5.75 thf(fact_8210_filter__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: nat > nat,P: nat > $o] :
% 7.75/5.75 ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [X2: nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [X2: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X2 ) @ ( M7 @ X2 ) @ zero_zero_nat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % filter_preserves_multiset
% 7.75/5.75 thf(fact_8211_filter__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: int > nat,P: int > $o] :
% 7.75/5.75 ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [X2: int] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [X2: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X2 ) @ ( M7 @ X2 ) @ zero_zero_nat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % filter_preserves_multiset
% 7.75/5.75 thf(fact_8212_filter__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: complex > nat,P: complex > $o] :
% 7.75/5.75 ( ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [X2: complex] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [X2: complex] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X2 ) @ ( M7 @ X2 ) @ zero_zero_nat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % filter_preserves_multiset
% 7.75/5.75 thf(fact_8213_filter__preserves__multiset,axiom,
% 7.75/5.75 ! [M7: code_integer > nat,P: code_integer > $o] :
% 7.75/5.75 ( ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [X2: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X2 ) ) ) )
% 7.75/5.75 => ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [X2: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X2 ) @ ( M7 @ X2 ) @ zero_zero_nat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % filter_preserves_multiset
% 7.75/5.75 thf(fact_8214_and__int_Osimps,axiom,
% 7.75/5.75 ( bit_se725231765392027082nd_int
% 7.75/5.75 = ( ^ [K3: int,L2: int] :
% 7.75/5.75 ( if_int
% 7.75/5.75 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 7.75/5.75 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 7.75/5.75 @ ( uminus_uminus_int
% 7.75/5.75 @ ( zero_n2684676970156552555ol_int
% 7.75/5.75 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 7.75/5.75 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 7.75/5.75 @ ( plus_plus_int
% 7.75/5.75 @ ( zero_n2684676970156552555ol_int
% 7.75/5.75 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 7.75/5.75 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 7.75/5.75 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % and_int.simps
% 7.75/5.75 thf(fact_8215_and__int_Oelims,axiom,
% 7.75/5.75 ! [X: int,Xa3: int,Y: int] :
% 7.75/5.75 ( ( ( bit_se725231765392027082nd_int @ X @ Xa3 )
% 7.75/5.75 = Y )
% 7.75/5.75 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 7.75/5.75 & ( member_int @ Xa3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 7.75/5.75 => ( Y
% 7.75/5.75 = ( uminus_uminus_int
% 7.75/5.75 @ ( zero_n2684676970156552555ol_int
% 7.75/5.75 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 7.75/5.75 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa3 ) ) ) ) ) )
% 7.75/5.75 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 7.75/5.75 & ( member_int @ Xa3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 7.75/5.75 => ( Y
% 7.75/5.75 = ( plus_plus_int
% 7.75/5.75 @ ( zero_n2684676970156552555ol_int
% 7.75/5.75 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 7.75/5.75 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa3 ) ) )
% 7.75/5.75 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % and_int.elims
% 7.75/5.75 thf(fact_8216_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_real,X: real,G: real > assn] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ~ ( member_real @ X @ A2 )
% 7.75/5.75 => ( ( groups1155561341820557179l_assn @ G @ ( insert_real @ X @ A2 ) )
% 7.75/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups1155561341820557179l_assn @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8217_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > assn] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.75 => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 7.75/5.75 => ( ( groups569574905686396791T_assn @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 7.75/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups569574905686396791T_assn @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8218_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_nat,X: nat,G: nat > assn] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ~ ( member_nat @ X @ A2 )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn @ G @ ( insert_nat @ X @ A2 ) )
% 7.75/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups6906906614972039071t_assn @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8219_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_int,X: int,G: int > assn] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ~ ( member_int @ X @ A2 )
% 7.75/5.75 => ( ( groups7882442080178216443t_assn @ G @ ( insert_int @ X @ A2 ) )
% 7.75/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups7882442080178216443t_assn @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8220_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_complex,X: complex,G: complex > assn] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ~ ( member_complex @ X @ A2 )
% 7.75/5.75 => ( ( groups4150731942483176573x_assn @ G @ ( insert_complex @ X @ A2 ) )
% 7.75/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups4150731942483176573x_assn @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8221_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,X: code_integer,G: code_integer > assn] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ~ ( member_Code_integer @ X @ A2 )
% 7.75/5.75 => ( ( groups1304777262505850412r_assn @ G @ ( insert_Code_integer @ X @ A2 ) )
% 7.75/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups1304777262505850412r_assn @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8222_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_real,X: real,G: real > real] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ~ ( member_real @ X @ A2 )
% 7.75/5.75 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 7.75/5.75 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8223_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.75 => ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 7.75/5.75 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 7.75/5.75 = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8224_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_nat,X: nat,G: nat > real] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ~ ( member_nat @ X @ A2 )
% 7.75/5.75 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 7.75/5.75 = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8225_prod_Oinsert,axiom,
% 7.75/5.75 ! [A2: set_int,X: int,G: int > real] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ~ ( member_int @ X @ A2 )
% 7.75/5.75 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 7.75/5.75 = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.insert
% 7.75/5.75 thf(fact_8226_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_real,A: real,B: real > assn] :
% 7.75/5.75 ( ( finite_finite_real @ S3 )
% 7.75/5.75 => ( ( ( member_real @ A @ S3 )
% 7.75/5.75 => ( ( groups1155561341820557179l_assn
% 7.75/5.75 @ ^ [K3: real] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_real @ A @ S3 )
% 7.75/5.75 => ( ( groups1155561341820557179l_assn
% 7.75/5.75 @ ^ [K3: real] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8227_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > assn] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ S3 )
% 7.75/5.75 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 7.75/5.75 => ( ( groups569574905686396791T_assn
% 7.75/5.75 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 7.75/5.75 => ( ( groups569574905686396791T_assn
% 7.75/5.75 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8228_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_nat,A: nat,B: nat > assn] :
% 7.75/5.75 ( ( finite_finite_nat @ S3 )
% 7.75/5.75 => ( ( ( member_nat @ A @ S3 )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn
% 7.75/5.75 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_nat @ A @ S3 )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn
% 7.75/5.75 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8229_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_int,A: int,B: int > assn] :
% 7.75/5.75 ( ( finite_finite_int @ S3 )
% 7.75/5.75 => ( ( ( member_int @ A @ S3 )
% 7.75/5.75 => ( ( groups7882442080178216443t_assn
% 7.75/5.75 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_int @ A @ S3 )
% 7.75/5.75 => ( ( groups7882442080178216443t_assn
% 7.75/5.75 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8230_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_complex,A: complex,B: complex > assn] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ S3 )
% 7.75/5.75 => ( ( ( member_complex @ A @ S3 )
% 7.75/5.75 => ( ( groups4150731942483176573x_assn
% 7.75/5.75 @ ^ [K3: complex] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_complex @ A @ S3 )
% 7.75/5.75 => ( ( groups4150731942483176573x_assn
% 7.75/5.75 @ ^ [K3: complex] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8231_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ S3 )
% 7.75/5.75 => ( ( ( member_Code_integer @ A @ S3 )
% 7.75/5.75 => ( ( groups1304777262505850412r_assn
% 7.75/5.75 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_Code_integer @ A @ S3 )
% 7.75/5.75 => ( ( groups1304777262505850412r_assn
% 7.75/5.75 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8232_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_real,A: real,B: real > real] :
% 7.75/5.75 ( ( finite_finite_real @ S3 )
% 7.75/5.75 => ( ( ( member_real @ A @ S3 )
% 7.75/5.75 => ( ( groups1681761925125756287l_real
% 7.75/5.75 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_real @ A @ S3 )
% 7.75/5.75 => ( ( groups1681761925125756287l_real
% 7.75/5.75 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_real ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8233_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ S3 )
% 7.75/5.75 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 7.75/5.75 => ( ( groups2703838992350267259T_real
% 7.75/5.75 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 7.75/5.75 => ( ( groups2703838992350267259T_real
% 7.75/5.75 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_real ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8234_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_nat,A: nat,B: nat > real] :
% 7.75/5.75 ( ( finite_finite_nat @ S3 )
% 7.75/5.75 => ( ( ( member_nat @ A @ S3 )
% 7.75/5.75 => ( ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_nat @ A @ S3 )
% 7.75/5.75 => ( ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_real ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8235_prod_Odelta,axiom,
% 7.75/5.75 ! [S3: set_int,A: int,B: int > real] :
% 7.75/5.75 ( ( finite_finite_int @ S3 )
% 7.75/5.75 => ( ( ( member_int @ A @ S3 )
% 7.75/5.75 => ( ( groups2316167850115554303t_real
% 7.75/5.75 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_int @ A @ S3 )
% 7.75/5.75 => ( ( groups2316167850115554303t_real
% 7.75/5.75 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_real ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta
% 7.75/5.75 thf(fact_8236_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_real,A: real,B: real > assn] :
% 7.75/5.75 ( ( finite_finite_real @ S3 )
% 7.75/5.75 => ( ( ( member_real @ A @ S3 )
% 7.75/5.75 => ( ( groups1155561341820557179l_assn
% 7.75/5.75 @ ^ [K3: real] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_real @ A @ S3 )
% 7.75/5.75 => ( ( groups1155561341820557179l_assn
% 7.75/5.75 @ ^ [K3: real] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8237_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > assn] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ S3 )
% 7.75/5.75 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 7.75/5.75 => ( ( groups569574905686396791T_assn
% 7.75/5.75 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 7.75/5.75 => ( ( groups569574905686396791T_assn
% 7.75/5.75 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8238_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_nat,A: nat,B: nat > assn] :
% 7.75/5.75 ( ( finite_finite_nat @ S3 )
% 7.75/5.75 => ( ( ( member_nat @ A @ S3 )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn
% 7.75/5.75 @ ^ [K3: nat] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_nat @ A @ S3 )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn
% 7.75/5.75 @ ^ [K3: nat] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8239_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_int,A: int,B: int > assn] :
% 7.75/5.75 ( ( finite_finite_int @ S3 )
% 7.75/5.75 => ( ( ( member_int @ A @ S3 )
% 7.75/5.75 => ( ( groups7882442080178216443t_assn
% 7.75/5.75 @ ^ [K3: int] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_int @ A @ S3 )
% 7.75/5.75 => ( ( groups7882442080178216443t_assn
% 7.75/5.75 @ ^ [K3: int] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8240_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_complex,A: complex,B: complex > assn] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ S3 )
% 7.75/5.75 => ( ( ( member_complex @ A @ S3 )
% 7.75/5.75 => ( ( groups4150731942483176573x_assn
% 7.75/5.75 @ ^ [K3: complex] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_complex @ A @ S3 )
% 7.75/5.75 => ( ( groups4150731942483176573x_assn
% 7.75/5.75 @ ^ [K3: complex] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8241_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ S3 )
% 7.75/5.75 => ( ( ( member_Code_integer @ A @ S3 )
% 7.75/5.75 => ( ( groups1304777262505850412r_assn
% 7.75/5.75 @ ^ [K3: code_integer] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_Code_integer @ A @ S3 )
% 7.75/5.75 => ( ( groups1304777262505850412r_assn
% 7.75/5.75 @ ^ [K3: code_integer] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_assn ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8242_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_real,A: real,B: real > real] :
% 7.75/5.75 ( ( finite_finite_real @ S3 )
% 7.75/5.75 => ( ( ( member_real @ A @ S3 )
% 7.75/5.75 => ( ( groups1681761925125756287l_real
% 7.75/5.75 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_real @ A @ S3 )
% 7.75/5.75 => ( ( groups1681761925125756287l_real
% 7.75/5.75 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_real ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8243_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ S3 )
% 7.75/5.75 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 7.75/5.75 => ( ( groups2703838992350267259T_real
% 7.75/5.75 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 7.75/5.75 => ( ( groups2703838992350267259T_real
% 7.75/5.75 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_real ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8244_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_nat,A: nat,B: nat > real] :
% 7.75/5.75 ( ( finite_finite_nat @ S3 )
% 7.75/5.75 => ( ( ( member_nat @ A @ S3 )
% 7.75/5.75 => ( ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_nat @ A @ S3 )
% 7.75/5.75 => ( ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [K3: nat] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_real ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8245_prod_Odelta_H,axiom,
% 7.75/5.75 ! [S3: set_int,A: int,B: int > real] :
% 7.75/5.75 ( ( finite_finite_int @ S3 )
% 7.75/5.75 => ( ( ( member_int @ A @ S3 )
% 7.75/5.75 => ( ( groups2316167850115554303t_real
% 7.75/5.75 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = ( B @ A ) ) )
% 7.75/5.75 & ( ~ ( member_int @ A @ S3 )
% 7.75/5.75 => ( ( groups2316167850115554303t_real
% 7.75/5.75 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ one_one_real )
% 7.75/5.75 @ S3 )
% 7.75/5.75 = one_one_real ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.delta'
% 7.75/5.75 thf(fact_8246_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_real,A: real,F: real > nat] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ( member_real @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8247_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.75 => ( ( member_VEBT_VEBT @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups6361806394783013919BT_nat @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8248_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_int,A: int,F: int > nat] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( member_int @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8249_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_complex,A: complex,F: complex > nat] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( member_complex @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8250_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,A: code_integer,F: code_integer > nat] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( member_Code_integer @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups3190895334310489300er_nat @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8251_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_real,A: real,F: real > int] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ( member_real @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_int @ ( F @ A ) @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8252_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > int] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.75 => ( ( member_VEBT_VEBT @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_int @ ( F @ A ) @ ( groups6359315924273963643BT_int @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8253_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_complex,A: complex,F: complex > int] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( member_complex @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_int @ ( F @ A ) @ ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8254_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,A: code_integer,F: code_integer > int] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( member_Code_integer @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_int @ ( F @ A ) @ ( groups3188404863801439024er_int @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8255_dvd__prodI,axiom,
% 7.75/5.75 ! [A2: set_nat,A: nat,F: nat > nat] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( member_nat @ A @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A ) @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prodI
% 7.75/5.75 thf(fact_8256_prod_Oneutral__const,axiom,
% 7.75/5.75 ! [A2: set_nat] :
% 7.75/5.75 ( ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [Uu3: nat] : one_one_nat
% 7.75/5.75 @ A2 )
% 7.75/5.75 = one_one_nat ) ).
% 7.75/5.75
% 7.75/5.75 % prod.neutral_const
% 7.75/5.75 thf(fact_8257_prod_Oneutral__const,axiom,
% 7.75/5.75 ! [A2: set_nat] :
% 7.75/5.75 ( ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [Uu3: nat] : one_one_int
% 7.75/5.75 @ A2 )
% 7.75/5.75 = one_one_int ) ).
% 7.75/5.75
% 7.75/5.75 % prod.neutral_const
% 7.75/5.75 thf(fact_8258_prod_Oneutral__const,axiom,
% 7.75/5.75 ! [A2: set_int] :
% 7.75/5.75 ( ( groups1705073143266064639nt_int
% 7.75/5.75 @ ^ [Uu3: int] : one_one_int
% 7.75/5.75 @ A2 )
% 7.75/5.75 = one_one_int ) ).
% 7.75/5.75
% 7.75/5.75 % prod.neutral_const
% 7.75/5.75 thf(fact_8259_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > complex] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( ( groups6464643781859351333omplex @ F @ A2 )
% 7.75/5.75 = zero_zero_complex )
% 7.75/5.75 = ( ? [X2: nat] :
% 7.75/5.75 ( ( member_nat @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_complex ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8260_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > complex] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( ( groups7440179247065528705omplex @ F @ A2 )
% 7.75/5.75 = zero_zero_complex )
% 7.75/5.75 = ( ? [X2: int] :
% 7.75/5.75 ( ( member_int @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_complex ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8261_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > complex] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( ( groups3708469109370488835omplex @ F @ A2 )
% 7.75/5.75 = zero_zero_complex )
% 7.75/5.75 = ( ? [X2: complex] :
% 7.75/5.75 ( ( member_complex @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_complex ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8262_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,F: code_integer > complex] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( ( groups862514429393162674omplex @ F @ A2 )
% 7.75/5.75 = zero_zero_complex )
% 7.75/5.75 = ( ? [X2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_complex ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8263_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > real] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( ( groups129246275422532515t_real @ F @ A2 )
% 7.75/5.75 = zero_zero_real )
% 7.75/5.75 = ( ? [X2: nat] :
% 7.75/5.75 ( ( member_nat @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_real ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8264_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > real] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( ( groups2316167850115554303t_real @ F @ A2 )
% 7.75/5.75 = zero_zero_real )
% 7.75/5.75 = ( ? [X2: int] :
% 7.75/5.75 ( ( member_int @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_real ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8265_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > real] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( ( groups766887009212190081x_real @ F @ A2 )
% 7.75/5.75 = zero_zero_real )
% 7.75/5.75 = ( ? [X2: complex] :
% 7.75/5.75 ( ( member_complex @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_real ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8266_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,F: code_integer > real] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( ( groups9004974159866482096r_real @ F @ A2 )
% 7.75/5.75 = zero_zero_real )
% 7.75/5.75 = ( ? [X2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_real ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8267_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > rat] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( ( groups73079841787564623at_rat @ F @ A2 )
% 7.75/5.75 = zero_zero_rat )
% 7.75/5.75 = ( ? [X2: nat] :
% 7.75/5.75 ( ( member_nat @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_rat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8268_prod__zero__iff,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > rat] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( ( groups1072433553688619179nt_rat @ F @ A2 )
% 7.75/5.75 = zero_zero_rat )
% 7.75/5.75 = ( ? [X2: int] :
% 7.75/5.75 ( ( member_int @ X2 @ A2 )
% 7.75/5.75 & ( ( F @ X2 )
% 7.75/5.75 = zero_zero_rat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero_iff
% 7.75/5.75 thf(fact_8269_prod_Oempty,axiom,
% 7.75/5.75 ! [G: real > assn] :
% 7.75/5.75 ( ( groups1155561341820557179l_assn @ G @ bot_bot_set_real )
% 7.75/5.75 = one_one_assn ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8270_prod_Oempty,axiom,
% 7.75/5.75 ! [G: real > real] :
% 7.75/5.75 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 7.75/5.75 = one_one_real ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8271_prod_Oempty,axiom,
% 7.75/5.75 ! [G: real > rat] :
% 7.75/5.75 ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 7.75/5.75 = one_one_rat ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8272_prod_Oempty,axiom,
% 7.75/5.75 ! [G: real > nat] :
% 7.75/5.75 ( ( groups4696554848551431203al_nat @ G @ bot_bot_set_real )
% 7.75/5.75 = one_one_nat ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8273_prod_Oempty,axiom,
% 7.75/5.75 ! [G: real > int] :
% 7.75/5.75 ( ( groups4694064378042380927al_int @ G @ bot_bot_set_real )
% 7.75/5.75 = one_one_int ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8274_prod_Oempty,axiom,
% 7.75/5.75 ! [G: nat > assn] :
% 7.75/5.75 ( ( groups6906906614972039071t_assn @ G @ bot_bot_set_nat )
% 7.75/5.75 = one_one_assn ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8275_prod_Oempty,axiom,
% 7.75/5.75 ! [G: nat > real] :
% 7.75/5.75 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 7.75/5.75 = one_one_real ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8276_prod_Oempty,axiom,
% 7.75/5.75 ! [G: nat > rat] :
% 7.75/5.75 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 7.75/5.75 = one_one_rat ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8277_prod_Oempty,axiom,
% 7.75/5.75 ! [G: int > assn] :
% 7.75/5.75 ( ( groups7882442080178216443t_assn @ G @ bot_bot_set_int )
% 7.75/5.75 = one_one_assn ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8278_prod_Oempty,axiom,
% 7.75/5.75 ! [G: int > real] :
% 7.75/5.75 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 7.75/5.75 = one_one_real ) ).
% 7.75/5.75
% 7.75/5.75 % prod.empty
% 7.75/5.75 thf(fact_8279_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_nat,G: nat > assn] :
% 7.75/5.75 ( ~ ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn @ G @ A2 )
% 7.75/5.75 = one_one_assn ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8280_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_int,G: int > assn] :
% 7.75/5.75 ( ~ ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( groups7882442080178216443t_assn @ G @ A2 )
% 7.75/5.75 = one_one_assn ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8281_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_complex,G: complex > assn] :
% 7.75/5.75 ( ~ ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( groups4150731942483176573x_assn @ G @ A2 )
% 7.75/5.75 = one_one_assn ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8282_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,G: code_integer > assn] :
% 7.75/5.75 ( ~ ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( groups1304777262505850412r_assn @ G @ A2 )
% 7.75/5.75 = one_one_assn ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8283_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_nat,G: nat > real] :
% 7.75/5.75 ( ~ ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( groups129246275422532515t_real @ G @ A2 )
% 7.75/5.75 = one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8284_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_int,G: int > real] :
% 7.75/5.75 ( ~ ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 7.75/5.75 = one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8285_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_complex,G: complex > real] :
% 7.75/5.75 ( ~ ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( groups766887009212190081x_real @ G @ A2 )
% 7.75/5.75 = one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8286_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,G: code_integer > real] :
% 7.75/5.75 ( ~ ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( groups9004974159866482096r_real @ G @ A2 )
% 7.75/5.75 = one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8287_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_nat,G: nat > rat] :
% 7.75/5.75 ( ~ ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( groups73079841787564623at_rat @ G @ A2 )
% 7.75/5.75 = one_one_rat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8288_prod_Oinfinite,axiom,
% 7.75/5.75 ! [A2: set_int,G: int > rat] :
% 7.75/5.75 ( ~ ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( groups1072433553688619179nt_rat @ G @ A2 )
% 7.75/5.75 = one_one_rat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.infinite
% 7.75/5.75 thf(fact_8289_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_real,A: real,B: nat,F: real > nat] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ( member_real @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_nat @ B @ ( groups4696554848551431203al_nat @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8290_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B: nat,F: vEBT_VEBT > nat] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.75 => ( ( member_VEBT_VEBT @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_nat @ B @ ( groups6361806394783013919BT_nat @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8291_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_int,A: int,B: nat,F: int > nat] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( member_int @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_nat @ B @ ( groups1707563613775114915nt_nat @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8292_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_complex,A: complex,B: nat,F: complex > nat] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( member_complex @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_nat @ B @ ( groups861055069439313189ex_nat @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8293_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,A: code_integer,B: nat,F: code_integer > nat] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( member_Code_integer @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_nat @ B @ ( groups3190895334310489300er_nat @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8294_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_real,A: real,B: int,F: real > int] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ( member_real @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_int @ B @ ( groups4694064378042380927al_int @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8295_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,A: vEBT_VEBT,B: int,F: vEBT_VEBT > int] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.75 => ( ( member_VEBT_VEBT @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_int @ B @ ( groups6359315924273963643BT_int @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8296_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_complex,A: complex,B: int,F: complex > int] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( member_complex @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_int @ B @ ( groups858564598930262913ex_int @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8297_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,A: code_integer,B: int,F: code_integer > int] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( member_Code_integer @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_int @ B @ ( groups3188404863801439024er_int @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8298_dvd__prod__eqI,axiom,
% 7.75/5.75 ! [A2: set_nat,A: nat,B: nat,F: nat > nat] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( member_nat @ A @ A2 )
% 7.75/5.75 => ( ( B
% 7.75/5.75 = ( F @ A ) )
% 7.75/5.75 => ( dvd_dvd_nat @ B @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % dvd_prod_eqI
% 7.75/5.75 thf(fact_8299_prod__eq__1__iff,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > nat] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( ( groups1707563613775114915nt_nat @ F @ A2 )
% 7.75/5.75 = one_one_nat )
% 7.75/5.75 = ( ! [X2: int] :
% 7.75/5.75 ( ( member_int @ X2 @ A2 )
% 7.75/5.75 => ( ( F @ X2 )
% 7.75/5.75 = one_one_nat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_eq_1_iff
% 7.75/5.75 thf(fact_8300_prod__eq__1__iff,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > nat] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( ( groups861055069439313189ex_nat @ F @ A2 )
% 7.75/5.75 = one_one_nat )
% 7.75/5.75 = ( ! [X2: complex] :
% 7.75/5.75 ( ( member_complex @ X2 @ A2 )
% 7.75/5.75 => ( ( F @ X2 )
% 7.75/5.75 = one_one_nat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_eq_1_iff
% 7.75/5.75 thf(fact_8301_prod__eq__1__iff,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,F: code_integer > nat] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( ( groups3190895334310489300er_nat @ F @ A2 )
% 7.75/5.75 = one_one_nat )
% 7.75/5.75 = ( ! [X2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X2 @ A2 )
% 7.75/5.75 => ( ( F @ X2 )
% 7.75/5.75 = one_one_nat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_eq_1_iff
% 7.75/5.75 thf(fact_8302_prod__eq__1__iff,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > nat] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( ( groups708209901874060359at_nat @ F @ A2 )
% 7.75/5.75 = one_one_nat )
% 7.75/5.75 = ( ! [X2: nat] :
% 7.75/5.75 ( ( member_nat @ X2 @ A2 )
% 7.75/5.75 => ( ( F @ X2 )
% 7.75/5.75 = one_one_nat ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_eq_1_iff
% 7.75/5.75 thf(fact_8303_prod__pos__nat__iff,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > nat] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) )
% 7.75/5.75 = ( ! [X2: int] :
% 7.75/5.75 ( ( member_int @ X2 @ A2 )
% 7.75/5.75 => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_pos_nat_iff
% 7.75/5.75 thf(fact_8304_prod__pos__nat__iff,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > nat] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) )
% 7.75/5.75 = ( ! [X2: complex] :
% 7.75/5.75 ( ( member_complex @ X2 @ A2 )
% 7.75/5.75 => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_pos_nat_iff
% 7.75/5.75 thf(fact_8305_prod__pos__nat__iff,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,F: code_integer > nat] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( ord_less_nat @ zero_zero_nat @ ( groups3190895334310489300er_nat @ F @ A2 ) )
% 7.75/5.75 = ( ! [X2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X2 @ A2 )
% 7.75/5.75 => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_pos_nat_iff
% 7.75/5.75 thf(fact_8306_prod__pos__nat__iff,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > nat] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) )
% 7.75/5.75 = ( ! [X2: nat] :
% 7.75/5.75 ( ( member_nat @ X2 @ A2 )
% 7.75/5.75 => ( ord_less_nat @ zero_zero_nat @ ( F @ X2 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_pos_nat_iff
% 7.75/5.75 thf(fact_8307_prod__int__plus__eq,axiom,
% 7.75/5.75 ! [I: nat,J: nat] :
% 7.75/5.75 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 7.75/5.75 = ( groups1705073143266064639nt_int
% 7.75/5.75 @ ^ [X2: int] : X2
% 7.75/5.75 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_int_plus_eq
% 7.75/5.75 thf(fact_8308_prod_Oneutral,axiom,
% 7.75/5.75 ! [A2: set_nat,G: nat > nat] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ( G @ X3 )
% 7.75/5.75 = one_one_nat ) )
% 7.75/5.75 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 7.75/5.75 = one_one_nat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.neutral
% 7.75/5.75 thf(fact_8309_prod_Oneutral,axiom,
% 7.75/5.75 ! [A2: set_nat,G: nat > int] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ( G @ X3 )
% 7.75/5.75 = one_one_int ) )
% 7.75/5.75 => ( ( groups705719431365010083at_int @ G @ A2 )
% 7.75/5.75 = one_one_int ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.neutral
% 7.75/5.75 thf(fact_8310_prod_Oneutral,axiom,
% 7.75/5.75 ! [A2: set_int,G: int > int] :
% 7.75/5.75 ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ A2 )
% 7.75/5.75 => ( ( G @ X3 )
% 7.75/5.75 = one_one_int ) )
% 7.75/5.75 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 7.75/5.75 = one_one_int ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.neutral
% 7.75/5.75 thf(fact_8311_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: nat > assn,A2: set_nat] :
% 7.75/5.75 ( ( ( groups6906906614972039071t_assn @ G @ A2 )
% 7.75/5.75 != one_one_assn )
% 7.75/5.75 => ~ ! [A5: nat] :
% 7.75/5.75 ( ( member_nat @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_assn ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8312_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: real > assn,A2: set_real] :
% 7.75/5.75 ( ( ( groups1155561341820557179l_assn @ G @ A2 )
% 7.75/5.75 != one_one_assn )
% 7.75/5.75 => ~ ! [A5: real] :
% 7.75/5.75 ( ( member_real @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_assn ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8313_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: int > assn,A2: set_int] :
% 7.75/5.75 ( ( ( groups7882442080178216443t_assn @ G @ A2 )
% 7.75/5.75 != one_one_assn )
% 7.75/5.75 => ~ ! [A5: int] :
% 7.75/5.75 ( ( member_int @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_assn ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8314_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: vEBT_VEBT > assn,A2: set_VEBT_VEBT] :
% 7.75/5.75 ( ( ( groups569574905686396791T_assn @ G @ A2 )
% 7.75/5.75 != one_one_assn )
% 7.75/5.75 => ~ ! [A5: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_assn ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8315_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: complex > assn,A2: set_complex] :
% 7.75/5.75 ( ( ( groups4150731942483176573x_assn @ G @ A2 )
% 7.75/5.75 != one_one_assn )
% 7.75/5.75 => ~ ! [A5: complex] :
% 7.75/5.75 ( ( member_complex @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_assn ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8316_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: nat > real,A2: set_nat] :
% 7.75/5.75 ( ( ( groups129246275422532515t_real @ G @ A2 )
% 7.75/5.75 != one_one_real )
% 7.75/5.75 => ~ ! [A5: nat] :
% 7.75/5.75 ( ( member_nat @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8317_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: real > real,A2: set_real] :
% 7.75/5.75 ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 7.75/5.75 != one_one_real )
% 7.75/5.75 => ~ ! [A5: real] :
% 7.75/5.75 ( ( member_real @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8318_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: int > real,A2: set_int] :
% 7.75/5.75 ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 7.75/5.75 != one_one_real )
% 7.75/5.75 => ~ ! [A5: int] :
% 7.75/5.75 ( ( member_int @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8319_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: vEBT_VEBT > real,A2: set_VEBT_VEBT] :
% 7.75/5.75 ( ( ( groups2703838992350267259T_real @ G @ A2 )
% 7.75/5.75 != one_one_real )
% 7.75/5.75 => ~ ! [A5: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8320_prod_Onot__neutral__contains__not__neutral,axiom,
% 7.75/5.75 ! [G: complex > real,A2: set_complex] :
% 7.75/5.75 ( ( ( groups766887009212190081x_real @ G @ A2 )
% 7.75/5.75 != one_one_real )
% 7.75/5.75 => ~ ! [A5: complex] :
% 7.75/5.75 ( ( member_complex @ A5 @ A2 )
% 7.75/5.75 => ( ( G @ A5 )
% 7.75/5.75 = one_one_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.not_neutral_contains_not_neutral
% 7.75/5.75 thf(fact_8321_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_real,F: real > nat,G: real > nat] :
% 7.75/5.75 ( ! [A5: real] :
% 7.75/5.75 ( ( member_real @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8322_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > nat,G: int > nat] :
% 7.75/5.75 ( ! [A5: int] :
% 7.75/5.75 ( ( member_int @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8323_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 7.75/5.75 ( ! [A5: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) @ ( groups6361806394783013919BT_nat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8324_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 7.75/5.75 ( ! [A5: complex] :
% 7.75/5.75 ( ( member_complex @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8325_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_real,F: real > int,G: real > int] :
% 7.75/5.75 ( ! [A5: real] :
% 7.75/5.75 ( ( member_real @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8326_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 7.75/5.75 ( ! [A5: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_int @ ( groups6359315924273963643BT_int @ F @ A2 ) @ ( groups6359315924273963643BT_int @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8327_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 7.75/5.75 ( ! [A5: complex] :
% 7.75/5.75 ( ( member_complex @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8328_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 7.75/5.75 ( ! [A5: nat] :
% 7.75/5.75 ( ( member_nat @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8329_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 7.75/5.75 ( ! [A5: nat] :
% 7.75/5.75 ( ( member_nat @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8330_prod__dvd__prod,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > int,G: int > int] :
% 7.75/5.75 ( ! [A5: int] :
% 7.75/5.75 ( ( member_int @ A5 @ A2 )
% 7.75/5.75 => ( dvd_dvd_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.75/5.75 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_dvd_prod
% 7.75/5.75 thf(fact_8331_prod_Odistrib,axiom,
% 7.75/5.75 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 7.75/5.75 ( ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 7.75/5.75 @ A2 )
% 7.75/5.75 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.distrib
% 7.75/5.75 thf(fact_8332_prod_Odistrib,axiom,
% 7.75/5.75 ! [G: nat > int,H2: nat > int,A2: set_nat] :
% 7.75/5.75 ( ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [X2: nat] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 7.75/5.75 @ A2 )
% 7.75/5.75 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A2 ) @ ( groups705719431365010083at_int @ H2 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.distrib
% 7.75/5.75 thf(fact_8333_prod_Odistrib,axiom,
% 7.75/5.75 ! [G: int > int,H2: int > int,A2: set_int] :
% 7.75/5.75 ( ( groups1705073143266064639nt_int
% 7.75/5.75 @ ^ [X2: int] : ( times_times_int @ ( G @ X2 ) @ ( H2 @ X2 ) )
% 7.75/5.75 @ A2 )
% 7.75/5.75 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A2 ) @ ( groups1705073143266064639nt_int @ H2 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.distrib
% 7.75/5.75 thf(fact_8334_prod__power__distrib,axiom,
% 7.75/5.75 ! [F: nat > nat,A2: set_nat,N: nat] :
% 7.75/5.75 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N )
% 7.75/5.75 = ( groups708209901874060359at_nat
% 7.75/5.75 @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N )
% 7.75/5.75 @ A2 ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_power_distrib
% 7.75/5.75 thf(fact_8335_prod__power__distrib,axiom,
% 7.75/5.75 ! [F: nat > int,A2: set_nat,N: nat] :
% 7.75/5.75 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N )
% 7.75/5.75 = ( groups705719431365010083at_int
% 7.75/5.75 @ ^ [X2: nat] : ( power_power_int @ ( F @ X2 ) @ N )
% 7.75/5.75 @ A2 ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_power_distrib
% 7.75/5.75 thf(fact_8336_prod__power__distrib,axiom,
% 7.75/5.75 ! [F: int > int,A2: set_int,N: nat] :
% 7.75/5.75 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N )
% 7.75/5.75 = ( groups1705073143266064639nt_int
% 7.75/5.75 @ ^ [X2: int] : ( power_power_int @ ( F @ X2 ) @ N )
% 7.75/5.75 @ A2 ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_power_distrib
% 7.75/5.75 thf(fact_8337_prod__nonneg,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > nat] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_nonneg
% 7.75/5.75 thf(fact_8338_prod__nonneg,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > int] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_nonneg
% 7.75/5.75 thf(fact_8339_prod__nonneg,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > int] :
% 7.75/5.75 ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_nonneg
% 7.75/5.75 thf(fact_8340_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 7.75/5.75 ( ! [I3: nat] :
% 7.75/5.75 ( ( member_nat @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8341_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_real,F: real > real,G: real > real] :
% 7.75/5.75 ( ! [I3: real] :
% 7.75/5.75 ( ( member_real @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8342_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > real,G: int > real] :
% 7.75/5.75 ( ! [I3: int] :
% 7.75/5.75 ( ( member_int @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8343_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 7.75/5.75 ( ! [I3: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8344_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 7.75/5.75 ( ! [I3: complex] :
% 7.75/5.75 ( ( member_complex @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8345_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 7.75/5.75 ( ! [I3: nat] :
% 7.75/5.75 ( ( member_nat @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ ( groups73079841787564623at_rat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8346_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_real,F: real > rat,G: real > rat] :
% 7.75/5.75 ( ! [I3: real] :
% 7.75/5.75 ( ( member_real @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8347_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > rat,G: int > rat] :
% 7.75/5.75 ( ! [I3: int] :
% 7.75/5.75 ( ( member_int @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8348_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 7.75/5.75 ( ! [I3: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8349_prod__mono,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 7.75/5.75 ( ! [I3: complex] :
% 7.75/5.75 ( ( member_complex @ I3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_mono
% 7.75/5.75 thf(fact_8350_prod__pos,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > nat] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_pos
% 7.75/5.75 thf(fact_8351_prod__pos,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > int] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_pos
% 7.75/5.75 thf(fact_8352_prod__pos,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > int] :
% 7.75/5.75 ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_pos
% 7.75/5.75 thf(fact_8353_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > real] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8354_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_real,F: real > real] :
% 7.75/5.75 ( ! [X3: real] :
% 7.75/5.75 ( ( member_real @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8355_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > real] :
% 7.75/5.75 ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8356_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 7.75/5.75 ( ! [X3: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8357_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > real] :
% 7.75/5.75 ( ! [X3: complex] :
% 7.75/5.75 ( ( member_complex @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8358_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > rat] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8359_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_real,F: real > rat] :
% 7.75/5.75 ( ! [X3: real] :
% 7.75/5.75 ( ( member_real @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8360_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > rat] :
% 7.75/5.75 ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8361_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 7.75/5.75 ( ! [X3: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8362_prod__ge__1,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > rat] :
% 7.75/5.75 ( ! [X3: complex] :
% 7.75/5.75 ( ( member_complex @ X3 @ A2 )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_ge_1
% 7.75/5.75 thf(fact_8363_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > complex] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ? [X5: nat] :
% 7.75/5.75 ( ( member_nat @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_complex ) )
% 7.75/5.75 => ( ( groups6464643781859351333omplex @ F @ A2 )
% 7.75/5.75 = zero_zero_complex ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8364_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > complex] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ? [X5: int] :
% 7.75/5.75 ( ( member_int @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_complex ) )
% 7.75/5.75 => ( ( groups7440179247065528705omplex @ F @ A2 )
% 7.75/5.75 = zero_zero_complex ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8365_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > complex] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ? [X5: complex] :
% 7.75/5.75 ( ( member_complex @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_complex ) )
% 7.75/5.75 => ( ( groups3708469109370488835omplex @ F @ A2 )
% 7.75/5.75 = zero_zero_complex ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8366_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,F: code_integer > complex] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ? [X5: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_complex ) )
% 7.75/5.75 => ( ( groups862514429393162674omplex @ F @ A2 )
% 7.75/5.75 = zero_zero_complex ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8367_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > real] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ? [X5: nat] :
% 7.75/5.75 ( ( member_nat @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_real ) )
% 7.75/5.75 => ( ( groups129246275422532515t_real @ F @ A2 )
% 7.75/5.75 = zero_zero_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8368_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > real] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ? [X5: int] :
% 7.75/5.75 ( ( member_int @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_real ) )
% 7.75/5.75 => ( ( groups2316167850115554303t_real @ F @ A2 )
% 7.75/5.75 = zero_zero_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8369_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > real] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ? [X5: complex] :
% 7.75/5.75 ( ( member_complex @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_real ) )
% 7.75/5.75 => ( ( groups766887009212190081x_real @ F @ A2 )
% 7.75/5.75 = zero_zero_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8370_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,F: code_integer > real] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ? [X5: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_real ) )
% 7.75/5.75 => ( ( groups9004974159866482096r_real @ F @ A2 )
% 7.75/5.75 = zero_zero_real ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8371_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > rat] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ? [X5: nat] :
% 7.75/5.75 ( ( member_nat @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_rat ) )
% 7.75/5.75 => ( ( groups73079841787564623at_rat @ F @ A2 )
% 7.75/5.75 = zero_zero_rat ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8372_prod__zero,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > rat] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ? [X5: int] :
% 7.75/5.75 ( ( member_int @ X5 @ A2 )
% 7.75/5.75 & ( ( F @ X5 )
% 7.75/5.75 = zero_zero_rat ) )
% 7.75/5.75 => ( ( groups1072433553688619179nt_rat @ F @ A2 )
% 7.75/5.75 = zero_zero_rat ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_zero
% 7.75/5.75 thf(fact_8373_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_real,X: real > complex,Y: real > complex] :
% 7.75/5.75 ( ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_complex @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_complex ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8374_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_VEBT_VEBT,X: vEBT_VEBT > complex,Y: vEBT_VEBT > complex] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_complex @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_complex ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8375_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 7.75/5.75 ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_complex @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_complex ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8376_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_int,X: int > complex,Y: int > complex] :
% 7.75/5.75 ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_complex @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_complex ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8377_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 7.75/5.75 ( ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [I2: complex] :
% 7.75/5.75 ( ( member_complex @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [I2: complex] :
% 7.75/5.75 ( ( member_complex @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [I2: complex] :
% 7.75/5.75 ( ( member_complex @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_complex @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_complex ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8378_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_Code_integer,X: code_integer > complex,Y: code_integer > complex] :
% 7.75/5.75 ( ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [I2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [I2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_complex ) ) ) )
% 7.75/5.75 => ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [I2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_complex @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_complex ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8379_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_real,X: real > real,Y: real > real] :
% 7.75/5.75 ( ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_real ) ) ) )
% 7.75/5.75 => ( ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_real ) ) ) )
% 7.75/5.75 => ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_real @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8380_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_VEBT_VEBT,X: vEBT_VEBT > real,Y: vEBT_VEBT > real] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_real ) ) ) )
% 7.75/5.75 => ( ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_real ) ) ) )
% 7.75/5.75 => ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_real @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8381_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 7.75/5.75 ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_real ) ) ) )
% 7.75/5.75 => ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_real ) ) ) )
% 7.75/5.75 => ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_real @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8382_sum_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_int,X: int > real,Y: int > real] :
% 7.75/5.75 ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != zero_zero_real ) ) ) )
% 7.75/5.75 => ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != zero_zero_real ) ) ) )
% 7.75/5.75 => ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( plus_plus_real @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != zero_zero_real ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % sum.finite_Collect_op
% 7.75/5.75 thf(fact_8383_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_real,X: real > rat,Y: real > rat] :
% 7.75/5.75 ( ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_rat @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_rat ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8384_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_VEBT_VEBT,X: vEBT_VEBT > rat,Y: vEBT_VEBT > rat] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_rat @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_rat ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8385_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_nat,X: nat > rat,Y: nat > rat] :
% 7.75/5.75 ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_rat @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_rat ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8386_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_int,X: int > rat,Y: int > rat] :
% 7.75/5.75 ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_rat @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_rat ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8387_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_complex,X: complex > rat,Y: complex > rat] :
% 7.75/5.75 ( ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [I2: complex] :
% 7.75/5.75 ( ( member_complex @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [I2: complex] :
% 7.75/5.75 ( ( member_complex @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( finite3207457112153483333omplex
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [I2: complex] :
% 7.75/5.75 ( ( member_complex @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_rat @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_rat ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8388_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_Code_integer,X: code_integer > rat,Y: code_integer > rat] :
% 7.75/5.75 ( ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [I2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [I2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_rat ) ) ) )
% 7.75/5.75 => ( finite6017078050557962740nteger
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [I2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_rat @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_rat ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8389_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_real,X: real > assn,Y: real > assn] :
% 7.75/5.75 ( ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_assn ) ) ) )
% 7.75/5.75 => ( ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_assn ) ) ) )
% 7.75/5.75 => ( finite_finite_real
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [I2: real] :
% 7.75/5.75 ( ( member_real @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_assn @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_assn ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8390_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_VEBT_VEBT,X: vEBT_VEBT > assn,Y: vEBT_VEBT > assn] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_assn ) ) ) )
% 7.75/5.75 => ( ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_assn ) ) ) )
% 7.75/5.75 => ( finite5795047828879050333T_VEBT
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [I2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_assn @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_assn ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8391_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_nat,X: nat > assn,Y: nat > assn] :
% 7.75/5.75 ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_assn ) ) ) )
% 7.75/5.75 => ( ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_assn ) ) ) )
% 7.75/5.75 => ( finite_finite_nat
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [I2: nat] :
% 7.75/5.75 ( ( member_nat @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_assn @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_assn ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8392_prod_Ofinite__Collect__op,axiom,
% 7.75/5.75 ! [I6: set_int,X: int > assn,Y: int > assn] :
% 7.75/5.75 ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( X @ I2 )
% 7.75/5.75 != one_one_assn ) ) ) )
% 7.75/5.75 => ( ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( Y @ I2 )
% 7.75/5.75 != one_one_assn ) ) ) )
% 7.75/5.75 => ( finite_finite_int
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [I2: int] :
% 7.75/5.75 ( ( member_int @ I2 @ I6 )
% 7.75/5.75 & ( ( times_times_assn @ ( X @ I2 ) @ ( Y @ I2 ) )
% 7.75/5.75 != one_one_assn ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.finite_Collect_op
% 7.75/5.75 thf(fact_8393_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_real,G: real > assn,P: real > $o] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ( groups1155561341820557179l_assn @ G
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [X2: real] :
% 7.75/5.75 ( ( member_real @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups1155561341820557179l_assn
% 7.75/5.75 @ ^ [X2: real] : ( if_assn @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_assn )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8394_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > assn,P: vEBT_VEBT > $o] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.75 => ( ( groups569574905686396791T_assn @ G
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [X2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups569574905686396791T_assn
% 7.75/5.75 @ ^ [X2: vEBT_VEBT] : ( if_assn @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_assn )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8395_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_nat,G: nat > assn,P: nat > $o] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( groups6906906614972039071t_assn @ G
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [X2: nat] :
% 7.75/5.75 ( ( member_nat @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups6906906614972039071t_assn
% 7.75/5.75 @ ^ [X2: nat] : ( if_assn @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_assn )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8396_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_int,G: int > assn,P: int > $o] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( groups7882442080178216443t_assn @ G
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [X2: int] :
% 7.75/5.75 ( ( member_int @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups7882442080178216443t_assn
% 7.75/5.75 @ ^ [X2: int] : ( if_assn @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_assn )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8397_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_complex,G: complex > assn,P: complex > $o] :
% 7.75/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.75/5.75 => ( ( groups4150731942483176573x_assn @ G
% 7.75/5.75 @ ( collect_complex
% 7.75/5.75 @ ^ [X2: complex] :
% 7.75/5.75 ( ( member_complex @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups4150731942483176573x_assn
% 7.75/5.75 @ ^ [X2: complex] : ( if_assn @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_assn )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8398_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_Code_integer,G: code_integer > assn,P: code_integer > $o] :
% 7.75/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.75/5.75 => ( ( groups1304777262505850412r_assn @ G
% 7.75/5.75 @ ( collect_Code_integer
% 7.75/5.75 @ ^ [X2: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups1304777262505850412r_assn
% 7.75/5.75 @ ^ [X2: code_integer] : ( if_assn @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_assn )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8399_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_real,G: real > real,P: real > $o] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ( groups1681761925125756287l_real @ G
% 7.75/5.75 @ ( collect_real
% 7.75/5.75 @ ^ [X2: real] :
% 7.75/5.75 ( ( member_real @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups1681761925125756287l_real
% 7.75/5.75 @ ^ [X2: real] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8400_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,P: vEBT_VEBT > $o] :
% 7.75/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.75/5.75 => ( ( groups2703838992350267259T_real @ G
% 7.75/5.75 @ ( collect_VEBT_VEBT
% 7.75/5.75 @ ^ [X2: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups2703838992350267259T_real
% 7.75/5.75 @ ^ [X2: vEBT_VEBT] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8401_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_nat,G: nat > real,P: nat > $o] :
% 7.75/5.75 ( ( finite_finite_nat @ A2 )
% 7.75/5.75 => ( ( groups129246275422532515t_real @ G
% 7.75/5.75 @ ( collect_nat
% 7.75/5.75 @ ^ [X2: nat] :
% 7.75/5.75 ( ( member_nat @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups129246275422532515t_real
% 7.75/5.75 @ ^ [X2: nat] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8402_prod_Ointer__filter,axiom,
% 7.75/5.75 ! [A2: set_int,G: int > real,P: int > $o] :
% 7.75/5.75 ( ( finite_finite_int @ A2 )
% 7.75/5.75 => ( ( groups2316167850115554303t_real @ G
% 7.75/5.75 @ ( collect_int
% 7.75/5.75 @ ^ [X2: int] :
% 7.75/5.75 ( ( member_int @ X2 @ A2 )
% 7.75/5.75 & ( P @ X2 ) ) ) )
% 7.75/5.75 = ( groups2316167850115554303t_real
% 7.75/5.75 @ ^ [X2: int] : ( if_real @ ( P @ X2 ) @ ( G @ X2 ) @ one_one_real )
% 7.75/5.75 @ A2 ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.inter_filter
% 7.75/5.75 thf(fact_8403_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > real] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A2 ) @ one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8404_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_real,F: real > real] :
% 7.75/5.75 ( ! [X3: real] :
% 7.75/5.75 ( ( member_real @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8405_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > real] :
% 7.75/5.75 ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8406_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 7.75/5.75 ( ! [X3: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8407_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > real] :
% 7.75/5.75 ( ! [X3: complex] :
% 7.75/5.75 ( ( member_complex @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_real @ ( F @ X3 ) @ one_one_real ) ) )
% 7.75/5.75 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ one_one_real ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8408_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_nat,F: nat > rat] :
% 7.75/5.75 ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8409_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_real,F: real > rat] :
% 7.75/5.75 ( ! [X3: real] :
% 7.75/5.75 ( ( member_real @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8410_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_int,F: int > rat] :
% 7.75/5.75 ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8411_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 7.75/5.75 ( ! [X3: vEBT_VEBT] :
% 7.75/5.75 ( ( member_VEBT_VEBT @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8412_prod__le__1,axiom,
% 7.75/5.75 ! [A2: set_complex,F: complex > rat] :
% 7.75/5.75 ( ! [X3: complex] :
% 7.75/5.75 ( ( member_complex @ X3 @ A2 )
% 7.75/5.75 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 7.75/5.75 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 7.75/5.75 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ one_one_rat ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod_le_1
% 7.75/5.75 thf(fact_8413_prod_Orelated,axiom,
% 7.75/5.75 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 7.75/5.75 ( ( R @ one_one_rat @ one_one_rat )
% 7.75/5.75 => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite_finite_nat @ S3 )
% 7.75/5.75 => ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups73079841787564623at_rat @ H2 @ S3 ) @ ( groups73079841787564623at_rat @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8414_prod_Orelated,axiom,
% 7.75/5.75 ! [R: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 7.75/5.75 ( ( R @ one_one_rat @ one_one_rat )
% 7.75/5.75 => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite_finite_int @ S3 )
% 7.75/5.75 => ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups1072433553688619179nt_rat @ H2 @ S3 ) @ ( groups1072433553688619179nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8415_prod_Orelated,axiom,
% 7.75/5.75 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 7.75/5.75 ( ( R @ one_one_rat @ one_one_rat )
% 7.75/5.75 => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite3207457112153483333omplex @ S3 )
% 7.75/5.75 => ( ! [X3: complex] :
% 7.75/5.75 ( ( member_complex @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups225925009352817453ex_rat @ H2 @ S3 ) @ ( groups225925009352817453ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8416_prod_Orelated,axiom,
% 7.75/5.75 ! [R: rat > rat > $o,S3: set_Code_integer,H2: code_integer > rat,G: code_integer > rat] :
% 7.75/5.75 ( ( R @ one_one_rat @ one_one_rat )
% 7.75/5.75 => ( ! [X1: rat,Y1: rat,X23: rat,Y23: rat] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_rat @ X1 @ Y1 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite6017078050557962740nteger @ S3 )
% 7.75/5.75 => ( ! [X3: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups2555765274223993564er_rat @ H2 @ S3 ) @ ( groups2555765274223993564er_rat @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8417_prod_Orelated,axiom,
% 7.75/5.75 ! [R: assn > assn > $o,S3: set_nat,H2: nat > assn,G: nat > assn] :
% 7.75/5.75 ( ( R @ one_one_assn @ one_one_assn )
% 7.75/5.75 => ( ! [X1: assn,Y1: assn,X23: assn,Y23: assn] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_assn @ X1 @ Y1 ) @ ( times_times_assn @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite_finite_nat @ S3 )
% 7.75/5.75 => ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups6906906614972039071t_assn @ H2 @ S3 ) @ ( groups6906906614972039071t_assn @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8418_prod_Orelated,axiom,
% 7.75/5.75 ! [R: assn > assn > $o,S3: set_int,H2: int > assn,G: int > assn] :
% 7.75/5.75 ( ( R @ one_one_assn @ one_one_assn )
% 7.75/5.75 => ( ! [X1: assn,Y1: assn,X23: assn,Y23: assn] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_assn @ X1 @ Y1 ) @ ( times_times_assn @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite_finite_int @ S3 )
% 7.75/5.75 => ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups7882442080178216443t_assn @ H2 @ S3 ) @ ( groups7882442080178216443t_assn @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8419_prod_Orelated,axiom,
% 7.75/5.75 ! [R: assn > assn > $o,S3: set_complex,H2: complex > assn,G: complex > assn] :
% 7.75/5.75 ( ( R @ one_one_assn @ one_one_assn )
% 7.75/5.75 => ( ! [X1: assn,Y1: assn,X23: assn,Y23: assn] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_assn @ X1 @ Y1 ) @ ( times_times_assn @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite3207457112153483333omplex @ S3 )
% 7.75/5.75 => ( ! [X3: complex] :
% 7.75/5.75 ( ( member_complex @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups4150731942483176573x_assn @ H2 @ S3 ) @ ( groups4150731942483176573x_assn @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8420_prod_Orelated,axiom,
% 7.75/5.75 ! [R: assn > assn > $o,S3: set_Code_integer,H2: code_integer > assn,G: code_integer > assn] :
% 7.75/5.75 ( ( R @ one_one_assn @ one_one_assn )
% 7.75/5.75 => ( ! [X1: assn,Y1: assn,X23: assn,Y23: assn] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_assn @ X1 @ Y1 ) @ ( times_times_assn @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite6017078050557962740nteger @ S3 )
% 7.75/5.75 => ( ! [X3: code_integer] :
% 7.75/5.75 ( ( member_Code_integer @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups1304777262505850412r_assn @ H2 @ S3 ) @ ( groups1304777262505850412r_assn @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8421_prod_Orelated,axiom,
% 7.75/5.75 ! [R: real > real > $o,S3: set_nat,H2: nat > real,G: nat > real] :
% 7.75/5.75 ( ( R @ one_one_real @ one_one_real )
% 7.75/5.75 => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite_finite_nat @ S3 )
% 7.75/5.75 => ( ! [X3: nat] :
% 7.75/5.75 ( ( member_nat @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups129246275422532515t_real @ H2 @ S3 ) @ ( groups129246275422532515t_real @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8422_prod_Orelated,axiom,
% 7.75/5.75 ! [R: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 7.75/5.75 ( ( R @ one_one_real @ one_one_real )
% 7.75/5.75 => ( ! [X1: real,Y1: real,X23: real,Y23: real] :
% 7.75/5.75 ( ( ( R @ X1 @ X23 )
% 7.75/5.75 & ( R @ Y1 @ Y23 ) )
% 7.75/5.75 => ( R @ ( times_times_real @ X1 @ Y1 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 7.75/5.75 => ( ( finite_finite_int @ S3 )
% 7.75/5.75 => ( ! [X3: int] :
% 7.75/5.75 ( ( member_int @ X3 @ S3 )
% 7.75/5.75 => ( R @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 7.75/5.75 => ( R @ ( groups2316167850115554303t_real @ H2 @ S3 ) @ ( groups2316167850115554303t_real @ G @ S3 ) ) ) ) ) ) ).
% 7.75/5.75
% 7.75/5.75 % prod.related
% 7.75/5.75 thf(fact_8423_prod_Oinsert__if,axiom,
% 7.75/5.75 ! [A2: set_real,X: real,G: real > assn] :
% 7.75/5.75 ( ( finite_finite_real @ A2 )
% 7.75/5.75 => ( ( ( member_real @ X @ A2 )
% 7.75/5.75 => ( ( groups1155561341820557179l_assn @ G @ ( insert_real @ X @ A2 ) )
% 7.94/5.75 = ( groups1155561341820557179l_assn @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_real @ X @ A2 )
% 7.94/5.75 => ( ( groups1155561341820557179l_assn @ G @ ( insert_real @ X @ A2 ) )
% 7.94/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups1155561341820557179l_assn @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8424_prod_Oinsert__if,axiom,
% 7.94/5.75 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.75 => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 7.94/5.75 = ( groups569574905686396791T_assn @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 7.94/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups569574905686396791T_assn @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8425_prod_Oinsert__if,axiom,
% 7.94/5.75 ! [A2: set_nat,X: nat,G: nat > assn] :
% 7.94/5.75 ( ( finite_finite_nat @ A2 )
% 7.94/5.75 => ( ( ( member_nat @ X @ A2 )
% 7.94/5.75 => ( ( groups6906906614972039071t_assn @ G @ ( insert_nat @ X @ A2 ) )
% 7.94/5.75 = ( groups6906906614972039071t_assn @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_nat @ X @ A2 )
% 7.94/5.75 => ( ( groups6906906614972039071t_assn @ G @ ( insert_nat @ X @ A2 ) )
% 7.94/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups6906906614972039071t_assn @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8426_prod_Oinsert__if,axiom,
% 7.94/5.75 ! [A2: set_int,X: int,G: int > assn] :
% 7.94/5.75 ( ( finite_finite_int @ A2 )
% 7.94/5.75 => ( ( ( member_int @ X @ A2 )
% 7.94/5.75 => ( ( groups7882442080178216443t_assn @ G @ ( insert_int @ X @ A2 ) )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_int @ X @ A2 )
% 7.94/5.75 => ( ( groups7882442080178216443t_assn @ G @ ( insert_int @ X @ A2 ) )
% 7.94/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups7882442080178216443t_assn @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8427_prod_Oinsert__if,axiom,
% 7.94/5.75 ! [A2: set_complex,X: complex,G: complex > assn] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.75 => ( ( ( member_complex @ X @ A2 )
% 7.94/5.75 => ( ( groups4150731942483176573x_assn @ G @ ( insert_complex @ X @ A2 ) )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_complex @ X @ A2 )
% 7.94/5.75 => ( ( groups4150731942483176573x_assn @ G @ ( insert_complex @ X @ A2 ) )
% 7.94/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups4150731942483176573x_assn @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8428_prod_Oinsert__if,axiom,
% 7.94/5.75 ! [A2: set_Code_integer,X: code_integer,G: code_integer > assn] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.75 => ( ( ( member_Code_integer @ X @ A2 )
% 7.94/5.75 => ( ( groups1304777262505850412r_assn @ G @ ( insert_Code_integer @ X @ A2 ) )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_Code_integer @ X @ A2 )
% 7.94/5.75 => ( ( groups1304777262505850412r_assn @ G @ ( insert_Code_integer @ X @ A2 ) )
% 7.94/5.75 = ( times_times_assn @ ( G @ X ) @ ( groups1304777262505850412r_assn @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8429_prod_Oinsert__if,axiom,
% 7.94/5.75 ! [A2: set_real,X: real,G: real > real] :
% 7.94/5.75 ( ( finite_finite_real @ A2 )
% 7.94/5.75 => ( ( ( member_real @ X @ A2 )
% 7.94/5.75 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 7.94/5.75 = ( groups1681761925125756287l_real @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_real @ X @ A2 )
% 7.94/5.75 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 7.94/5.75 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8430_prod_Oinsert__if,axiom,
% 7.94/5.75 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.75 => ( ( ( member_VEBT_VEBT @ X @ A2 )
% 7.94/5.75 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 7.94/5.75 = ( groups2703838992350267259T_real @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_VEBT_VEBT @ X @ A2 )
% 7.94/5.75 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 7.94/5.75 = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8431_prod_Oinsert__if,axiom,
% 7.94/5.75 ! [A2: set_nat,X: nat,G: nat > real] :
% 7.94/5.75 ( ( finite_finite_nat @ A2 )
% 7.94/5.75 => ( ( ( member_nat @ X @ A2 )
% 7.94/5.75 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 7.94/5.75 = ( groups129246275422532515t_real @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_nat @ X @ A2 )
% 7.94/5.75 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X @ A2 ) )
% 7.94/5.75 = ( times_times_real @ ( G @ X ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8432_prod_Oinsert__if,axiom,
% 7.94/5.75 ! [A2: set_int,X: int,G: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ A2 )
% 7.94/5.75 => ( ( ( member_int @ X @ A2 )
% 7.94/5.75 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 7.94/5.75 = ( groups2316167850115554303t_real @ G @ A2 ) ) )
% 7.94/5.75 & ( ~ ( member_int @ X @ A2 )
% 7.94/5.75 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X @ A2 ) )
% 7.94/5.75 = ( times_times_real @ ( G @ X ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.insert_if
% 7.94/5.75 thf(fact_8433_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_real,A2: set_real,F: real > nat,G: real > nat] :
% 7.94/5.75 ( ( finite_finite_real @ B3 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups4696554848551431203al_nat @ F @ A2 ) @ ( groups4696554848551431203al_nat @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8434_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ B3 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups6361806394783013919BT_nat @ F @ A2 ) @ ( groups6361806394783013919BT_nat @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8435_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_int,A2: set_int,F: int > nat,G: int > nat] :
% 7.94/5.75 ( ( finite_finite_int @ B3 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: int] :
% 7.94/5.75 ( ( member_int @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8436_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_complex,A2: set_complex,F: complex > nat,G: complex > nat] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: complex] :
% 7.94/5.75 ( ( member_complex @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8437_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_Code_integer,A2: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ B3 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups3190895334310489300er_nat @ F @ A2 ) @ ( groups3190895334310489300er_nat @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8438_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_real,A2: set_real,F: real > int,G: real > int] :
% 7.94/5.75 ( ( finite_finite_real @ B3 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_int @ ( groups4694064378042380927al_int @ F @ A2 ) @ ( groups4694064378042380927al_int @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8439_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ B3 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_int @ ( groups6359315924273963643BT_int @ F @ A2 ) @ ( groups6359315924273963643BT_int @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8440_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_complex,A2: set_complex,F: complex > int,G: complex > int] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: complex] :
% 7.94/5.75 ( ( member_complex @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8441_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_Code_integer,A2: set_Code_integer,F: code_integer > int,G: code_integer > int] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ B3 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_int @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_int @ ( groups3188404863801439024er_int @ F @ A2 ) @ ( groups3188404863801439024er_int @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8442_prod__dvd__prod__subset2,axiom,
% 7.94/5.75 ! [B3: set_nat,A2: set_nat,F: nat > nat,G: nat > nat] :
% 7.94/5.75 ( ( finite_finite_nat @ B3 )
% 7.94/5.75 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 7.94/5.75 => ( ! [A5: nat] :
% 7.94/5.75 ( ( member_nat @ A5 @ A2 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( F @ A5 ) @ ( G @ A5 ) ) )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset2
% 7.94/5.75 thf(fact_8443_prod__dvd__prod__subset,axiom,
% 7.94/5.75 ! [B3: set_int,A2: set_int,F: int > nat] :
% 7.94/5.75 ( ( finite_finite_int @ B3 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A2 ) @ ( groups1707563613775114915nt_nat @ F @ B3 ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset
% 7.94/5.75 thf(fact_8444_prod__dvd__prod__subset,axiom,
% 7.94/5.75 ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups861055069439313189ex_nat @ F @ A2 ) @ ( groups861055069439313189ex_nat @ F @ B3 ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset
% 7.94/5.75 thf(fact_8445_prod__dvd__prod__subset,axiom,
% 7.94/5.75 ! [B3: set_Code_integer,A2: set_Code_integer,F: code_integer > nat] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ B3 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ A2 @ B3 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups3190895334310489300er_nat @ F @ A2 ) @ ( groups3190895334310489300er_nat @ F @ B3 ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset
% 7.94/5.75 thf(fact_8446_prod__dvd__prod__subset,axiom,
% 7.94/5.75 ! [B3: set_complex,A2: set_complex,F: complex > int] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 7.94/5.75 => ( dvd_dvd_int @ ( groups858564598930262913ex_int @ F @ A2 ) @ ( groups858564598930262913ex_int @ F @ B3 ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset
% 7.94/5.75 thf(fact_8447_prod__dvd__prod__subset,axiom,
% 7.94/5.75 ! [B3: set_Code_integer,A2: set_Code_integer,F: code_integer > int] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ B3 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ A2 @ B3 )
% 7.94/5.75 => ( dvd_dvd_int @ ( groups3188404863801439024er_int @ F @ A2 ) @ ( groups3188404863801439024er_int @ F @ B3 ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset
% 7.94/5.75 thf(fact_8448_prod__dvd__prod__subset,axiom,
% 7.94/5.75 ! [B3: set_nat,A2: set_nat,F: nat > nat] :
% 7.94/5.75 ( ( finite_finite_nat @ B3 )
% 7.94/5.75 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 7.94/5.75 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ ( groups708209901874060359at_nat @ F @ B3 ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset
% 7.94/5.75 thf(fact_8449_prod__dvd__prod__subset,axiom,
% 7.94/5.75 ! [B3: set_nat,A2: set_nat,F: nat > int] :
% 7.94/5.75 ( ( finite_finite_nat @ B3 )
% 7.94/5.75 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 7.94/5.75 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A2 ) @ ( groups705719431365010083at_int @ F @ B3 ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset
% 7.94/5.75 thf(fact_8450_prod__dvd__prod__subset,axiom,
% 7.94/5.75 ! [B3: set_int,A2: set_int,F: int > int] :
% 7.94/5.75 ( ( finite_finite_int @ B3 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 7.94/5.75 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ F @ B3 ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod_dvd_prod_subset
% 7.94/5.75 thf(fact_8451_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_real,T4: set_real,S3: set_real,I: real > real,J: real > real,T5: set_real,G: real > assn,H2: real > assn] :
% 7.94/5.75 ( ( finite_finite_real @ S4 )
% 7.94/5.75 => ( ( finite_finite_real @ T4 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 7.94/5.75 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups1155561341820557179l_assn @ G @ S3 )
% 7.94/5.75 = ( groups1155561341820557179l_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8452_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_real,T4: set_VEBT_VEBT,S3: set_real,I: vEBT_VEBT > real,J: real > vEBT_VEBT,T5: set_VEBT_VEBT,G: real > assn,H2: vEBT_VEBT > assn] :
% 7.94/5.75 ( ( finite_finite_real @ S4 )
% 7.94/5.75 => ( ( finite5795047828879050333T_VEBT @ T4 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( member_VEBT_VEBT @ ( J @ A5 ) @ ( minus_5127226145743854075T_VEBT @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ T5 @ T4 ) )
% 7.94/5.75 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups1155561341820557179l_assn @ G @ S3 )
% 7.94/5.75 = ( groups569574905686396791T_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8453_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_VEBT_VEBT,T4: set_real,S3: set_VEBT_VEBT,I: real > vEBT_VEBT,J: vEBT_VEBT > real,T5: set_real,G: vEBT_VEBT > assn,H2: real > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ S4 )
% 7.94/5.75 => ( ( finite_finite_real @ T4 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 7.94/5.75 => ( member_VEBT_VEBT @ ( I @ B2 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ S3 )
% 7.94/5.75 = ( groups1155561341820557179l_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8454_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_VEBT_VEBT,T4: set_VEBT_VEBT,S3: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T5: set_VEBT_VEBT,G: vEBT_VEBT > assn,H2: vEBT_VEBT > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ S4 )
% 7.94/5.75 => ( ( finite5795047828879050333T_VEBT @ T4 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( member_VEBT_VEBT @ ( J @ A5 ) @ ( minus_5127226145743854075T_VEBT @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ T5 @ T4 ) )
% 7.94/5.75 => ( member_VEBT_VEBT @ ( I @ B2 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ S3 )
% 7.94/5.75 = ( groups569574905686396791T_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8455_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_real,T4: set_int,S3: set_real,I: int > real,J: real > int,T5: set_int,G: real > assn,H2: int > assn] :
% 7.94/5.75 ( ( finite_finite_real @ S4 )
% 7.94/5.75 => ( ( finite_finite_int @ T4 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 7.94/5.75 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups1155561341820557179l_assn @ G @ S3 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8456_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_VEBT_VEBT,T4: set_int,S3: set_VEBT_VEBT,I: int > vEBT_VEBT,J: vEBT_VEBT > int,T5: set_int,G: vEBT_VEBT > assn,H2: int > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ S4 )
% 7.94/5.75 => ( ( finite_finite_int @ T4 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 7.94/5.75 => ( member_VEBT_VEBT @ ( I @ B2 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ S3 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8457_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_real,T4: set_complex,S3: set_real,I: complex > real,J: real > complex,T5: set_complex,G: real > assn,H2: complex > assn] :
% 7.94/5.75 ( ( finite_finite_real @ S4 )
% 7.94/5.75 => ( ( finite3207457112153483333omplex @ T4 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 7.94/5.75 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups1155561341820557179l_assn @ G @ S3 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8458_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_VEBT_VEBT,T4: set_complex,S3: set_VEBT_VEBT,I: complex > vEBT_VEBT,J: vEBT_VEBT > complex,T5: set_complex,G: vEBT_VEBT > assn,H2: complex > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ S4 )
% 7.94/5.75 => ( ( finite3207457112153483333omplex @ T4 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 7.94/5.75 => ( member_VEBT_VEBT @ ( I @ B2 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ S3 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8459_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_real,T4: set_Code_integer,S3: set_real,I: code_integer > real,J: real > code_integer,T5: set_Code_integer,G: real > assn,H2: code_integer > assn] :
% 7.94/5.75 ( ( finite_finite_real @ S4 )
% 7.94/5.75 => ( ( finite6017078050557962740nteger @ T4 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S4 ) )
% 7.94/5.75 => ( member_Code_integer @ ( J @ A5 ) @ ( minus_2355218937544613996nteger @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 7.94/5.75 => ( member_real @ ( I @ B2 ) @ ( minus_minus_set_real @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups1155561341820557179l_assn @ G @ S3 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8460_prod_Oreindex__bij__witness__not__neutral,axiom,
% 7.94/5.75 ! [S4: set_VEBT_VEBT,T4: set_Code_integer,S3: set_VEBT_VEBT,I: code_integer > vEBT_VEBT,J: vEBT_VEBT > code_integer,T5: set_Code_integer,G: vEBT_VEBT > assn,H2: code_integer > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ S4 )
% 7.94/5.75 => ( ( finite6017078050557962740nteger @ T4 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( ( I @ ( J @ A5 ) )
% 7.94/5.75 = A5 ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) )
% 7.94/5.75 => ( member_Code_integer @ ( J @ A5 ) @ ( minus_2355218937544613996nteger @ T5 @ T4 ) ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 7.94/5.75 => ( ( J @ ( I @ B2 ) )
% 7.94/5.75 = B2 ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T5 @ T4 ) )
% 7.94/5.75 => ( member_VEBT_VEBT @ ( I @ B2 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S4 ) ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S4 )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ T4 )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ S3 )
% 7.94/5.75 => ( ( H2 @ ( J @ A5 ) )
% 7.94/5.75 = ( G @ A5 ) ) )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ S3 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ H2 @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.reindex_bij_witness_not_neutral
% 7.94/5.75 thf(fact_8461_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_int,G: int > assn] :
% 7.94/5.75 ( ( finite_finite_int @ A2 )
% 7.94/5.75 => ( ( groups7882442080178216443t_assn @ G
% 7.94/5.75 @ ( minus_minus_set_int @ A2
% 7.94/5.75 @ ( collect_int
% 7.94/5.75 @ ^ [X2: int] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_assn ) ) ) )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8462_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_complex,G: complex > assn] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.75 => ( ( groups4150731942483176573x_assn @ G
% 7.94/5.75 @ ( minus_811609699411566653omplex @ A2
% 7.94/5.75 @ ( collect_complex
% 7.94/5.75 @ ^ [X2: complex] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_assn ) ) ) )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8463_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_Code_integer,G: code_integer > assn] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.75 => ( ( groups1304777262505850412r_assn @ G
% 7.94/5.75 @ ( minus_2355218937544613996nteger @ A2
% 7.94/5.75 @ ( collect_Code_integer
% 7.94/5.75 @ ^ [X2: code_integer] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_assn ) ) ) )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8464_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_int,G: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ A2 )
% 7.94/5.75 => ( ( groups2316167850115554303t_real @ G
% 7.94/5.75 @ ( minus_minus_set_int @ A2
% 7.94/5.75 @ ( collect_int
% 7.94/5.75 @ ^ [X2: int] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_real ) ) ) )
% 7.94/5.75 = ( groups2316167850115554303t_real @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8465_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_complex,G: complex > real] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.75 => ( ( groups766887009212190081x_real @ G
% 7.94/5.75 @ ( minus_811609699411566653omplex @ A2
% 7.94/5.75 @ ( collect_complex
% 7.94/5.75 @ ^ [X2: complex] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_real ) ) ) )
% 7.94/5.75 = ( groups766887009212190081x_real @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8466_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_Code_integer,G: code_integer > real] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.75 => ( ( groups9004974159866482096r_real @ G
% 7.94/5.75 @ ( minus_2355218937544613996nteger @ A2
% 7.94/5.75 @ ( collect_Code_integer
% 7.94/5.75 @ ^ [X2: code_integer] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_real ) ) ) )
% 7.94/5.75 = ( groups9004974159866482096r_real @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8467_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_int,G: int > rat] :
% 7.94/5.75 ( ( finite_finite_int @ A2 )
% 7.94/5.75 => ( ( groups1072433553688619179nt_rat @ G
% 7.94/5.75 @ ( minus_minus_set_int @ A2
% 7.94/5.75 @ ( collect_int
% 7.94/5.75 @ ^ [X2: int] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_rat ) ) ) )
% 7.94/5.75 = ( groups1072433553688619179nt_rat @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8468_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_complex,G: complex > rat] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.75 => ( ( groups225925009352817453ex_rat @ G
% 7.94/5.75 @ ( minus_811609699411566653omplex @ A2
% 7.94/5.75 @ ( collect_complex
% 7.94/5.75 @ ^ [X2: complex] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_rat ) ) ) )
% 7.94/5.75 = ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8469_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_Code_integer,G: code_integer > rat] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.75 => ( ( groups2555765274223993564er_rat @ G
% 7.94/5.75 @ ( minus_2355218937544613996nteger @ A2
% 7.94/5.75 @ ( collect_Code_integer
% 7.94/5.75 @ ^ [X2: code_integer] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_rat ) ) ) )
% 7.94/5.75 = ( groups2555765274223993564er_rat @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8470_prod_Osetdiff__irrelevant,axiom,
% 7.94/5.75 ! [A2: set_int,G: int > nat] :
% 7.94/5.75 ( ( finite_finite_int @ A2 )
% 7.94/5.75 => ( ( groups1707563613775114915nt_nat @ G
% 7.94/5.75 @ ( minus_minus_set_int @ A2
% 7.94/5.75 @ ( collect_int
% 7.94/5.75 @ ^ [X2: int] :
% 7.94/5.75 ( ( G @ X2 )
% 7.94/5.75 = one_one_nat ) ) ) )
% 7.94/5.75 = ( groups1707563613775114915nt_nat @ G @ A2 ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.setdiff_irrelevant
% 7.94/5.75 thf(fact_8471_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_real,I: real,F: real > real] :
% 7.94/5.75 ( ( finite_finite_real @ I6 )
% 7.94/5.75 => ( ( member_real @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: real] :
% 7.94/5.75 ( ( member_real @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8472_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > real] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ I6 )
% 7.94/5.75 => ( ( member_VEBT_VEBT @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8473_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_nat,I: nat,F: nat > real] :
% 7.94/5.75 ( ( finite_finite_nat @ I6 )
% 7.94/5.75 => ( ( member_nat @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: nat] :
% 7.94/5.75 ( ( member_nat @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8474_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_int,I: int,F: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ I6 )
% 7.94/5.75 => ( ( member_int @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: int] :
% 7.94/5.75 ( ( member_int @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8475_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_complex,I: complex,F: complex > real] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ I6 )
% 7.94/5.75 => ( ( member_complex @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: complex] :
% 7.94/5.75 ( ( member_complex @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8476_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_Code_integer,I: code_integer,F: code_integer > real] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ I6 )
% 7.94/5.75 => ( ( member_Code_integer @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups9004974159866482096r_real @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8477_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_real,I: real,F: real > rat] :
% 7.94/5.75 ( ( finite_finite_real @ I6 )
% 7.94/5.75 => ( ( member_real @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: real] :
% 7.94/5.75 ( ( member_real @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8478_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ I6 )
% 7.94/5.75 => ( ( member_VEBT_VEBT @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8479_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_nat,I: nat,F: nat > rat] :
% 7.94/5.75 ( ( finite_finite_nat @ I6 )
% 7.94/5.75 => ( ( member_nat @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: nat] :
% 7.94/5.75 ( ( member_nat @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8480_less__1__prod2,axiom,
% 7.94/5.75 ! [I6: set_int,I: int,F: int > rat] :
% 7.94/5.75 ( ( finite_finite_int @ I6 )
% 7.94/5.75 => ( ( member_int @ I @ I6 )
% 7.94/5.75 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 7.94/5.75 => ( ! [I3: int] :
% 7.94/5.75 ( ( member_int @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod2
% 7.94/5.75 thf(fact_8481_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 7.94/5.75 => ( ! [I3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups2703838992350267259T_real @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8482_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_complex,F: complex > real] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bot_set_complex )
% 7.94/5.75 => ( ! [I3: complex] :
% 7.94/5.75 ( ( member_complex @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8483_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_Code_integer,F: code_integer > real] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bo3990330152332043303nteger )
% 7.94/5.75 => ( ! [I3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups9004974159866482096r_real @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8484_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_real,F: real > real] :
% 7.94/5.75 ( ( finite_finite_real @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bot_set_real )
% 7.94/5.75 => ( ! [I3: real] :
% 7.94/5.75 ( ( member_real @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8485_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_nat,F: nat > real] :
% 7.94/5.75 ( ( finite_finite_nat @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bot_set_nat )
% 7.94/5.75 => ( ! [I3: nat] :
% 7.94/5.75 ( ( member_nat @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8486_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_int,F: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bot_set_int )
% 7.94/5.75 => ( ! [I3: int] :
% 7.94/5.75 ( ( member_int @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8487_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bo8194388402131092736T_VEBT )
% 7.94/5.75 => ( ! [I3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( groups5726676334696518183BT_rat @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8488_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_complex,F: complex > rat] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bot_set_complex )
% 7.94/5.75 => ( ! [I3: complex] :
% 7.94/5.75 ( ( member_complex @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8489_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_Code_integer,F: code_integer > rat] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bo3990330152332043303nteger )
% 7.94/5.75 => ( ! [I3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8490_less__1__prod,axiom,
% 7.94/5.75 ! [I6: set_real,F: real > rat] :
% 7.94/5.75 ( ( finite_finite_real @ I6 )
% 7.94/5.75 => ( ( I6 != bot_bot_set_real )
% 7.94/5.75 => ( ! [I3: real] :
% 7.94/5.75 ( ( member_real @ I3 @ I6 )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 7.94/5.75 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I6 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % less_1_prod
% 7.94/5.75 thf(fact_8491_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_real,A2: set_real,B3: set_real,G: real > assn,H2: real > assn] :
% 7.94/5.75 ( ( finite_finite_real @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups1155561341820557179l_assn @ G @ A2 )
% 7.94/5.75 = ( groups1155561341820557179l_assn @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups1155561341820557179l_assn @ G @ C5 )
% 7.94/5.75 = ( groups1155561341820557179l_assn @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8492_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_VEBT_VEBT,A2: set_VEBT_VEBT,B3: set_VEBT_VEBT,G: vEBT_VEBT > assn,H2: vEBT_VEBT > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ C5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups569574905686396791T_assn @ G @ A2 )
% 7.94/5.75 = ( groups569574905686396791T_assn @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups569574905686396791T_assn @ G @ C5 )
% 7.94/5.75 = ( groups569574905686396791T_assn @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8493_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_int,A2: set_int,B3: set_int,G: int > assn,H2: int > assn] :
% 7.94/5.75 ( ( finite_finite_int @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: int] :
% 7.94/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups7882442080178216443t_assn @ G @ A2 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups7882442080178216443t_assn @ G @ C5 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8494_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_complex,A2: set_complex,B3: set_complex,G: complex > assn,H2: complex > assn] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ C5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: complex] :
% 7.94/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups4150731942483176573x_assn @ G @ A2 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups4150731942483176573x_assn @ G @ C5 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8495_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_Code_integer,A2: set_Code_integer,B3: set_Code_integer,G: code_integer > assn,H2: code_integer > assn] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ C5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ A5 @ ( minus_2355218937544613996nteger @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups1304777262505850412r_assn @ G @ A2 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups1304777262505850412r_assn @ G @ C5 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8496_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 7.94/5.75 ( ( finite_finite_real @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 7.94/5.75 = ( groups1681761925125756287l_real @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups1681761925125756287l_real @ G @ C5 )
% 7.94/5.75 = ( groups1681761925125756287l_real @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8497_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_VEBT_VEBT,A2: set_VEBT_VEBT,B3: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ C5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups2703838992350267259T_real @ G @ A2 )
% 7.94/5.75 = ( groups2703838992350267259T_real @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups2703838992350267259T_real @ G @ C5 )
% 7.94/5.75 = ( groups2703838992350267259T_real @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8498_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_int,A2: set_int,B3: set_int,G: int > real,H2: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: int] :
% 7.94/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 7.94/5.75 = ( groups2316167850115554303t_real @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups2316167850115554303t_real @ G @ C5 )
% 7.94/5.75 = ( groups2316167850115554303t_real @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8499_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ C5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: complex] :
% 7.94/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups766887009212190081x_real @ G @ A2 )
% 7.94/5.75 = ( groups766887009212190081x_real @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups766887009212190081x_real @ G @ C5 )
% 7.94/5.75 = ( groups766887009212190081x_real @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8500_prod_Osame__carrier,axiom,
% 7.94/5.75 ! [C5: set_Code_integer,A2: set_Code_integer,B3: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ C5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ A5 @ ( minus_2355218937544613996nteger @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups9004974159866482096r_real @ G @ A2 )
% 7.94/5.75 = ( groups9004974159866482096r_real @ H2 @ B3 ) )
% 7.94/5.75 = ( ( groups9004974159866482096r_real @ G @ C5 )
% 7.94/5.75 = ( groups9004974159866482096r_real @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrier
% 7.94/5.75 thf(fact_8501_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_real,A2: set_real,B3: set_real,G: real > assn,H2: real > assn] :
% 7.94/5.75 ( ( finite_finite_real @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups1155561341820557179l_assn @ G @ C5 )
% 7.94/5.75 = ( groups1155561341820557179l_assn @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups1155561341820557179l_assn @ G @ A2 )
% 7.94/5.75 = ( groups1155561341820557179l_assn @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8502_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_VEBT_VEBT,A2: set_VEBT_VEBT,B3: set_VEBT_VEBT,G: vEBT_VEBT > assn,H2: vEBT_VEBT > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ C5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups569574905686396791T_assn @ G @ C5 )
% 7.94/5.75 = ( groups569574905686396791T_assn @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ A2 )
% 7.94/5.75 = ( groups569574905686396791T_assn @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8503_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_int,A2: set_int,B3: set_int,G: int > assn,H2: int > assn] :
% 7.94/5.75 ( ( finite_finite_int @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: int] :
% 7.94/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups7882442080178216443t_assn @ G @ C5 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups7882442080178216443t_assn @ G @ A2 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8504_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_complex,A2: set_complex,B3: set_complex,G: complex > assn,H2: complex > assn] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ C5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: complex] :
% 7.94/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups4150731942483176573x_assn @ G @ C5 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups4150731942483176573x_assn @ G @ A2 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8505_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_Code_integer,A2: set_Code_integer,B3: set_Code_integer,G: code_integer > assn,H2: code_integer > assn] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ C5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ A5 @ ( minus_2355218937544613996nteger @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( ( groups1304777262505850412r_assn @ G @ C5 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups1304777262505850412r_assn @ G @ A2 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8506_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 7.94/5.75 ( ( finite_finite_real @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: real] :
% 7.94/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: real] :
% 7.94/5.75 ( ( member_real @ B2 @ ( minus_minus_set_real @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups1681761925125756287l_real @ G @ C5 )
% 7.94/5.75 = ( groups1681761925125756287l_real @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 7.94/5.75 = ( groups1681761925125756287l_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8507_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_VEBT_VEBT,A2: set_VEBT_VEBT,B3: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ C5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ A5 @ ( minus_5127226145743854075T_VEBT @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups2703838992350267259T_real @ G @ C5 )
% 7.94/5.75 = ( groups2703838992350267259T_real @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups2703838992350267259T_real @ G @ A2 )
% 7.94/5.75 = ( groups2703838992350267259T_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8508_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_int,A2: set_int,B3: set_int,G: int > real,H2: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: int] :
% 7.94/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: int] :
% 7.94/5.75 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups2316167850115554303t_real @ G @ C5 )
% 7.94/5.75 = ( groups2316167850115554303t_real @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 7.94/5.75 = ( groups2316167850115554303t_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8509_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ C5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: complex] :
% 7.94/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: complex] :
% 7.94/5.75 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups766887009212190081x_real @ G @ C5 )
% 7.94/5.75 = ( groups766887009212190081x_real @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups766887009212190081x_real @ G @ A2 )
% 7.94/5.75 = ( groups766887009212190081x_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8510_prod_Osame__carrierI,axiom,
% 7.94/5.75 ! [C5: set_Code_integer,A2: set_Code_integer,B3: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ C5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ A2 @ C5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ B3 @ C5 )
% 7.94/5.75 => ( ! [A5: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ A5 @ ( minus_2355218937544613996nteger @ C5 @ A2 ) )
% 7.94/5.75 => ( ( G @ A5 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [B2: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C5 @ B3 ) )
% 7.94/5.75 => ( ( H2 @ B2 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( ( groups9004974159866482096r_real @ G @ C5 )
% 7.94/5.75 = ( groups9004974159866482096r_real @ H2 @ C5 ) )
% 7.94/5.75 => ( ( groups9004974159866482096r_real @ G @ A2 )
% 7.94/5.75 = ( groups9004974159866482096r_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.same_carrierI
% 7.94/5.75 thf(fact_8511_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > assn] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( groups7882442080178216443t_assn @ G @ S3 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8512_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,G: complex > assn] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( groups4150731942483176573x_assn @ G @ S3 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8513_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,G: code_integer > assn] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( groups1304777262505850412r_assn @ G @ S3 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8514_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( groups2316167850115554303t_real @ G @ S3 )
% 7.94/5.75 = ( groups2316167850115554303t_real @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8515_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,G: complex > real] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( groups766887009212190081x_real @ G @ S3 )
% 7.94/5.75 = ( groups766887009212190081x_real @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8516_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,G: code_integer > real] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( groups9004974159866482096r_real @ G @ S3 )
% 7.94/5.75 = ( groups9004974159866482096r_real @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8517_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > rat] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_rat ) )
% 7.94/5.75 => ( ( groups1072433553688619179nt_rat @ G @ S3 )
% 7.94/5.75 = ( groups1072433553688619179nt_rat @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8518_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,G: complex > rat] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_rat ) )
% 7.94/5.75 => ( ( groups225925009352817453ex_rat @ G @ S3 )
% 7.94/5.75 = ( groups225925009352817453ex_rat @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8519_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,G: code_integer > rat] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_rat ) )
% 7.94/5.75 => ( ( groups2555765274223993564er_rat @ G @ S3 )
% 7.94/5.75 = ( groups2555765274223993564er_rat @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8520_prod_Omono__neutral__left,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > nat] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_nat ) )
% 7.94/5.75 => ( ( groups1707563613775114915nt_nat @ G @ S3 )
% 7.94/5.75 = ( groups1707563613775114915nt_nat @ G @ T5 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_left
% 7.94/5.75 thf(fact_8521_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > assn] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( groups7882442080178216443t_assn @ G @ T5 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8522_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,G: complex > assn] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( groups4150731942483176573x_assn @ G @ T5 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8523_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,G: code_integer > assn] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ( groups1304777262505850412r_assn @ G @ T5 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8524_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( groups2316167850115554303t_real @ G @ T5 )
% 7.94/5.75 = ( groups2316167850115554303t_real @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8525_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,G: complex > real] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( groups766887009212190081x_real @ G @ T5 )
% 7.94/5.75 = ( groups766887009212190081x_real @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8526_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,G: code_integer > real] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ( groups9004974159866482096r_real @ G @ T5 )
% 7.94/5.75 = ( groups9004974159866482096r_real @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8527_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > rat] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_rat ) )
% 7.94/5.75 => ( ( groups1072433553688619179nt_rat @ G @ T5 )
% 7.94/5.75 = ( groups1072433553688619179nt_rat @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8528_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,G: complex > rat] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_rat ) )
% 7.94/5.75 => ( ( groups225925009352817453ex_rat @ G @ T5 )
% 7.94/5.75 = ( groups225925009352817453ex_rat @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8529_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,G: code_integer > rat] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_rat ) )
% 7.94/5.75 => ( ( groups2555765274223993564er_rat @ G @ T5 )
% 7.94/5.75 = ( groups2555765274223993564er_rat @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8530_prod_Omono__neutral__right,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > nat] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_nat ) )
% 7.94/5.75 => ( ( groups1707563613775114915nt_nat @ G @ T5 )
% 7.94/5.75 = ( groups1707563613775114915nt_nat @ G @ S3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_right
% 7.94/5.75 thf(fact_8531_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_real,S3: set_real,H2: real > assn,G: real > assn] :
% 7.94/5.75 ( ( finite_finite_real @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: real] :
% 7.94/5.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: real] :
% 7.94/5.75 ( ( member_real @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups1155561341820557179l_assn @ G @ S3 )
% 7.94/5.75 = ( groups1155561341820557179l_assn @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8532_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_VEBT_VEBT,S3: set_VEBT_VEBT,H2: vEBT_VEBT > assn,G: vEBT_VEBT > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ T5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ S3 )
% 7.94/5.75 = ( groups569574905686396791T_assn @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8533_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,H2: int > assn,G: int > assn] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups7882442080178216443t_assn @ G @ S3 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8534_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,H2: complex > assn,G: complex > assn] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups4150731942483176573x_assn @ G @ S3 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8535_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,H2: code_integer > assn,G: code_integer > assn] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups1304777262505850412r_assn @ G @ S3 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8536_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_real,S3: set_real,H2: real > real,G: real > real] :
% 7.94/5.75 ( ( finite_finite_real @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: real] :
% 7.94/5.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: real] :
% 7.94/5.75 ( ( member_real @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups1681761925125756287l_real @ G @ S3 )
% 7.94/5.75 = ( groups1681761925125756287l_real @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8537_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_VEBT_VEBT,S3: set_VEBT_VEBT,H2: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ T5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups2703838992350267259T_real @ G @ S3 )
% 7.94/5.75 = ( groups2703838992350267259T_real @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8538_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,H2: int > real,G: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups2316167850115554303t_real @ G @ S3 )
% 7.94/5.75 = ( groups2316167850115554303t_real @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8539_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,H2: complex > real,G: complex > real] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups766887009212190081x_real @ G @ S3 )
% 7.94/5.75 = ( groups766887009212190081x_real @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8540_prod_Omono__neutral__cong__left,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,H2: code_integer > real,G: code_integer > real] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( H2 @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups9004974159866482096r_real @ G @ S3 )
% 7.94/5.75 = ( groups9004974159866482096r_real @ H2 @ T5 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_left
% 7.94/5.75 thf(fact_8541_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_real,S3: set_real,G: real > assn,H2: real > assn] :
% 7.94/5.75 ( ( finite_finite_real @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: real] :
% 7.94/5.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: real] :
% 7.94/5.75 ( ( member_real @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups1155561341820557179l_assn @ G @ T5 )
% 7.94/5.75 = ( groups1155561341820557179l_assn @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8542_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_VEBT_VEBT,S3: set_VEBT_VEBT,G: vEBT_VEBT > assn,H2: vEBT_VEBT > assn] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ T5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups569574905686396791T_assn @ G @ T5 )
% 7.94/5.75 = ( groups569574905686396791T_assn @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8543_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > assn,H2: int > assn] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups7882442080178216443t_assn @ G @ T5 )
% 7.94/5.75 = ( groups7882442080178216443t_assn @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8544_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,G: complex > assn,H2: complex > assn] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups4150731942483176573x_assn @ G @ T5 )
% 7.94/5.75 = ( groups4150731942483176573x_assn @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8545_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,G: code_integer > assn,H2: code_integer > assn] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_assn ) )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups1304777262505850412r_assn @ G @ T5 )
% 7.94/5.75 = ( groups1304777262505850412r_assn @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8546_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_real,S3: set_real,G: real > real,H2: real > real] :
% 7.94/5.75 ( ( finite_finite_real @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: real] :
% 7.94/5.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: real] :
% 7.94/5.75 ( ( member_real @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups1681761925125756287l_real @ G @ T5 )
% 7.94/5.75 = ( groups1681761925125756287l_real @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8547_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_VEBT_VEBT,S3: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 7.94/5.75 ( ( finite5795047828879050333T_VEBT @ T5 )
% 7.94/5.75 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.75 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups2703838992350267259T_real @ G @ T5 )
% 7.94/5.75 = ( groups2703838992350267259T_real @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8548_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_int,S3: set_int,G: int > real,H2: int > real] :
% 7.94/5.75 ( ( finite_finite_int @ T5 )
% 7.94/5.75 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: int] :
% 7.94/5.75 ( ( member_int @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups2316167850115554303t_real @ G @ T5 )
% 7.94/5.75 = ( groups2316167850115554303t_real @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8549_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_complex,S3: set_complex,G: complex > real,H2: complex > real] :
% 7.94/5.75 ( ( finite3207457112153483333omplex @ T5 )
% 7.94/5.75 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: complex] :
% 7.94/5.75 ( ( member_complex @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups766887009212190081x_real @ G @ T5 )
% 7.94/5.75 = ( groups766887009212190081x_real @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8550_prod_Omono__neutral__cong__right,axiom,
% 7.94/5.75 ! [T5: set_Code_integer,S3: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 7.94/5.75 ( ( finite6017078050557962740nteger @ T5 )
% 7.94/5.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T5 )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T5 @ S3 ) )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = one_one_real ) )
% 7.94/5.75 => ( ! [X3: code_integer] :
% 7.94/5.75 ( ( member_Code_integer @ X3 @ S3 )
% 7.94/5.75 => ( ( G @ X3 )
% 7.94/5.75 = ( H2 @ X3 ) ) )
% 7.94/5.75 => ( ( groups9004974159866482096r_real @ G @ T5 )
% 7.94/5.75 = ( groups9004974159866482096r_real @ H2 @ S3 ) ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.mono_neutral_cong_right
% 7.94/5.75 thf(fact_8551_prod_Osubset__diff,axiom,
% 7.94/5.75 ! [B3: set_int,A2: set_int,G: int > assn] :
% 7.94/5.75 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 7.94/5.75 => ( ( finite_finite_int @ A2 )
% 7.94/5.75 => ( ( groups7882442080178216443t_assn @ G @ A2 )
% 7.94/5.75 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups7882442080178216443t_assn @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.subset_diff
% 7.94/5.75 thf(fact_8552_prod_Osubset__diff,axiom,
% 7.94/5.75 ! [B3: set_complex,A2: set_complex,G: complex > assn] :
% 7.94/5.75 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 7.94/5.75 => ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.75 => ( ( groups4150731942483176573x_assn @ G @ A2 )
% 7.94/5.75 = ( times_times_assn @ ( groups4150731942483176573x_assn @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups4150731942483176573x_assn @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.subset_diff
% 7.94/5.75 thf(fact_8553_prod_Osubset__diff,axiom,
% 7.94/5.75 ! [B3: set_Code_integer,A2: set_Code_integer,G: code_integer > assn] :
% 7.94/5.75 ( ( ord_le7084787975880047091nteger @ B3 @ A2 )
% 7.94/5.75 => ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.75 => ( ( groups1304777262505850412r_assn @ G @ A2 )
% 7.94/5.75 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A2 @ B3 ) ) @ ( groups1304777262505850412r_assn @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.subset_diff
% 7.94/5.75 thf(fact_8554_prod_Osubset__diff,axiom,
% 7.94/5.75 ! [B3: set_int,A2: set_int,G: int > real] :
% 7.94/5.75 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 7.94/5.75 => ( ( finite_finite_int @ A2 )
% 7.94/5.75 => ( ( groups2316167850115554303t_real @ G @ A2 )
% 7.94/5.75 = ( times_times_real @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups2316167850115554303t_real @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.subset_diff
% 7.94/5.75 thf(fact_8555_prod_Osubset__diff,axiom,
% 7.94/5.75 ! [B3: set_complex,A2: set_complex,G: complex > real] :
% 7.94/5.75 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 7.94/5.75 => ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.75 => ( ( groups766887009212190081x_real @ G @ A2 )
% 7.94/5.75 = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups766887009212190081x_real @ G @ B3 ) ) ) ) ) ).
% 7.94/5.75
% 7.94/5.75 % prod.subset_diff
% 7.94/5.75 thf(fact_8556_prod_Osubset__diff,axiom,
% 7.94/5.75 ! [B3: set_Code_integer,A2: set_Code_integer,G: code_integer > real] :
% 7.94/5.75 ( ( ord_le7084787975880047091nteger @ B3 @ A2 )
% 7.94/5.75 => ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.75 => ( ( groups9004974159866482096r_real @ G @ A2 )
% 7.94/5.75 = ( times_times_real @ ( groups9004974159866482096r_real @ G @ ( minus_2355218937544613996nteger @ A2 @ B3 ) ) @ ( groups9004974159866482096r_real @ G @ B3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.subset_diff
% 7.94/5.76 thf(fact_8557_prod_Osubset__diff,axiom,
% 7.94/5.76 ! [B3: set_int,A2: set_int,G: int > nat] :
% 7.94/5.76 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 7.94/5.76 => ( ( finite_finite_int @ A2 )
% 7.94/5.76 => ( ( groups1707563613775114915nt_nat @ G @ A2 )
% 7.94/5.76 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups1707563613775114915nt_nat @ G @ B3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.subset_diff
% 7.94/5.76 thf(fact_8558_prod_Osubset__diff,axiom,
% 7.94/5.76 ! [B3: set_complex,A2: set_complex,G: complex > nat] :
% 7.94/5.76 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 7.94/5.76 => ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ( groups861055069439313189ex_nat @ G @ A2 )
% 7.94/5.76 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups861055069439313189ex_nat @ G @ B3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.subset_diff
% 7.94/5.76 thf(fact_8559_prod_Osubset__diff,axiom,
% 7.94/5.76 ! [B3: set_Code_integer,A2: set_Code_integer,G: code_integer > nat] :
% 7.94/5.76 ( ( ord_le7084787975880047091nteger @ B3 @ A2 )
% 7.94/5.76 => ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.76 => ( ( groups3190895334310489300er_nat @ G @ A2 )
% 7.94/5.76 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ A2 @ B3 ) ) @ ( groups3190895334310489300er_nat @ G @ B3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.subset_diff
% 7.94/5.76 thf(fact_8560_prod_Osubset__diff,axiom,
% 7.94/5.76 ! [B3: set_complex,A2: set_complex,G: complex > int] :
% 7.94/5.76 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 7.94/5.76 => ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ( groups858564598930262913ex_int @ G @ A2 )
% 7.94/5.76 = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups858564598930262913ex_int @ G @ B3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.subset_diff
% 7.94/5.76 thf(fact_8561_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.76 => ( ! [I3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 7.94/5.76 => ( ord_less_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( groups2703838992350267259T_real @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8562_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ! [I3: complex] :
% 7.94/5.76 ( ( member_complex @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bot_set_complex )
% 7.94/5.76 => ( ord_less_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8563_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_Code_integer,F: code_integer > real,G: code_integer > real] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.76 => ( ! [I3: code_integer] :
% 7.94/5.76 ( ( member_Code_integer @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bo3990330152332043303nteger )
% 7.94/5.76 => ( ord_less_real @ ( groups9004974159866482096r_real @ F @ A2 ) @ ( groups9004974159866482096r_real @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8564_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_real,F: real > real,G: real > real] :
% 7.94/5.76 ( ( finite_finite_real @ A2 )
% 7.94/5.76 => ( ! [I3: real] :
% 7.94/5.76 ( ( member_real @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bot_set_real )
% 7.94/5.76 => ( ord_less_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8565_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 7.94/5.76 ( ( finite_finite_nat @ A2 )
% 7.94/5.76 => ( ! [I3: nat] :
% 7.94/5.76 ( ( member_nat @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bot_set_nat )
% 7.94/5.76 => ( ord_less_real @ ( groups129246275422532515t_real @ F @ A2 ) @ ( groups129246275422532515t_real @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8566_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_int,F: int > real,G: int > real] :
% 7.94/5.76 ( ( finite_finite_int @ A2 )
% 7.94/5.76 => ( ! [I3: int] :
% 7.94/5.76 ( ( member_int @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bot_set_int )
% 7.94/5.76 => ( ord_less_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8567_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.76 => ( ! [I3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bo8194388402131092736T_VEBT )
% 7.94/5.76 => ( ord_less_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( groups5726676334696518183BT_rat @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8568_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ! [I3: complex] :
% 7.94/5.76 ( ( member_complex @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bot_set_complex )
% 7.94/5.76 => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8569_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.76 => ( ! [I3: code_integer] :
% 7.94/5.76 ( ( member_Code_integer @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bo3990330152332043303nteger )
% 7.94/5.76 => ( ord_less_rat @ ( groups2555765274223993564er_rat @ F @ A2 ) @ ( groups2555765274223993564er_rat @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8570_prod__mono__strict,axiom,
% 7.94/5.76 ! [A2: set_real,F: real > rat,G: real > rat] :
% 7.94/5.76 ( ( finite_finite_real @ A2 )
% 7.94/5.76 => ( ! [I3: real] :
% 7.94/5.76 ( ( member_real @ I3 @ A2 )
% 7.94/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 7.94/5.76 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 7.94/5.76 => ( ( A2 != bot_bot_set_real )
% 7.94/5.76 => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ G @ A2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono_strict
% 7.94/5.76 thf(fact_8571_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > assn] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.76 => ( ( member_VEBT_VEBT @ X @ A2 )
% 7.94/5.76 => ( ( groups569574905686396791T_assn @ G @ A2 )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups569574905686396791T_assn @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8572_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_complex,X: complex,G: complex > assn] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ( member_complex @ X @ A2 )
% 7.94/5.76 => ( ( groups4150731942483176573x_assn @ G @ A2 )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups4150731942483176573x_assn @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8573_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_Code_integer,X: code_integer,G: code_integer > assn] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.76 => ( ( member_Code_integer @ X @ A2 )
% 7.94/5.76 => ( ( groups1304777262505850412r_assn @ G @ A2 )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8574_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_real,X: real,G: real > assn] :
% 7.94/5.76 ( ( finite_finite_real @ A2 )
% 7.94/5.76 => ( ( member_real @ X @ A2 )
% 7.94/5.76 => ( ( groups1155561341820557179l_assn @ G @ A2 )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups1155561341820557179l_assn @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8575_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_int,X: int,G: int > assn] :
% 7.94/5.76 ( ( finite_finite_int @ A2 )
% 7.94/5.76 => ( ( member_int @ X @ A2 )
% 7.94/5.76 => ( ( groups7882442080178216443t_assn @ G @ A2 )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8576_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_nat,X: nat,G: nat > assn] :
% 7.94/5.76 ( ( finite_finite_nat @ A2 )
% 7.94/5.76 => ( ( member_nat @ X @ A2 )
% 7.94/5.76 => ( ( groups6906906614972039071t_assn @ G @ A2 )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8577_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.76 => ( ( member_VEBT_VEBT @ X @ A2 )
% 7.94/5.76 => ( ( groups2703838992350267259T_real @ G @ A2 )
% 7.94/5.76 = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8578_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_complex,X: complex,G: complex > real] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ( member_complex @ X @ A2 )
% 7.94/5.76 => ( ( groups766887009212190081x_real @ G @ A2 )
% 7.94/5.76 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8579_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_Code_integer,X: code_integer,G: code_integer > real] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.76 => ( ( member_Code_integer @ X @ A2 )
% 7.94/5.76 => ( ( groups9004974159866482096r_real @ G @ A2 )
% 7.94/5.76 = ( times_times_real @ ( G @ X ) @ ( groups9004974159866482096r_real @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8580_prod_Oremove,axiom,
% 7.94/5.76 ! [A2: set_real,X: real,G: real > real] :
% 7.94/5.76 ( ( finite_finite_real @ A2 )
% 7.94/5.76 => ( ( member_real @ X @ A2 )
% 7.94/5.76 => ( ( groups1681761925125756287l_real @ G @ A2 )
% 7.94/5.76 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.remove
% 7.94/5.76 thf(fact_8581_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > assn,X: vEBT_VEBT] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.76 => ( ( groups569574905686396791T_assn @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups569574905686396791T_assn @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8582_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_complex,G: complex > assn,X: complex] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ( groups4150731942483176573x_assn @ G @ ( insert_complex @ X @ A2 ) )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups4150731942483176573x_assn @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8583_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_Code_integer,G: code_integer > assn,X: code_integer] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.76 => ( ( groups1304777262505850412r_assn @ G @ ( insert_Code_integer @ X @ A2 ) )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8584_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_real,G: real > assn,X: real] :
% 7.94/5.76 ( ( finite_finite_real @ A2 )
% 7.94/5.76 => ( ( groups1155561341820557179l_assn @ G @ ( insert_real @ X @ A2 ) )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups1155561341820557179l_assn @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8585_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_int,G: int > assn,X: int] :
% 7.94/5.76 ( ( finite_finite_int @ A2 )
% 7.94/5.76 => ( ( groups7882442080178216443t_assn @ G @ ( insert_int @ X @ A2 ) )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8586_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_nat,G: nat > assn,X: nat] :
% 7.94/5.76 ( ( finite_finite_nat @ A2 )
% 7.94/5.76 => ( ( groups6906906614972039071t_assn @ G @ ( insert_nat @ X @ A2 ) )
% 7.94/5.76 = ( times_times_assn @ ( G @ X ) @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8587_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_VEBT_VEBT,G: vEBT_VEBT > real,X: vEBT_VEBT] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.76 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X @ A2 ) )
% 7.94/5.76 = ( times_times_real @ ( G @ X ) @ ( groups2703838992350267259T_real @ G @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8588_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_complex,G: complex > real,X: complex] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X @ A2 ) )
% 7.94/5.76 = ( times_times_real @ ( G @ X ) @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8589_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_Code_integer,G: code_integer > real,X: code_integer] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.76 => ( ( groups9004974159866482096r_real @ G @ ( insert_Code_integer @ X @ A2 ) )
% 7.94/5.76 = ( times_times_real @ ( G @ X ) @ ( groups9004974159866482096r_real @ G @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8590_prod_Oinsert__remove,axiom,
% 7.94/5.76 ! [A2: set_real,G: real > real,X: real] :
% 7.94/5.76 ( ( finite_finite_real @ A2 )
% 7.94/5.76 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X @ A2 ) )
% 7.94/5.76 = ( times_times_real @ ( G @ X ) @ ( groups1681761925125756287l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.insert_remove
% 7.94/5.76 thf(fact_8591_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > assn,C: vEBT_VEBT > assn] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ S3 )
% 7.94/5.76 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 7.94/5.76 => ( ( groups569574905686396791T_assn
% 7.94/5.76 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_assn @ ( B @ A ) @ ( groups569574905686396791T_assn @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 7.94/5.76 => ( ( groups569574905686396791T_assn
% 7.94/5.76 @ ^ [K3: vEBT_VEBT] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups569574905686396791T_assn @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8592_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_complex,A: complex,B: complex > assn,C: complex > assn] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ S3 )
% 7.94/5.76 => ( ( ( member_complex @ A @ S3 )
% 7.94/5.76 => ( ( groups4150731942483176573x_assn
% 7.94/5.76 @ ^ [K3: complex] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_assn @ ( B @ A ) @ ( groups4150731942483176573x_assn @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_complex @ A @ S3 )
% 7.94/5.76 => ( ( groups4150731942483176573x_assn
% 7.94/5.76 @ ^ [K3: complex] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups4150731942483176573x_assn @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8593_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_Code_integer,A: code_integer,B: code_integer > assn,C: code_integer > assn] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ S3 )
% 7.94/5.76 => ( ( ( member_Code_integer @ A @ S3 )
% 7.94/5.76 => ( ( groups1304777262505850412r_assn
% 7.94/5.76 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_assn @ ( B @ A ) @ ( groups1304777262505850412r_assn @ C @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_Code_integer @ A @ S3 )
% 7.94/5.76 => ( ( groups1304777262505850412r_assn
% 7.94/5.76 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups1304777262505850412r_assn @ C @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8594_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_real,A: real,B: real > assn,C: real > assn] :
% 7.94/5.76 ( ( finite_finite_real @ S3 )
% 7.94/5.76 => ( ( ( member_real @ A @ S3 )
% 7.94/5.76 => ( ( groups1155561341820557179l_assn
% 7.94/5.76 @ ^ [K3: real] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_assn @ ( B @ A ) @ ( groups1155561341820557179l_assn @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_real @ A @ S3 )
% 7.94/5.76 => ( ( groups1155561341820557179l_assn
% 7.94/5.76 @ ^ [K3: real] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups1155561341820557179l_assn @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8595_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_int,A: int,B: int > assn,C: int > assn] :
% 7.94/5.76 ( ( finite_finite_int @ S3 )
% 7.94/5.76 => ( ( ( member_int @ A @ S3 )
% 7.94/5.76 => ( ( groups7882442080178216443t_assn
% 7.94/5.76 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_assn @ ( B @ A ) @ ( groups7882442080178216443t_assn @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_int @ A @ S3 )
% 7.94/5.76 => ( ( groups7882442080178216443t_assn
% 7.94/5.76 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups7882442080178216443t_assn @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8596_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_nat,A: nat,B: nat > assn,C: nat > assn] :
% 7.94/5.76 ( ( finite_finite_nat @ S3 )
% 7.94/5.76 => ( ( ( member_nat @ A @ S3 )
% 7.94/5.76 => ( ( groups6906906614972039071t_assn
% 7.94/5.76 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_assn @ ( B @ A ) @ ( groups6906906614972039071t_assn @ C @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_nat @ A @ S3 )
% 7.94/5.76 => ( ( groups6906906614972039071t_assn
% 7.94/5.76 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups6906906614972039071t_assn @ C @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8597_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ S3 )
% 7.94/5.76 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 7.94/5.76 => ( ( groups2703838992350267259T_real
% 7.94/5.76 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_real @ ( B @ A ) @ ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 7.94/5.76 => ( ( groups2703838992350267259T_real
% 7.94/5.76 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups2703838992350267259T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8598_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_complex,A: complex,B: complex > real,C: complex > real] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ S3 )
% 7.94/5.76 => ( ( ( member_complex @ A @ S3 )
% 7.94/5.76 => ( ( groups766887009212190081x_real
% 7.94/5.76 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_complex @ A @ S3 )
% 7.94/5.76 => ( ( groups766887009212190081x_real
% 7.94/5.76 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups766887009212190081x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8599_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_Code_integer,A: code_integer,B: code_integer > real,C: code_integer > real] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ S3 )
% 7.94/5.76 => ( ( ( member_Code_integer @ A @ S3 )
% 7.94/5.76 => ( ( groups9004974159866482096r_real
% 7.94/5.76 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_real @ ( B @ A ) @ ( groups9004974159866482096r_real @ C @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_Code_integer @ A @ S3 )
% 7.94/5.76 => ( ( groups9004974159866482096r_real
% 7.94/5.76 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups9004974159866482096r_real @ C @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8600_prod_Odelta__remove,axiom,
% 7.94/5.76 ! [S3: set_real,A: real,B: real > real,C: real > real] :
% 7.94/5.76 ( ( finite_finite_real @ S3 )
% 7.94/5.76 => ( ( ( member_real @ A @ S3 )
% 7.94/5.76 => ( ( groups1681761925125756287l_real
% 7.94/5.76 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( member_real @ A @ S3 )
% 7.94/5.76 => ( ( groups1681761925125756287l_real
% 7.94/5.76 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C @ K3 ) )
% 7.94/5.76 @ S3 )
% 7.94/5.76 = ( groups1681761925125756287l_real @ C @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.delta_remove
% 7.94/5.76 thf(fact_8601_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_real,A2: set_real,F: real > real] :
% 7.94/5.76 ( ( finite_finite_real @ B3 )
% 7.94/5.76 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: real] :
% 7.94/5.76 ( ( member_real @ B2 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: real] :
% 7.94/5.76 ( ( member_real @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( groups1681761925125756287l_real @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8602_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ B3 )
% 7.94/5.76 => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( groups2703838992350267259T_real @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8603_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_int,A2: set_int,F: int > real] :
% 7.94/5.76 ( ( finite_finite_int @ B3 )
% 7.94/5.76 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: int] :
% 7.94/5.76 ( ( member_int @ B2 @ ( minus_minus_set_int @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: int] :
% 7.94/5.76 ( ( member_int @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A2 ) @ ( groups2316167850115554303t_real @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8604_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_complex,A2: set_complex,F: complex > real] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ B3 )
% 7.94/5.76 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: complex] :
% 7.94/5.76 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: complex] :
% 7.94/5.76 ( ( member_complex @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( groups766887009212190081x_real @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8605_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_Code_integer,A2: set_Code_integer,F: code_integer > real] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ B3 )
% 7.94/5.76 => ( ( ord_le7084787975880047091nteger @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: code_integer] :
% 7.94/5.76 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ one_one_real @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: code_integer] :
% 7.94/5.76 ( ( member_Code_integer @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( groups9004974159866482096r_real @ F @ A2 ) @ ( groups9004974159866482096r_real @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8606_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_real,A2: set_real,F: real > rat] :
% 7.94/5.76 ( ( finite_finite_real @ B3 )
% 7.94/5.76 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: real] :
% 7.94/5.76 ( ( member_real @ B2 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: real] :
% 7.94/5.76 ( ( member_real @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A2 ) @ ( groups4061424788464935467al_rat @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8607_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_VEBT_VEBT,A2: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ B3 )
% 7.94/5.76 => ( ( ord_le4337996190870823476T_VEBT @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ B2 @ ( minus_5127226145743854075T_VEBT @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_rat @ ( groups5726676334696518183BT_rat @ F @ A2 ) @ ( groups5726676334696518183BT_rat @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8608_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_int,A2: set_int,F: int > rat] :
% 7.94/5.76 ( ( finite_finite_int @ B3 )
% 7.94/5.76 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: int] :
% 7.94/5.76 ( ( member_int @ B2 @ ( minus_minus_set_int @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: int] :
% 7.94/5.76 ( ( member_int @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A2 ) @ ( groups1072433553688619179nt_rat @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8609_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_complex,A2: set_complex,F: complex > rat] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ B3 )
% 7.94/5.76 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: complex] :
% 7.94/5.76 ( ( member_complex @ B2 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: complex] :
% 7.94/5.76 ( ( member_complex @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A2 ) @ ( groups225925009352817453ex_rat @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8610_prod__mono2,axiom,
% 7.94/5.76 ! [B3: set_Code_integer,A2: set_Code_integer,F: code_integer > rat] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ B3 )
% 7.94/5.76 => ( ( ord_le7084787975880047091nteger @ A2 @ B3 )
% 7.94/5.76 => ( ! [B2: code_integer] :
% 7.94/5.76 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B3 @ A2 ) )
% 7.94/5.76 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 7.94/5.76 => ( ! [A5: code_integer] :
% 7.94/5.76 ( ( member_Code_integer @ A5 @ A2 )
% 7.94/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A5 ) ) )
% 7.94/5.76 => ( ord_less_eq_rat @ ( groups2555765274223993564er_rat @ F @ A2 ) @ ( groups2555765274223993564er_rat @ F @ B3 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_mono2
% 7.94/5.76 thf(fact_8611_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > complex,A: vEBT_VEBT] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_complex )
% 7.94/5.76 => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 7.94/5.76 => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 7.94/5.76 = ( divide1717551699836669952omplex @ ( groups127312072573709053omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 7.94/5.76 => ( ( groups127312072573709053omplex @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 7.94/5.76 = ( groups127312072573709053omplex @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8612_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_complex,F: complex > complex,A: complex] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_complex )
% 7.94/5.76 => ( ( ( member_complex @ A @ A2 )
% 7.94/5.76 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 7.94/5.76 = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_complex @ A @ A2 )
% 7.94/5.76 => ( ( groups3708469109370488835omplex @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 7.94/5.76 = ( groups3708469109370488835omplex @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8613_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_Code_integer,F: code_integer > complex,A: code_integer] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_complex )
% 7.94/5.76 => ( ( ( member_Code_integer @ A @ A2 )
% 7.94/5.76 => ( ( groups862514429393162674omplex @ F @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 7.94/5.76 = ( divide1717551699836669952omplex @ ( groups862514429393162674omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_Code_integer @ A @ A2 )
% 7.94/5.76 => ( ( groups862514429393162674omplex @ F @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 7.94/5.76 = ( groups862514429393162674omplex @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8614_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_real,F: real > complex,A: real] :
% 7.94/5.76 ( ( finite_finite_real @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_complex )
% 7.94/5.76 => ( ( ( member_real @ A @ A2 )
% 7.94/5.76 => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 7.94/5.76 = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_real @ A @ A2 )
% 7.94/5.76 => ( ( groups713298508707869441omplex @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 7.94/5.76 = ( groups713298508707869441omplex @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8615_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_int,F: int > complex,A: int] :
% 7.94/5.76 ( ( finite_finite_int @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_complex )
% 7.94/5.76 => ( ( ( member_int @ A @ A2 )
% 7.94/5.76 => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 7.94/5.76 = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_int @ A @ A2 )
% 7.94/5.76 => ( ( groups7440179247065528705omplex @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 7.94/5.76 = ( groups7440179247065528705omplex @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8616_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_nat,F: nat > complex,A: nat] :
% 7.94/5.76 ( ( finite_finite_nat @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_complex )
% 7.94/5.76 => ( ( ( member_nat @ A @ A2 )
% 7.94/5.76 => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 7.94/5.76 = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_nat @ A @ A2 )
% 7.94/5.76 => ( ( groups6464643781859351333omplex @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 7.94/5.76 = ( groups6464643781859351333omplex @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8617_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_VEBT_VEBT,F: vEBT_VEBT > real,A: vEBT_VEBT] :
% 7.94/5.76 ( ( finite5795047828879050333T_VEBT @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_real )
% 7.94/5.76 => ( ( ( member_VEBT_VEBT @ A @ A2 )
% 7.94/5.76 => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 7.94/5.76 = ( divide_divide_real @ ( groups2703838992350267259T_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_VEBT_VEBT @ A @ A2 )
% 7.94/5.76 => ( ( groups2703838992350267259T_real @ F @ ( minus_5127226145743854075T_VEBT @ A2 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 7.94/5.76 = ( groups2703838992350267259T_real @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8618_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_complex,F: complex > real,A: complex] :
% 7.94/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_real )
% 7.94/5.76 => ( ( ( member_complex @ A @ A2 )
% 7.94/5.76 => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 7.94/5.76 = ( divide_divide_real @ ( groups766887009212190081x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_complex @ A @ A2 )
% 7.94/5.76 => ( ( groups766887009212190081x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 7.94/5.76 = ( groups766887009212190081x_real @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8619_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_Code_integer,F: code_integer > real,A: code_integer] :
% 7.94/5.76 ( ( finite6017078050557962740nteger @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_real )
% 7.94/5.76 => ( ( ( member_Code_integer @ A @ A2 )
% 7.94/5.76 => ( ( groups9004974159866482096r_real @ F @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 7.94/5.76 = ( divide_divide_real @ ( groups9004974159866482096r_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_Code_integer @ A @ A2 )
% 7.94/5.76 => ( ( groups9004974159866482096r_real @ F @ ( minus_2355218937544613996nteger @ A2 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 7.94/5.76 = ( groups9004974159866482096r_real @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8620_prod__diff1,axiom,
% 7.94/5.76 ! [A2: set_real,F: real > real,A: real] :
% 7.94/5.76 ( ( finite_finite_real @ A2 )
% 7.94/5.76 => ( ( ( F @ A )
% 7.94/5.76 != zero_zero_real )
% 7.94/5.76 => ( ( ( member_real @ A @ A2 )
% 7.94/5.76 => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 7.94/5.76 = ( divide_divide_real @ ( groups1681761925125756287l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 7.94/5.76 & ( ~ ( member_real @ A @ A2 )
% 7.94/5.76 => ( ( groups1681761925125756287l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 7.94/5.76 = ( groups1681761925125756287l_real @ F @ A2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_diff1
% 7.94/5.76 thf(fact_8621_list__every__elemnt__bound__sum__bound__real,axiom,
% 7.94/5.76 ! [Xs2: list_VEBT_VEBT,F: vEBT_VEBT > real,Bound: real,I: real] :
% 7.94/5.76 ( ! [X3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ F @ Xs2 ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound_real
% 7.94/5.76 thf(fact_8622_list__every__elemnt__bound__sum__bound__real,axiom,
% 7.94/5.76 ! [Xs2: list_real,F: real > real,Bound: real,I: real] :
% 7.94/5.76 ( ! [X3: real] :
% 7.94/5.76 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_real_real @ F @ Xs2 ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_real @ Xs2 ) ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound_real
% 7.94/5.76 thf(fact_8623_list__every__elemnt__bound__sum__bound__real,axiom,
% 7.94/5.76 ! [Xs2: list_o,F: $o > real,Bound: real,I: real] :
% 7.94/5.76 ( ! [X3: $o] :
% 7.94/5.76 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_o_real @ F @ Xs2 ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_o @ Xs2 ) ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound_real
% 7.94/5.76 thf(fact_8624_list__every__elemnt__bound__sum__bound__real,axiom,
% 7.94/5.76 ! [Xs2: list_nat,F: nat > real,Bound: real,I: real] :
% 7.94/5.76 ( ! [X3: nat] :
% 7.94/5.76 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ F @ Xs2 ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_nat @ Xs2 ) ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound_real
% 7.94/5.76 thf(fact_8625_list__every__elemnt__bound__sum__bound__real,axiom,
% 7.94/5.76 ! [Xs2: list_int,F: int > real,Bound: real,I: real] :
% 7.94/5.76 ( ! [X3: int] :
% 7.94/5.76 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_int_real @ F @ Xs2 ) @ I ) @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_int @ Xs2 ) ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound_real
% 7.94/5.76 thf(fact_8626_ln__series,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 => ( ( ln_ln_real @ X )
% 7.94/5.76 = ( suminf_real
% 7.94/5.76 @ ^ [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 ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % ln_series
% 7.94/5.76 thf(fact_8627_f__g__map__foldr__bound,axiom,
% 7.94/5.76 ! [Xs2: list_VEBT_VEBT,F: vEBT_VEBT > real,C: real,G: vEBT_VEBT > real,D2: real] :
% 7.94/5.76 ( ! [X3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( F @ X3 ) @ ( times_times_real @ C @ ( G @ X3 ) ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ F @ Xs2 ) @ D2 ) @ ( plus_plus_real @ ( times_times_real @ C @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ G @ Xs2 ) @ zero_zero_real ) ) @ D2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % f_g_map_foldr_bound
% 7.94/5.76 thf(fact_8628_f__g__map__foldr__bound,axiom,
% 7.94/5.76 ! [Xs2: list_nat,F: nat > real,C: real,G: nat > real,D2: real] :
% 7.94/5.76 ( ! [X3: nat] :
% 7.94/5.76 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( F @ X3 ) @ ( times_times_real @ C @ ( G @ X3 ) ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ F @ Xs2 ) @ D2 ) @ ( plus_plus_real @ ( times_times_real @ C @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ G @ Xs2 ) @ zero_zero_real ) ) @ D2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % f_g_map_foldr_bound
% 7.94/5.76 thf(fact_8629_f__g__map__foldr__bound,axiom,
% 7.94/5.76 ! [Xs2: list_real,F: real > real,C: real,G: real > real,D2: real] :
% 7.94/5.76 ( ! [X3: real] :
% 7.94/5.76 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( F @ X3 ) @ ( times_times_real @ C @ ( G @ X3 ) ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_real_real @ F @ Xs2 ) @ D2 ) @ ( plus_plus_real @ ( times_times_real @ C @ ( foldr_real_real @ plus_plus_real @ ( map_real_real @ G @ Xs2 ) @ zero_zero_real ) ) @ D2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % f_g_map_foldr_bound
% 7.94/5.76 thf(fact_8630_f__g__map__foldr__bound,axiom,
% 7.94/5.76 ! [Xs2: list_int,F: int > real,C: real,G: int > real,D2: real] :
% 7.94/5.76 ( ! [X3: int] :
% 7.94/5.76 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( F @ X3 ) @ ( times_times_real @ C @ ( G @ X3 ) ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( foldr_real_real @ plus_plus_real @ ( map_int_real @ F @ Xs2 ) @ D2 ) @ ( plus_plus_real @ ( times_times_real @ C @ ( foldr_real_real @ plus_plus_real @ ( map_int_real @ G @ Xs2 ) @ zero_zero_real ) ) @ D2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % f_g_map_foldr_bound
% 7.94/5.76 thf(fact_8631_list__every__elemnt__bound__sum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_VEBT_VEBT,F: vEBT_VEBT > nat,Bound: nat,I: nat] :
% 7.94/5.76 ( ! [X3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ F @ Xs2 ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound
% 7.94/5.76 thf(fact_8632_list__every__elemnt__bound__sum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_real,F: real > nat,Bound: nat,I: nat] :
% 7.94/5.76 ( ! [X3: real] :
% 7.94/5.76 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_real_nat @ F @ Xs2 ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_real @ Xs2 ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound
% 7.94/5.76 thf(fact_8633_list__every__elemnt__bound__sum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_o,F: $o > nat,Bound: nat,I: nat] :
% 7.94/5.76 ( ! [X3: $o] :
% 7.94/5.76 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_o_nat @ F @ Xs2 ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound
% 7.94/5.76 thf(fact_8634_list__every__elemnt__bound__sum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_nat,F: nat > nat,Bound: nat,I: nat] :
% 7.94/5.76 ( ! [X3: nat] :
% 7.94/5.76 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_nat_nat @ F @ Xs2 ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound
% 7.94/5.76 thf(fact_8635_list__every__elemnt__bound__sum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_int,F: int > nat,Bound: nat,I: nat] :
% 7.94/5.76 ( ! [X3: int] :
% 7.94/5.76 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( F @ X3 ) @ Bound ) )
% 7.94/5.76 => ( ord_less_eq_nat @ ( foldr_nat_nat @ plus_plus_nat @ ( map_int_nat @ F @ Xs2 ) @ I ) @ ( plus_plus_nat @ ( times_times_nat @ ( size_size_list_int @ Xs2 ) @ Bound ) @ I ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_every_elemnt_bound_sum_bound
% 7.94/5.76 thf(fact_8636_map__ident,axiom,
% 7.94/5.76 ( ( map_nat_nat
% 7.94/5.76 @ ^ [X2: nat] : X2 )
% 7.94/5.76 = ( ^ [Xs: list_nat] : Xs ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_ident
% 7.94/5.76 thf(fact_8637_listsum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_complex,F: complex > real,Y: real] :
% 7.94/5.76 ( ! [X3: complex] :
% 7.94/5.76 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ Y @ ( foldr_real_real @ plus_plus_real @ ( map_complex_real @ F @ Xs2 ) @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % listsum_bound
% 7.94/5.76 thf(fact_8638_listsum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_VEBT_VEBT,F: vEBT_VEBT > real,Y: real] :
% 7.94/5.76 ( ! [X3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ Y @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ F @ Xs2 ) @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % listsum_bound
% 7.94/5.76 thf(fact_8639_listsum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_nat,F: nat > real,Y: real] :
% 7.94/5.76 ( ! [X3: nat] :
% 7.94/5.76 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ Y @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ F @ Xs2 ) @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % listsum_bound
% 7.94/5.76 thf(fact_8640_listsum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_real,F: real > real,Y: real] :
% 7.94/5.76 ( ! [X3: real] :
% 7.94/5.76 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ Y @ ( foldr_real_real @ plus_plus_real @ ( map_real_real @ F @ Xs2 ) @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % listsum_bound
% 7.94/5.76 thf(fact_8641_listsum__bound,axiom,
% 7.94/5.76 ! [Xs2: list_int,F: int > real,Y: real] :
% 7.94/5.76 ( ! [X3: int] :
% 7.94/5.76 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ Y @ ( foldr_real_real @ plus_plus_real @ ( map_int_real @ F @ Xs2 ) @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % listsum_bound
% 7.94/5.76 thf(fact_8642_length__map,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > real,Xs2: list_VEBT_VEBT] :
% 7.94/5.76 ( ( size_size_list_real @ ( map_VEBT_VEBT_real @ F @ Xs2 ) )
% 7.94/5.76 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8643_length__map,axiom,
% 7.94/5.76 ! [F: real > real,Xs2: list_real] :
% 7.94/5.76 ( ( size_size_list_real @ ( map_real_real @ F @ Xs2 ) )
% 7.94/5.76 = ( size_size_list_real @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8644_length__map,axiom,
% 7.94/5.76 ! [F: $o > real,Xs2: list_o] :
% 7.94/5.76 ( ( size_size_list_real @ ( map_o_real @ F @ Xs2 ) )
% 7.94/5.76 = ( size_size_list_o @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8645_length__map,axiom,
% 7.94/5.76 ! [F: nat > real,Xs2: list_nat] :
% 7.94/5.76 ( ( size_size_list_real @ ( map_nat_real @ F @ Xs2 ) )
% 7.94/5.76 = ( size_size_list_nat @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8646_length__map,axiom,
% 7.94/5.76 ! [F: int > real,Xs2: list_int] :
% 7.94/5.76 ( ( size_size_list_real @ ( map_int_real @ F @ Xs2 ) )
% 7.94/5.76 = ( size_size_list_int @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8647_length__map,axiom,
% 7.94/5.76 ! [F: real > $o,Xs2: list_real] :
% 7.94/5.76 ( ( size_size_list_o @ ( map_real_o @ F @ Xs2 ) )
% 7.94/5.76 = ( size_size_list_real @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8648_length__map,axiom,
% 7.94/5.76 ! [F: $o > $o,Xs2: list_o] :
% 7.94/5.76 ( ( size_size_list_o @ ( map_o_o @ F @ Xs2 ) )
% 7.94/5.76 = ( size_size_list_o @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8649_length__map,axiom,
% 7.94/5.76 ! [F: nat > $o,Xs2: list_nat] :
% 7.94/5.76 ( ( size_size_list_o @ ( map_nat_o @ F @ Xs2 ) )
% 7.94/5.76 = ( size_size_list_nat @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8650_length__map,axiom,
% 7.94/5.76 ! [F: int > $o,Xs2: list_int] :
% 7.94/5.76 ( ( size_size_list_o @ ( map_int_o @ F @ Xs2 ) )
% 7.94/5.76 = ( size_size_list_int @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8651_length__map,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,Xs2: list_VEBT_VEBT] :
% 7.94/5.76 ( ( size_size_list_nat @ ( map_VEBT_VEBT_nat @ F @ Xs2 ) )
% 7.94/5.76 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % length_map
% 7.94/5.76 thf(fact_8652_map__eq__conv,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,Xs2: list_VEBT_VEBT,G: vEBT_VEBT > nat] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_VEBT_VEBT_nat @ G @ Xs2 ) )
% 7.94/5.76 = ( ! [X2: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X2 )
% 7.94/5.76 = ( G @ X2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_conv
% 7.94/5.76 thf(fact_8653_map__eq__conv,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > real,Xs2: list_VEBT_VEBT,G: vEBT_VEBT > real] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_real @ F @ Xs2 )
% 7.94/5.76 = ( map_VEBT_VEBT_real @ G @ Xs2 ) )
% 7.94/5.76 = ( ! [X2: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X2 )
% 7.94/5.76 = ( G @ X2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_conv
% 7.94/5.76 thf(fact_8654_map__eq__conv,axiom,
% 7.94/5.76 ! [F: nat > nat,Xs2: list_nat,G: nat > nat] :
% 7.94/5.76 ( ( ( map_nat_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_nat_nat @ G @ Xs2 ) )
% 7.94/5.76 = ( ! [X2: nat] :
% 7.94/5.76 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X2 )
% 7.94/5.76 = ( G @ X2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_conv
% 7.94/5.76 thf(fact_8655_map__eq__conv,axiom,
% 7.94/5.76 ! [F: nat > $o,Xs2: list_nat,G: nat > $o] :
% 7.94/5.76 ( ( ( map_nat_o @ F @ Xs2 )
% 7.94/5.76 = ( map_nat_o @ G @ Xs2 ) )
% 7.94/5.76 = ( ! [X2: nat] :
% 7.94/5.76 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X2 )
% 7.94/5.76 = ( G @ X2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_conv
% 7.94/5.76 thf(fact_8656_map__replicate,axiom,
% 7.94/5.76 ! [F: nat > nat,N: nat,X: nat] :
% 7.94/5.76 ( ( map_nat_nat @ F @ ( replicate_nat @ N @ X ) )
% 7.94/5.76 = ( replicate_nat @ N @ ( F @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate
% 7.94/5.76 thf(fact_8657_map__replicate,axiom,
% 7.94/5.76 ! [F: nat > $o,N: nat,X: nat] :
% 7.94/5.76 ( ( map_nat_o @ F @ ( replicate_nat @ N @ X ) )
% 7.94/5.76 = ( replicate_o @ N @ ( F @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate
% 7.94/5.76 thf(fact_8658_map__replicate,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,N: nat,X: vEBT_VEBT] :
% 7.94/5.76 ( ( map_VEBT_VEBT_nat @ F @ ( replicate_VEBT_VEBT @ N @ X ) )
% 7.94/5.76 = ( replicate_nat @ N @ ( F @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate
% 7.94/5.76 thf(fact_8659_map__replicate,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > real,N: nat,X: vEBT_VEBT] :
% 7.94/5.76 ( ( map_VEBT_VEBT_real @ F @ ( replicate_VEBT_VEBT @ N @ X ) )
% 7.94/5.76 = ( replicate_real @ N @ ( F @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate
% 7.94/5.76 thf(fact_8660_map__replicate,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > vEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 7.94/5.76 ( ( map_VE8901447254227204932T_VEBT @ F @ ( replicate_VEBT_VEBT @ N @ X ) )
% 7.94/5.76 = ( replicate_VEBT_VEBT @ N @ ( F @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate
% 7.94/5.76 thf(fact_8661_real__nat__list,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,Xs2: list_VEBT_VEBT,C: nat] :
% 7.94/5.76 ( ( semiri5074537144036343181t_real @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ F @ Xs2 ) @ C ) )
% 7.94/5.76 = ( foldr_real_real @ plus_plus_real
% 7.94/5.76 @ ( map_VEBT_VEBT_real
% 7.94/5.76 @ ^ [X2: vEBT_VEBT] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 7.94/5.76 @ Xs2 )
% 7.94/5.76 @ ( semiri5074537144036343181t_real @ C ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_nat_list
% 7.94/5.76 thf(fact_8662_real__nat__list,axiom,
% 7.94/5.76 ! [F: nat > nat,Xs2: list_nat,C: nat] :
% 7.94/5.76 ( ( semiri5074537144036343181t_real @ ( foldr_nat_nat @ plus_plus_nat @ ( map_nat_nat @ F @ Xs2 ) @ C ) )
% 7.94/5.76 = ( foldr_real_real @ plus_plus_real
% 7.94/5.76 @ ( map_nat_real
% 7.94/5.76 @ ^ [X2: nat] : ( semiri5074537144036343181t_real @ ( F @ X2 ) )
% 7.94/5.76 @ Xs2 )
% 7.94/5.76 @ ( semiri5074537144036343181t_real @ C ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_nat_list
% 7.94/5.76 thf(fact_8663_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.94/5.76 => ( ( nth_VEBT_VEBT @ ( map_VE8901447254227204932T_VEBT @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8664_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBTi,F: vEBT_VEBTi > vEBT_VEBT] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.94/5.76 => ( ( nth_VEBT_VEBT @ ( map_VE7998069337340375161T_VEBT @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_VEBT_VEBTi @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8665_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBTi,F: vEBT_VEBTi > nat] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.94/5.76 => ( ( nth_nat @ ( map_VEBT_VEBTi_nat @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_VEBT_VEBTi @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8666_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.94/5.76 => ( ( nth_VEBT_VEBTi @ ( map_VE7029150624388687525_VEBTi @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8667_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBTi,F: vEBT_VEBTi > vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.94/5.76 => ( ( nth_VEBT_VEBTi @ ( map_VE483055756984248624_VEBTi @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_VEBT_VEBTi @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8668_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBT,F: vEBT_VEBT > int] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.94/5.76 => ( ( nth_int @ ( map_VEBT_VEBT_int @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8669_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBTi,F: vEBT_VEBTi > int] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 7.94/5.76 => ( ( nth_int @ ( map_VEBT_VEBTi_int @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_VEBT_VEBTi @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8670_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.94/5.76 => ( ( nth_nat @ ( map_VEBT_VEBT_nat @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8671_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBT,F: vEBT_VEBT > real] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.94/5.76 => ( ( nth_real @ ( map_VEBT_VEBT_real @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8672_nth__map,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_real,F: real > vEBT_VEBT] :
% 7.94/5.76 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 7.94/5.76 => ( ( nth_VEBT_VEBT @ ( map_real_VEBT_VEBT @ F @ Xs2 ) @ N )
% 7.94/5.76 = ( F @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % nth_map
% 7.94/5.76 thf(fact_8673_powser__zero,axiom,
% 7.94/5.76 ! [F: nat > real] :
% 7.94/5.76 ( ( suminf_real
% 7.94/5.76 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) )
% 7.94/5.76 = ( F @ zero_zero_nat ) ) ).
% 7.94/5.76
% 7.94/5.76 % powser_zero
% 7.94/5.76 thf(fact_8674_powser__zero,axiom,
% 7.94/5.76 ! [F: nat > complex] :
% 7.94/5.76 ( ( suminf_complex
% 7.94/5.76 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) )
% 7.94/5.76 = ( F @ zero_zero_nat ) ) ).
% 7.94/5.76
% 7.94/5.76 % powser_zero
% 7.94/5.76 thf(fact_8675_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,Xs2: list_VEBT_VEBT,G: vEBT_VEBT > nat,Ys: list_VEBT_VEBT] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_VEBT_VEBT_nat @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8676_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > real,Xs2: list_VEBT_VEBT,G: vEBT_VEBT > real,Ys: list_VEBT_VEBT] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_real @ F @ Xs2 )
% 7.94/5.76 = ( map_VEBT_VEBT_real @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8677_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,Xs2: list_VEBT_VEBT,G: real > nat,Ys: list_real] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_real_nat @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_size_list_real @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8678_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > real,Xs2: list_VEBT_VEBT,G: real > real,Ys: list_real] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_real @ F @ Xs2 )
% 7.94/5.76 = ( map_real_real @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_size_list_real @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8679_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,Xs2: list_VEBT_VEBT,G: $o > nat,Ys: list_o] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_o_nat @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_size_list_o @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8680_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > real,Xs2: list_VEBT_VEBT,G: $o > real,Ys: list_o] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_real @ F @ Xs2 )
% 7.94/5.76 = ( map_o_real @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_size_list_o @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8681_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,Xs2: list_VEBT_VEBT,G: nat > nat,Ys: list_nat] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_nat_nat @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_size_list_nat @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8682_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > real,Xs2: list_VEBT_VEBT,G: nat > real,Ys: list_nat] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_real @ F @ Xs2 )
% 7.94/5.76 = ( map_nat_real @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_size_list_nat @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8683_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,Xs2: list_VEBT_VEBT,G: int > nat,Ys: list_int] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_int_nat @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_size_list_int @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8684_map__eq__imp__length__eq,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > real,Xs2: list_VEBT_VEBT,G: int > real,Ys: list_int] :
% 7.94/5.76 ( ( ( map_VEBT_VEBT_real @ F @ Xs2 )
% 7.94/5.76 = ( map_int_real @ G @ Ys ) )
% 7.94/5.76 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 7.94/5.76 = ( size_size_list_int @ Ys ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_eq_imp_length_eq
% 7.94/5.76 thf(fact_8685_map__update,axiom,
% 7.94/5.76 ! [F: nat > nat,Xs2: list_nat,K: nat,Y: nat] :
% 7.94/5.76 ( ( map_nat_nat @ F @ ( list_update_nat @ Xs2 @ K @ Y ) )
% 7.94/5.76 = ( list_update_nat @ ( map_nat_nat @ F @ Xs2 ) @ K @ ( F @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_update
% 7.94/5.76 thf(fact_8686_map__update,axiom,
% 7.94/5.76 ! [F: nat > $o,Xs2: list_nat,K: nat,Y: nat] :
% 7.94/5.76 ( ( map_nat_o @ F @ ( list_update_nat @ Xs2 @ K @ Y ) )
% 7.94/5.76 = ( list_update_o @ ( map_nat_o @ F @ Xs2 ) @ K @ ( F @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_update
% 7.94/5.76 thf(fact_8687_map__update,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > nat,Xs2: list_VEBT_VEBT,K: nat,Y: vEBT_VEBT] :
% 7.94/5.76 ( ( map_VEBT_VEBT_nat @ F @ ( list_u1324408373059187874T_VEBT @ Xs2 @ K @ Y ) )
% 7.94/5.76 = ( list_update_nat @ ( map_VEBT_VEBT_nat @ F @ Xs2 ) @ K @ ( F @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_update
% 7.94/5.76 thf(fact_8688_map__update,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > real,Xs2: list_VEBT_VEBT,K: nat,Y: vEBT_VEBT] :
% 7.94/5.76 ( ( map_VEBT_VEBT_real @ F @ ( list_u1324408373059187874T_VEBT @ Xs2 @ K @ Y ) )
% 7.94/5.76 = ( list_update_real @ ( map_VEBT_VEBT_real @ F @ Xs2 ) @ K @ ( F @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_update
% 7.94/5.76 thf(fact_8689_map__update,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > vEBT_VEBT,Xs2: list_VEBT_VEBT,K: nat,Y: vEBT_VEBT] :
% 7.94/5.76 ( ( map_VE8901447254227204932T_VEBT @ F @ ( list_u1324408373059187874T_VEBT @ Xs2 @ K @ Y ) )
% 7.94/5.76 = ( list_u1324408373059187874T_VEBT @ ( map_VE8901447254227204932T_VEBT @ F @ Xs2 ) @ K @ ( F @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_update
% 7.94/5.76 thf(fact_8690_map__update,axiom,
% 7.94/5.76 ! [F: vEBT_VEBT > vEBT_VEBTi,Xs2: list_VEBT_VEBT,K: nat,Y: vEBT_VEBT] :
% 7.94/5.76 ( ( map_VE7029150624388687525_VEBTi @ F @ ( list_u1324408373059187874T_VEBT @ Xs2 @ K @ Y ) )
% 7.94/5.76 = ( list_u6098035379799741383_VEBTi @ ( map_VE7029150624388687525_VEBTi @ F @ Xs2 ) @ K @ ( F @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_update
% 7.94/5.76 thf(fact_8691_map__update,axiom,
% 7.94/5.76 ! [F: vEBT_VEBTi > vEBT_VEBT,Xs2: list_VEBT_VEBTi,K: nat,Y: vEBT_VEBTi] :
% 7.94/5.76 ( ( map_VE7998069337340375161T_VEBT @ F @ ( list_u6098035379799741383_VEBTi @ Xs2 @ K @ Y ) )
% 7.94/5.76 = ( list_u1324408373059187874T_VEBT @ ( map_VE7998069337340375161T_VEBT @ F @ Xs2 ) @ K @ ( F @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_update
% 7.94/5.76 thf(fact_8692_map__update,axiom,
% 7.94/5.76 ! [F: vEBT_VEBTi > vEBT_VEBTi,Xs2: list_VEBT_VEBTi,K: nat,Y: vEBT_VEBTi] :
% 7.94/5.76 ( ( map_VE483055756984248624_VEBTi @ F @ ( list_u6098035379799741383_VEBTi @ Xs2 @ K @ Y ) )
% 7.94/5.76 = ( list_u6098035379799741383_VEBTi @ ( map_VE483055756984248624_VEBTi @ F @ Xs2 ) @ K @ ( F @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_update
% 7.94/5.76 thf(fact_8693_list_Omap__ident,axiom,
% 7.94/5.76 ! [T: list_nat] :
% 7.94/5.76 ( ( map_nat_nat
% 7.94/5.76 @ ^ [X2: nat] : X2
% 7.94/5.76 @ T )
% 7.94/5.76 = T ) ).
% 7.94/5.76
% 7.94/5.76 % list.map_ident
% 7.94/5.76 thf(fact_8694_list_Omap__cong,axiom,
% 7.94/5.76 ! [X: list_VEBT_VEBT,Ya: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 7.94/5.76 ( ( X = Ya )
% 7.94/5.76 => ( ! [Z3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ Ya ) )
% 7.94/5.76 => ( ( F @ Z3 )
% 7.94/5.76 = ( G @ Z3 ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_nat @ F @ X )
% 7.94/5.76 = ( map_VEBT_VEBT_nat @ G @ Ya ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.map_cong
% 7.94/5.76 thf(fact_8695_list_Omap__cong,axiom,
% 7.94/5.76 ! [X: list_VEBT_VEBT,Ya: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 7.94/5.76 ( ( X = Ya )
% 7.94/5.76 => ( ! [Z3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ Ya ) )
% 7.94/5.76 => ( ( F @ Z3 )
% 7.94/5.76 = ( G @ Z3 ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_real @ F @ X )
% 7.94/5.76 = ( map_VEBT_VEBT_real @ G @ Ya ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.map_cong
% 7.94/5.76 thf(fact_8696_list_Omap__cong,axiom,
% 7.94/5.76 ! [X: list_nat,Ya: list_nat,F: nat > nat,G: nat > nat] :
% 7.94/5.76 ( ( X = Ya )
% 7.94/5.76 => ( ! [Z3: nat] :
% 7.94/5.76 ( ( member_nat @ Z3 @ ( set_nat2 @ Ya ) )
% 7.94/5.76 => ( ( F @ Z3 )
% 7.94/5.76 = ( G @ Z3 ) ) )
% 7.94/5.76 => ( ( map_nat_nat @ F @ X )
% 7.94/5.76 = ( map_nat_nat @ G @ Ya ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.map_cong
% 7.94/5.76 thf(fact_8697_list_Omap__cong,axiom,
% 7.94/5.76 ! [X: list_nat,Ya: list_nat,F: nat > $o,G: nat > $o] :
% 7.94/5.76 ( ( X = Ya )
% 7.94/5.76 => ( ! [Z3: nat] :
% 7.94/5.76 ( ( member_nat @ Z3 @ ( set_nat2 @ Ya ) )
% 7.94/5.76 => ( ( F @ Z3 )
% 7.94/5.76 = ( G @ Z3 ) ) )
% 7.94/5.76 => ( ( map_nat_o @ F @ X )
% 7.94/5.76 = ( map_nat_o @ G @ Ya ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.map_cong
% 7.94/5.76 thf(fact_8698_list_Omap__cong0,axiom,
% 7.94/5.76 ! [X: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 7.94/5.76 ( ! [Z3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ X ) )
% 7.94/5.76 => ( ( F @ Z3 )
% 7.94/5.76 = ( G @ Z3 ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_nat @ F @ X )
% 7.94/5.76 = ( map_VEBT_VEBT_nat @ G @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.map_cong0
% 7.94/5.76 thf(fact_8699_list_Omap__cong0,axiom,
% 7.94/5.76 ! [X: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 7.94/5.76 ( ! [Z3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ X ) )
% 7.94/5.76 => ( ( F @ Z3 )
% 7.94/5.76 = ( G @ Z3 ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_real @ F @ X )
% 7.94/5.76 = ( map_VEBT_VEBT_real @ G @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.map_cong0
% 7.94/5.76 thf(fact_8700_list_Omap__cong0,axiom,
% 7.94/5.76 ! [X: list_nat,F: nat > nat,G: nat > nat] :
% 7.94/5.76 ( ! [Z3: nat] :
% 7.94/5.76 ( ( member_nat @ Z3 @ ( set_nat2 @ X ) )
% 7.94/5.76 => ( ( F @ Z3 )
% 7.94/5.76 = ( G @ Z3 ) ) )
% 7.94/5.76 => ( ( map_nat_nat @ F @ X )
% 7.94/5.76 = ( map_nat_nat @ G @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.map_cong0
% 7.94/5.76 thf(fact_8701_list_Omap__cong0,axiom,
% 7.94/5.76 ! [X: list_nat,F: nat > $o,G: nat > $o] :
% 7.94/5.76 ( ! [Z3: nat] :
% 7.94/5.76 ( ( member_nat @ Z3 @ ( set_nat2 @ X ) )
% 7.94/5.76 => ( ( F @ Z3 )
% 7.94/5.76 = ( G @ Z3 ) ) )
% 7.94/5.76 => ( ( map_nat_o @ F @ X )
% 7.94/5.76 = ( map_nat_o @ G @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.map_cong0
% 7.94/5.76 thf(fact_8702_list_Oinj__map__strong,axiom,
% 7.94/5.76 ! [X: list_VEBT_VEBT,Xa3: list_VEBT_VEBT,F: vEBT_VEBT > nat,Fa: vEBT_VEBT > nat] :
% 7.94/5.76 ( ! [Z3: vEBT_VEBT,Za: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ X ) )
% 7.94/5.76 => ( ( member_VEBT_VEBT @ Za @ ( set_VEBT_VEBT2 @ Xa3 ) )
% 7.94/5.76 => ( ( ( F @ Z3 )
% 7.94/5.76 = ( Fa @ Za ) )
% 7.94/5.76 => ( Z3 = Za ) ) ) )
% 7.94/5.76 => ( ( ( map_VEBT_VEBT_nat @ F @ X )
% 7.94/5.76 = ( map_VEBT_VEBT_nat @ Fa @ Xa3 ) )
% 7.94/5.76 => ( X = Xa3 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.inj_map_strong
% 7.94/5.76 thf(fact_8703_list_Oinj__map__strong,axiom,
% 7.94/5.76 ! [X: list_VEBT_VEBT,Xa3: list_VEBT_VEBT,F: vEBT_VEBT > real,Fa: vEBT_VEBT > real] :
% 7.94/5.76 ( ! [Z3: vEBT_VEBT,Za: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ Z3 @ ( set_VEBT_VEBT2 @ X ) )
% 7.94/5.76 => ( ( member_VEBT_VEBT @ Za @ ( set_VEBT_VEBT2 @ Xa3 ) )
% 7.94/5.76 => ( ( ( F @ Z3 )
% 7.94/5.76 = ( Fa @ Za ) )
% 7.94/5.76 => ( Z3 = Za ) ) ) )
% 7.94/5.76 => ( ( ( map_VEBT_VEBT_real @ F @ X )
% 7.94/5.76 = ( map_VEBT_VEBT_real @ Fa @ Xa3 ) )
% 7.94/5.76 => ( X = Xa3 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.inj_map_strong
% 7.94/5.76 thf(fact_8704_list_Oinj__map__strong,axiom,
% 7.94/5.76 ! [X: list_nat,Xa3: list_nat,F: nat > nat,Fa: nat > nat] :
% 7.94/5.76 ( ! [Z3: nat,Za: nat] :
% 7.94/5.76 ( ( member_nat @ Z3 @ ( set_nat2 @ X ) )
% 7.94/5.76 => ( ( member_nat @ Za @ ( set_nat2 @ Xa3 ) )
% 7.94/5.76 => ( ( ( F @ Z3 )
% 7.94/5.76 = ( Fa @ Za ) )
% 7.94/5.76 => ( Z3 = Za ) ) ) )
% 7.94/5.76 => ( ( ( map_nat_nat @ F @ X )
% 7.94/5.76 = ( map_nat_nat @ Fa @ Xa3 ) )
% 7.94/5.76 => ( X = Xa3 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.inj_map_strong
% 7.94/5.76 thf(fact_8705_list_Oinj__map__strong,axiom,
% 7.94/5.76 ! [X: list_nat,Xa3: list_nat,F: nat > $o,Fa: nat > $o] :
% 7.94/5.76 ( ! [Z3: nat,Za: nat] :
% 7.94/5.76 ( ( member_nat @ Z3 @ ( set_nat2 @ X ) )
% 7.94/5.76 => ( ( member_nat @ Za @ ( set_nat2 @ Xa3 ) )
% 7.94/5.76 => ( ( ( F @ Z3 )
% 7.94/5.76 = ( Fa @ Za ) )
% 7.94/5.76 => ( Z3 = Za ) ) ) )
% 7.94/5.76 => ( ( ( map_nat_o @ F @ X )
% 7.94/5.76 = ( map_nat_o @ Fa @ Xa3 ) )
% 7.94/5.76 => ( X = Xa3 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list.inj_map_strong
% 7.94/5.76 thf(fact_8706_map__ext,axiom,
% 7.94/5.76 ! [Xs2: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 7.94/5.76 ( ! [X3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = ( G @ X3 ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_VEBT_VEBT_nat @ G @ Xs2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_ext
% 7.94/5.76 thf(fact_8707_map__ext,axiom,
% 7.94/5.76 ! [Xs2: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 7.94/5.76 ( ! [X3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = ( G @ X3 ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_real @ F @ Xs2 )
% 7.94/5.76 = ( map_VEBT_VEBT_real @ G @ Xs2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_ext
% 7.94/5.76 thf(fact_8708_map__ext,axiom,
% 7.94/5.76 ! [Xs2: list_nat,F: nat > nat,G: nat > nat] :
% 7.94/5.76 ( ! [X3: nat] :
% 7.94/5.76 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = ( G @ X3 ) ) )
% 7.94/5.76 => ( ( map_nat_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_nat_nat @ G @ Xs2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_ext
% 7.94/5.76 thf(fact_8709_map__ext,axiom,
% 7.94/5.76 ! [Xs2: list_nat,F: nat > $o,G: nat > $o] :
% 7.94/5.76 ( ! [X3: nat] :
% 7.94/5.76 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = ( G @ X3 ) ) )
% 7.94/5.76 => ( ( map_nat_o @ F @ Xs2 )
% 7.94/5.76 = ( map_nat_o @ G @ Xs2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_ext
% 7.94/5.76 thf(fact_8710_map__idI,axiom,
% 7.94/5.76 ! [Xs2: list_complex,F: complex > complex] :
% 7.94/5.76 ( ! [X3: complex] :
% 7.94/5.76 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = X3 ) )
% 7.94/5.76 => ( ( map_complex_complex @ F @ Xs2 )
% 7.94/5.76 = Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_idI
% 7.94/5.76 thf(fact_8711_map__idI,axiom,
% 7.94/5.76 ! [Xs2: list_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 7.94/5.76 ( ! [X3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = X3 ) )
% 7.94/5.76 => ( ( map_VE8901447254227204932T_VEBT @ F @ Xs2 )
% 7.94/5.76 = Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_idI
% 7.94/5.76 thf(fact_8712_map__idI,axiom,
% 7.94/5.76 ! [Xs2: list_nat,F: nat > nat] :
% 7.94/5.76 ( ! [X3: nat] :
% 7.94/5.76 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = X3 ) )
% 7.94/5.76 => ( ( map_nat_nat @ F @ Xs2 )
% 7.94/5.76 = Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_idI
% 7.94/5.76 thf(fact_8713_map__idI,axiom,
% 7.94/5.76 ! [Xs2: list_real,F: real > real] :
% 7.94/5.76 ( ! [X3: real] :
% 7.94/5.76 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = X3 ) )
% 7.94/5.76 => ( ( map_real_real @ F @ Xs2 )
% 7.94/5.76 = Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_idI
% 7.94/5.76 thf(fact_8714_map__idI,axiom,
% 7.94/5.76 ! [Xs2: list_int,F: int > int] :
% 7.94/5.76 ( ! [X3: int] :
% 7.94/5.76 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = X3 ) )
% 7.94/5.76 => ( ( map_int_int @ F @ Xs2 )
% 7.94/5.76 = Xs2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_idI
% 7.94/5.76 thf(fact_8715_map__cong,axiom,
% 7.94/5.76 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 7.94/5.76 ( ( Xs2 = Ys )
% 7.94/5.76 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Ys ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = ( G @ X3 ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_VEBT_VEBT_nat @ G @ Ys ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_cong
% 7.94/5.76 thf(fact_8716_map__cong,axiom,
% 7.94/5.76 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 7.94/5.76 ( ( Xs2 = Ys )
% 7.94/5.76 => ( ! [X3: vEBT_VEBT] :
% 7.94/5.76 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Ys ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = ( G @ X3 ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_real @ F @ Xs2 )
% 7.94/5.76 = ( map_VEBT_VEBT_real @ G @ Ys ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_cong
% 7.94/5.76 thf(fact_8717_map__cong,axiom,
% 7.94/5.76 ! [Xs2: list_nat,Ys: list_nat,F: nat > nat,G: nat > nat] :
% 7.94/5.76 ( ( Xs2 = Ys )
% 7.94/5.76 => ( ! [X3: nat] :
% 7.94/5.76 ( ( member_nat @ X3 @ ( set_nat2 @ Ys ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = ( G @ X3 ) ) )
% 7.94/5.76 => ( ( map_nat_nat @ F @ Xs2 )
% 7.94/5.76 = ( map_nat_nat @ G @ Ys ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_cong
% 7.94/5.76 thf(fact_8718_map__cong,axiom,
% 7.94/5.76 ! [Xs2: list_nat,Ys: list_nat,F: nat > $o,G: nat > $o] :
% 7.94/5.76 ( ( Xs2 = Ys )
% 7.94/5.76 => ( ! [X3: nat] :
% 7.94/5.76 ( ( member_nat @ X3 @ ( set_nat2 @ Ys ) )
% 7.94/5.76 => ( ( F @ X3 )
% 7.94/5.76 = ( G @ X3 ) ) )
% 7.94/5.76 => ( ( map_nat_o @ F @ Xs2 )
% 7.94/5.76 = ( map_nat_o @ G @ Ys ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_cong
% 7.94/5.76 thf(fact_8719_ex__map__conv,axiom,
% 7.94/5.76 ! [Ys: list_o,F: nat > $o] :
% 7.94/5.76 ( ( ? [Xs: list_nat] :
% 7.94/5.76 ( Ys
% 7.94/5.76 = ( map_nat_o @ F @ Xs ) ) )
% 7.94/5.76 = ( ! [X2: $o] :
% 7.94/5.76 ( ( member_o @ X2 @ ( set_o2 @ Ys ) )
% 7.94/5.76 => ? [Y6: nat] :
% 7.94/5.76 ( X2
% 7.94/5.76 = ( F @ Y6 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % ex_map_conv
% 7.94/5.76 thf(fact_8720_ex__map__conv,axiom,
% 7.94/5.76 ! [Ys: list_nat,F: vEBT_VEBT > nat] :
% 7.94/5.76 ( ( ? [Xs: list_VEBT_VEBT] :
% 7.94/5.76 ( Ys
% 7.94/5.76 = ( map_VEBT_VEBT_nat @ F @ Xs ) ) )
% 7.94/5.76 = ( ! [X2: nat] :
% 7.94/5.76 ( ( member_nat @ X2 @ ( set_nat2 @ Ys ) )
% 7.94/5.76 => ? [Y6: vEBT_VEBT] :
% 7.94/5.76 ( X2
% 7.94/5.76 = ( F @ Y6 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % ex_map_conv
% 7.94/5.76 thf(fact_8721_ex__map__conv,axiom,
% 7.94/5.76 ! [Ys: list_nat,F: nat > nat] :
% 7.94/5.76 ( ( ? [Xs: list_nat] :
% 7.94/5.76 ( Ys
% 7.94/5.76 = ( map_nat_nat @ F @ Xs ) ) )
% 7.94/5.76 = ( ! [X2: nat] :
% 7.94/5.76 ( ( member_nat @ X2 @ ( set_nat2 @ Ys ) )
% 7.94/5.76 => ? [Y6: nat] :
% 7.94/5.76 ( X2
% 7.94/5.76 = ( F @ Y6 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % ex_map_conv
% 7.94/5.76 thf(fact_8722_ex__map__conv,axiom,
% 7.94/5.76 ! [Ys: list_real,F: vEBT_VEBT > real] :
% 7.94/5.76 ( ( ? [Xs: list_VEBT_VEBT] :
% 7.94/5.76 ( Ys
% 7.94/5.76 = ( map_VEBT_VEBT_real @ F @ Xs ) ) )
% 7.94/5.76 = ( ! [X2: real] :
% 7.94/5.76 ( ( member_real @ X2 @ ( set_real2 @ Ys ) )
% 7.94/5.76 => ? [Y6: vEBT_VEBT] :
% 7.94/5.76 ( X2
% 7.94/5.76 = ( F @ Y6 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % ex_map_conv
% 7.94/5.76 thf(fact_8723_map__replicate__const,axiom,
% 7.94/5.76 ! [K: nat,Lst: list_VEBT_VEBT] :
% 7.94/5.76 ( ( map_VEBT_VEBT_nat
% 7.94/5.76 @ ^ [X2: vEBT_VEBT] : K
% 7.94/5.76 @ Lst )
% 7.94/5.76 = ( replicate_nat @ ( size_s6755466524823107622T_VEBT @ Lst ) @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate_const
% 7.94/5.76 thf(fact_8724_map__replicate__const,axiom,
% 7.94/5.76 ! [K: real,Lst: list_VEBT_VEBT] :
% 7.94/5.76 ( ( map_VEBT_VEBT_real
% 7.94/5.76 @ ^ [X2: vEBT_VEBT] : K
% 7.94/5.76 @ Lst )
% 7.94/5.76 = ( replicate_real @ ( size_s6755466524823107622T_VEBT @ Lst ) @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate_const
% 7.94/5.76 thf(fact_8725_map__replicate__const,axiom,
% 7.94/5.76 ! [K: vEBT_VEBT,Lst: list_real] :
% 7.94/5.76 ( ( map_real_VEBT_VEBT
% 7.94/5.76 @ ^ [X2: real] : K
% 7.94/5.76 @ Lst )
% 7.94/5.76 = ( replicate_VEBT_VEBT @ ( size_size_list_real @ Lst ) @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate_const
% 7.94/5.76 thf(fact_8726_map__replicate__const,axiom,
% 7.94/5.76 ! [K: vEBT_VEBT,Lst: list_o] :
% 7.94/5.76 ( ( map_o_VEBT_VEBT
% 7.94/5.76 @ ^ [X2: $o] : K
% 7.94/5.76 @ Lst )
% 7.94/5.76 = ( replicate_VEBT_VEBT @ ( size_size_list_o @ Lst ) @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate_const
% 7.94/5.76 thf(fact_8727_map__replicate__const,axiom,
% 7.94/5.76 ! [K: nat,Lst: list_nat] :
% 7.94/5.76 ( ( map_nat_nat
% 7.94/5.76 @ ^ [X2: nat] : K
% 7.94/5.76 @ Lst )
% 7.94/5.76 = ( replicate_nat @ ( size_size_list_nat @ Lst ) @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate_const
% 7.94/5.76 thf(fact_8728_map__replicate__const,axiom,
% 7.94/5.76 ! [K: $o,Lst: list_nat] :
% 7.94/5.76 ( ( map_nat_o
% 7.94/5.76 @ ^ [X2: nat] : K
% 7.94/5.76 @ Lst )
% 7.94/5.76 = ( replicate_o @ ( size_size_list_nat @ Lst ) @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate_const
% 7.94/5.76 thf(fact_8729_map__replicate__const,axiom,
% 7.94/5.76 ! [K: vEBT_VEBT,Lst: list_nat] :
% 7.94/5.76 ( ( map_nat_VEBT_VEBT
% 7.94/5.76 @ ^ [X2: nat] : K
% 7.94/5.76 @ Lst )
% 7.94/5.76 = ( replicate_VEBT_VEBT @ ( size_size_list_nat @ Lst ) @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate_const
% 7.94/5.76 thf(fact_8730_map__replicate__const,axiom,
% 7.94/5.76 ! [K: vEBT_VEBT,Lst: list_int] :
% 7.94/5.76 ( ( map_int_VEBT_VEBT
% 7.94/5.76 @ ^ [X2: int] : K
% 7.94/5.76 @ Lst )
% 7.94/5.76 = ( replicate_VEBT_VEBT @ ( size_size_list_int @ Lst ) @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_replicate_const
% 7.94/5.76 thf(fact_8731_map__upd__eq,axiom,
% 7.94/5.76 ! [I: nat,L: list_VEBT_VEBT,F: vEBT_VEBT > nat,X: vEBT_VEBT] :
% 7.94/5.76 ( ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 7.94/5.76 => ( ( F @ ( nth_VEBT_VEBT @ L @ I ) )
% 7.94/5.76 = ( F @ X ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_nat @ F @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) )
% 7.94/5.76 = ( map_VEBT_VEBT_nat @ F @ L ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_upd_eq
% 7.94/5.76 thf(fact_8732_map__upd__eq,axiom,
% 7.94/5.76 ! [I: nat,L: list_VEBT_VEBT,F: vEBT_VEBT > real,X: vEBT_VEBT] :
% 7.94/5.76 ( ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 7.94/5.76 => ( ( F @ ( nth_VEBT_VEBT @ L @ I ) )
% 7.94/5.76 = ( F @ X ) ) )
% 7.94/5.76 => ( ( map_VEBT_VEBT_real @ F @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) )
% 7.94/5.76 = ( map_VEBT_VEBT_real @ F @ L ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_upd_eq
% 7.94/5.76 thf(fact_8733_map__upd__eq,axiom,
% 7.94/5.76 ! [I: nat,L: list_nat,F: nat > nat,X: nat] :
% 7.94/5.76 ( ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 7.94/5.76 => ( ( F @ ( nth_nat @ L @ I ) )
% 7.94/5.76 = ( F @ X ) ) )
% 7.94/5.76 => ( ( map_nat_nat @ F @ ( list_update_nat @ L @ I @ X ) )
% 7.94/5.76 = ( map_nat_nat @ F @ L ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_upd_eq
% 7.94/5.76 thf(fact_8734_map__upd__eq,axiom,
% 7.94/5.76 ! [I: nat,L: list_nat,F: nat > $o,X: nat] :
% 7.94/5.76 ( ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 7.94/5.76 => ( ( F @ ( nth_nat @ L @ I ) )
% 7.94/5.76 = ( F @ X ) ) )
% 7.94/5.76 => ( ( map_nat_o @ F @ ( list_update_nat @ L @ I @ X ) )
% 7.94/5.76 = ( map_nat_o @ F @ L ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % map_upd_eq
% 7.94/5.76 thf(fact_8735_VEBT__internal_Ocnt_H_Osimps_I2_J,axiom,
% 7.94/5.76 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.94/5.76 ( ( vEBT_VEBT_cnt2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 7.94/5.76 = ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_cnt2 @ Summary ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_cnt2 @ TreeList ) @ zero_zero_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBT_internal.cnt'.simps(2)
% 7.94/5.76 thf(fact_8736_VEBT__internal_Ocnt_Osimps_I2_J,axiom,
% 7.94/5.76 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.94/5.76 ( ( vEBT_VEBT_cnt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 7.94/5.76 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList ) @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBT_internal.cnt.simps(2)
% 7.94/5.76 thf(fact_8737_VEBT__internal_Ocnt_H_Oelims,axiom,
% 7.94/5.76 ! [X: vEBT_VEBT,Y: nat] :
% 7.94/5.76 ( ( ( vEBT_VEBT_cnt2 @ X )
% 7.94/5.76 = Y )
% 7.94/5.76 => ( ( ? [A5: $o,B2: $o] :
% 7.94/5.76 ( X
% 7.94/5.76 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.76 => ( Y != one_one_nat ) )
% 7.94/5.76 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.94/5.76 ( ( X
% 7.94/5.76 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.94/5.76 => ( Y
% 7.94/5.76 != ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_cnt2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_cnt2 @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBT_internal.cnt'.elims
% 7.94/5.76 thf(fact_8738_VEBT__internal_Ocnt_Oelims,axiom,
% 7.94/5.76 ! [X: vEBT_VEBT,Y: real] :
% 7.94/5.76 ( ( ( vEBT_VEBT_cnt @ X )
% 7.94/5.76 = Y )
% 7.94/5.76 => ( ( ? [A5: $o,B2: $o] :
% 7.94/5.76 ( X
% 7.94/5.76 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.76 => ( Y != one_one_real ) )
% 7.94/5.76 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.94/5.76 ( ( X
% 7.94/5.76 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.94/5.76 => ( Y
% 7.94/5.76 != ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary2 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBT_internal.cnt.elims
% 7.94/5.76 thf(fact_8739_VEBT__internal_Ospace_H_Osimps_I2_J,axiom,
% 7.94/5.76 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.94/5.76 ( ( vEBT_VEBT_space2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 7.94/5.76 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList ) @ zero_zero_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBT_internal.space'.simps(2)
% 7.94/5.76 thf(fact_8740_VEBT__internal_Ospace_H_Oelims,axiom,
% 7.94/5.76 ! [X: vEBT_VEBT,Y: nat] :
% 7.94/5.76 ( ( ( vEBT_VEBT_space2 @ X )
% 7.94/5.76 = Y )
% 7.94/5.76 => ( ( ? [A5: $o,B2: $o] :
% 7.94/5.76 ( X
% 7.94/5.76 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.76 => ( Y
% 7.94/5.76 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.94/5.76 ( ( X
% 7.94/5.76 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.94/5.76 => ( Y
% 7.94/5.76 != ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBT_internal.space'.elims
% 7.94/5.76 thf(fact_8741_VEBT__internal_Ospace_Osimps_I2_J,axiom,
% 7.94/5.76 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 7.94/5.76 ( ( vEBT_VEBT_space @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 7.94/5.76 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList ) @ zero_zero_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBT_internal.space.simps(2)
% 7.94/5.76 thf(fact_8742_VEBT__internal_Ospace_Oelims,axiom,
% 7.94/5.76 ! [X: vEBT_VEBT,Y: nat] :
% 7.94/5.76 ( ( ( vEBT_VEBT_space @ X )
% 7.94/5.76 = Y )
% 7.94/5.76 => ( ( ? [A5: $o,B2: $o] :
% 7.94/5.76 ( X
% 7.94/5.76 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.76 => ( Y
% 7.94/5.76 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 7.94/5.76 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.94/5.76 ( ( X
% 7.94/5.76 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.94/5.76 => ( Y
% 7.94/5.76 != ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary2 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBT_internal.space.elims
% 7.94/5.76 thf(fact_8743_arctan__series,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 => ( ( arctan @ X )
% 7.94/5.76 = ( suminf_real
% 7.94/5.76 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_series
% 7.94/5.76 thf(fact_8744_suminf__geometric,axiom,
% 7.94/5.76 ! [C: real] :
% 7.94/5.76 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 7.94/5.76 => ( ( suminf_real @ ( power_power_real @ C ) )
% 7.94/5.76 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % suminf_geometric
% 7.94/5.76 thf(fact_8745_suminf__geometric,axiom,
% 7.94/5.76 ! [C: complex] :
% 7.94/5.76 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 7.94/5.76 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 7.94/5.76 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % suminf_geometric
% 7.94/5.76 thf(fact_8746_suminf__zero,axiom,
% 7.94/5.76 ( ( suminf_complex
% 7.94/5.76 @ ^ [N3: nat] : zero_zero_complex )
% 7.94/5.76 = zero_zero_complex ) ).
% 7.94/5.76
% 7.94/5.76 % suminf_zero
% 7.94/5.76 thf(fact_8747_suminf__zero,axiom,
% 7.94/5.76 ( ( suminf_real
% 7.94/5.76 @ ^ [N3: nat] : zero_zero_real )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % suminf_zero
% 7.94/5.76 thf(fact_8748_suminf__zero,axiom,
% 7.94/5.76 ( ( suminf_nat
% 7.94/5.76 @ ^ [N3: nat] : zero_zero_nat )
% 7.94/5.76 = zero_zero_nat ) ).
% 7.94/5.76
% 7.94/5.76 % suminf_zero
% 7.94/5.76 thf(fact_8749_suminf__zero,axiom,
% 7.94/5.76 ( ( suminf_int
% 7.94/5.76 @ ^ [N3: nat] : zero_zero_int )
% 7.94/5.76 = zero_zero_int ) ).
% 7.94/5.76
% 7.94/5.76 % suminf_zero
% 7.94/5.76 thf(fact_8750_pi__series,axiom,
% 7.94/5.76 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = ( suminf_real
% 7.94/5.76 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % pi_series
% 7.94/5.76 thf(fact_8751_big__assn__simp,axiom,
% 7.94/5.76 ! [H2: nat,TreeList: list_VEBT_VEBT,L: nat,X: vEBT_VEBTi,Xaa: option_nat,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ H2 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( entails
% 7.94/5.76 @ ( times_times_assn
% 7.94/5.76 @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) @ X )
% 7.94/5.76 @ ( pure_assn
% 7.94/5.76 @ ( Xaa
% 7.94/5.76 = ( vEBT_vebt_mint @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) ) ) )
% 7.94/5.76 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ H2 @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) )
% 7.94/5.76 @ ( times_times_assn
% 7.94/5.76 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) )
% 7.94/5.76 @ ( pure_assn
% 7.94/5.76 @ ( Xaa
% 7.94/5.76 = ( vEBT_vebt_mint @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) ) ) )
% 7.94/5.76 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % big_assn_simp
% 7.94/5.76 thf(fact_8752_atLeastLessThan__iff,axiom,
% 7.94/5.76 ! [I: real,L: real,U: real] :
% 7.94/5.76 ( ( member_real @ I @ ( set_or66887138388493659n_real @ L @ U ) )
% 7.94/5.76 = ( ( ord_less_eq_real @ L @ I )
% 7.94/5.76 & ( ord_less_real @ I @ U ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_iff
% 7.94/5.76 thf(fact_8753_atLeastLessThan__iff,axiom,
% 7.94/5.76 ! [I: set_nat,L: set_nat,U: set_nat] :
% 7.94/5.76 ( ( member_set_nat @ I @ ( set_or3540276404033026485et_nat @ L @ U ) )
% 7.94/5.76 = ( ( ord_less_eq_set_nat @ L @ I )
% 7.94/5.76 & ( ord_less_set_nat @ I @ U ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_iff
% 7.94/5.76 thf(fact_8754_atLeastLessThan__iff,axiom,
% 7.94/5.76 ! [I: rat,L: rat,U: rat] :
% 7.94/5.76 ( ( member_rat @ I @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 7.94/5.76 = ( ( ord_less_eq_rat @ L @ I )
% 7.94/5.76 & ( ord_less_rat @ I @ U ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_iff
% 7.94/5.76 thf(fact_8755_atLeastLessThan__iff,axiom,
% 7.94/5.76 ! [I: num,L: num,U: num] :
% 7.94/5.76 ( ( member_num @ I @ ( set_or1222409239386451017an_num @ L @ U ) )
% 7.94/5.76 = ( ( ord_less_eq_num @ L @ I )
% 7.94/5.76 & ( ord_less_num @ I @ U ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_iff
% 7.94/5.76 thf(fact_8756_atLeastLessThan__iff,axiom,
% 7.94/5.76 ! [I: nat,L: nat,U: nat] :
% 7.94/5.76 ( ( member_nat @ I @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 7.94/5.76 = ( ( ord_less_eq_nat @ L @ I )
% 7.94/5.76 & ( ord_less_nat @ I @ U ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_iff
% 7.94/5.76 thf(fact_8757_atLeastLessThan__iff,axiom,
% 7.94/5.76 ! [I: code_integer,L: code_integer,U: code_integer] :
% 7.94/5.76 ( ( member_Code_integer @ I @ ( set_or8404916559141939852nteger @ L @ U ) )
% 7.94/5.76 = ( ( ord_le3102999989581377725nteger @ L @ I )
% 7.94/5.76 & ( ord_le6747313008572928689nteger @ I @ U ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_iff
% 7.94/5.76 thf(fact_8758_atLeastLessThan__iff,axiom,
% 7.94/5.76 ! [I: int,L: int,U: int] :
% 7.94/5.76 ( ( member_int @ I @ ( set_or4662586982721622107an_int @ L @ U ) )
% 7.94/5.76 = ( ( ord_less_eq_int @ L @ I )
% 7.94/5.76 & ( ord_less_int @ I @ U ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_iff
% 7.94/5.76 thf(fact_8759_atLeastLessThan__empty__iff2,axiom,
% 7.94/5.76 ! [A: real,B: real] :
% 7.94/5.76 ( ( bot_bot_set_real
% 7.94/5.76 = ( set_or66887138388493659n_real @ A @ B ) )
% 7.94/5.76 = ( ~ ( ord_less_real @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff2
% 7.94/5.76 thf(fact_8760_atLeastLessThan__empty__iff2,axiom,
% 7.94/5.76 ! [A: rat,B: rat] :
% 7.94/5.76 ( ( bot_bot_set_rat
% 7.94/5.76 = ( set_or4029947393144176647an_rat @ A @ B ) )
% 7.94/5.76 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff2
% 7.94/5.76 thf(fact_8761_atLeastLessThan__empty__iff2,axiom,
% 7.94/5.76 ! [A: num,B: num] :
% 7.94/5.76 ( ( bot_bot_set_num
% 7.94/5.76 = ( set_or1222409239386451017an_num @ A @ B ) )
% 7.94/5.76 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff2
% 7.94/5.76 thf(fact_8762_atLeastLessThan__empty__iff2,axiom,
% 7.94/5.76 ! [A: nat,B: nat] :
% 7.94/5.76 ( ( bot_bot_set_nat
% 7.94/5.76 = ( set_or4665077453230672383an_nat @ A @ B ) )
% 7.94/5.76 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff2
% 7.94/5.76 thf(fact_8763_atLeastLessThan__empty__iff2,axiom,
% 7.94/5.76 ! [A: code_integer,B: code_integer] :
% 7.94/5.76 ( ( bot_bo3990330152332043303nteger
% 7.94/5.76 = ( set_or8404916559141939852nteger @ A @ B ) )
% 7.94/5.76 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff2
% 7.94/5.76 thf(fact_8764_atLeastLessThan__empty__iff2,axiom,
% 7.94/5.76 ! [A: int,B: int] :
% 7.94/5.76 ( ( bot_bot_set_int
% 7.94/5.76 = ( set_or4662586982721622107an_int @ A @ B ) )
% 7.94/5.76 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff2
% 7.94/5.76 thf(fact_8765_atLeastLessThan__empty__iff,axiom,
% 7.94/5.76 ! [A: real,B: real] :
% 7.94/5.76 ( ( ( set_or66887138388493659n_real @ A @ B )
% 7.94/5.76 = bot_bot_set_real )
% 7.94/5.76 = ( ~ ( ord_less_real @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff
% 7.94/5.76 thf(fact_8766_atLeastLessThan__empty__iff,axiom,
% 7.94/5.76 ! [A: rat,B: rat] :
% 7.94/5.76 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 7.94/5.76 = bot_bot_set_rat )
% 7.94/5.76 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff
% 7.94/5.76 thf(fact_8767_atLeastLessThan__empty__iff,axiom,
% 7.94/5.76 ! [A: num,B: num] :
% 7.94/5.76 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 7.94/5.76 = bot_bot_set_num )
% 7.94/5.76 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff
% 7.94/5.76 thf(fact_8768_atLeastLessThan__empty__iff,axiom,
% 7.94/5.76 ! [A: nat,B: nat] :
% 7.94/5.76 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 7.94/5.76 = bot_bot_set_nat )
% 7.94/5.76 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff
% 7.94/5.76 thf(fact_8769_atLeastLessThan__empty__iff,axiom,
% 7.94/5.76 ! [A: code_integer,B: code_integer] :
% 7.94/5.76 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 7.94/5.76 = bot_bo3990330152332043303nteger )
% 7.94/5.76 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff
% 7.94/5.76 thf(fact_8770_atLeastLessThan__empty__iff,axiom,
% 7.94/5.76 ! [A: int,B: int] :
% 7.94/5.76 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 7.94/5.76 = bot_bot_set_int )
% 7.94/5.76 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_empty_iff
% 7.94/5.76 thf(fact_8771_infinite__Ico__iff,axiom,
% 7.94/5.76 ! [A: real,B: real] :
% 7.94/5.76 ( ( ~ ( finite_finite_real @ ( set_or66887138388493659n_real @ A @ B ) ) )
% 7.94/5.76 = ( ord_less_real @ A @ B ) ) ).
% 7.94/5.76
% 7.94/5.76 % infinite_Ico_iff
% 7.94/5.76 thf(fact_8772_infinite__Ico__iff,axiom,
% 7.94/5.76 ! [A: rat,B: rat] :
% 7.94/5.76 ( ( ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) )
% 7.94/5.76 = ( ord_less_rat @ A @ B ) ) ).
% 7.94/5.76
% 7.94/5.76 % infinite_Ico_iff
% 7.94/5.76 thf(fact_8773_local_Oext,axiom,
% 7.94/5.76 ! [Y: nat,TreeList: list_VEBT_VEBT,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ Y @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( entails @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % local.ext
% 7.94/5.76 thf(fact_8774_recomp,axiom,
% 7.94/5.76 ! [I: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ I ) @ ( nth_VEBT_VEBTi @ Tree_is @ I ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % recomp
% 7.94/5.76 thf(fact_8775_repack,axiom,
% 7.94/5.76 ! [I: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,Rest: assn,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ I ) @ ( nth_VEBT_VEBTi @ Tree_is @ I ) ) @ Rest ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ Rest @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % repack
% 7.94/5.76 thf(fact_8776_txe,axiom,
% 7.94/5.76 ! [Y: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ Y @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y ) ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % txe
% 7.94/5.76 thf(fact_8777_atLeastLessThan__singleton,axiom,
% 7.94/5.76 ! [M: nat] :
% 7.94/5.76 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 7.94/5.76 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_singleton
% 7.94/5.76 thf(fact_8778_tcd,axiom,
% 7.94/5.76 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList4: list_real,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 7.94/5.76 = ( size_size_list_real @ TreeList4 ) )
% 7.94/5.76 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tcd
% 7.94/5.76 thf(fact_8779_tcd,axiom,
% 7.94/5.76 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList4: list_o,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 7.94/5.76 = ( size_size_list_o @ TreeList4 ) )
% 7.94/5.76 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tcd
% 7.94/5.76 thf(fact_8780_tcd,axiom,
% 7.94/5.76 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList4: list_nat,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 7.94/5.76 = ( size_size_list_nat @ TreeList4 ) )
% 7.94/5.76 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tcd
% 7.94/5.76 thf(fact_8781_tcd,axiom,
% 7.94/5.76 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList4: list_int,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 7.94/5.76 = ( size_size_list_int @ TreeList4 ) )
% 7.94/5.76 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tcd
% 7.94/5.76 thf(fact_8782_big__assn__simp_H,axiom,
% 7.94/5.76 ! [H2: nat,TreeList: list_VEBT_VEBT,Xaa: vEBT_VEBT,L: nat,X: vEBT_VEBTi,Xb3: option_nat,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( ord_less_nat @ H2 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 7.94/5.76 => ( ( Xaa
% 7.94/5.76 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 7.94/5.76 => ( entails
% 7.94/5.76 @ ( times_times_assn
% 7.94/5.76 @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Xaa @ X )
% 7.94/5.76 @ ( pure_assn
% 7.94/5.76 @ ( Xb3
% 7.94/5.76 = ( vEBT_vebt_mint @ Xaa ) ) ) )
% 7.94/5.76 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ H2 @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) )
% 7.94/5.76 @ ( times_times_assn
% 7.94/5.76 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) )
% 7.94/5.76 @ ( pure_assn
% 7.94/5.76 @ ( Xb3
% 7.94/5.76 = ( vEBT_vebt_mint @ Xaa ) ) ) )
% 7.94/5.76 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Xaa ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % big_assn_simp'
% 7.94/5.76 thf(fact_8783_prod_Oop__ivl__Suc,axiom,
% 7.94/5.76 ! [N: nat,M: nat,G: nat > rat] :
% 7.94/5.76 ( ( ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = one_one_rat ) )
% 7.94/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.op_ivl_Suc
% 7.94/5.76 thf(fact_8784_prod_Oop__ivl__Suc,axiom,
% 7.94/5.76 ! [N: nat,M: nat,G: nat > assn] :
% 7.94/5.76 ( ( ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = one_one_assn ) )
% 7.94/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.op_ivl_Suc
% 7.94/5.76 thf(fact_8785_prod_Oop__ivl__Suc,axiom,
% 7.94/5.76 ! [N: nat,M: nat,G: nat > real] :
% 7.94/5.76 ( ( ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = one_one_real ) )
% 7.94/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.op_ivl_Suc
% 7.94/5.76 thf(fact_8786_prod_Oop__ivl__Suc,axiom,
% 7.94/5.76 ! [N: nat,M: nat,G: nat > code_integer] :
% 7.94/5.76 ( ( ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = one_one_Code_integer ) )
% 7.94/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.op_ivl_Suc
% 7.94/5.76 thf(fact_8787_prod_Oop__ivl__Suc,axiom,
% 7.94/5.76 ! [N: nat,M: nat,G: nat > complex] :
% 7.94/5.76 ( ( ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups6464643781859351333omplex @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = one_one_complex ) )
% 7.94/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups6464643781859351333omplex @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.op_ivl_Suc
% 7.94/5.76 thf(fact_8788_prod_Oop__ivl__Suc,axiom,
% 7.94/5.76 ! [N: nat,M: nat,G: nat > nat] :
% 7.94/5.76 ( ( ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = one_one_nat ) )
% 7.94/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.op_ivl_Suc
% 7.94/5.76 thf(fact_8789_prod_Oop__ivl__Suc,axiom,
% 7.94/5.76 ! [N: nat,M: nat,G: nat > int] :
% 7.94/5.76 ( ( ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = one_one_int ) )
% 7.94/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 7.94/5.76 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 7.94/5.76 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.op_ivl_Suc
% 7.94/5.76 thf(fact_8790_atLeastLessThan__eq__iff,axiom,
% 7.94/5.76 ! [A: real,B: real,C: real,D2: real] :
% 7.94/5.76 ( ( ord_less_real @ A @ B )
% 7.94/5.76 => ( ( ord_less_real @ C @ D2 )
% 7.94/5.76 => ( ( ( set_or66887138388493659n_real @ A @ B )
% 7.94/5.76 = ( set_or66887138388493659n_real @ C @ D2 ) )
% 7.94/5.76 = ( ( A = C )
% 7.94/5.76 & ( B = D2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_eq_iff
% 7.94/5.76 thf(fact_8791_atLeastLessThan__eq__iff,axiom,
% 7.94/5.76 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.94/5.76 ( ( ord_less_rat @ A @ B )
% 7.94/5.76 => ( ( ord_less_rat @ C @ D2 )
% 7.94/5.76 => ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 7.94/5.76 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 7.94/5.76 = ( ( A = C )
% 7.94/5.76 & ( B = D2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_eq_iff
% 7.94/5.76 thf(fact_8792_atLeastLessThan__eq__iff,axiom,
% 7.94/5.76 ! [A: num,B: num,C: num,D2: num] :
% 7.94/5.76 ( ( ord_less_num @ A @ B )
% 7.94/5.76 => ( ( ord_less_num @ C @ D2 )
% 7.94/5.76 => ( ( ( set_or1222409239386451017an_num @ A @ B )
% 7.94/5.76 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 7.94/5.76 = ( ( A = C )
% 7.94/5.76 & ( B = D2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_eq_iff
% 7.94/5.76 thf(fact_8793_atLeastLessThan__eq__iff,axiom,
% 7.94/5.76 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.94/5.76 ( ( ord_less_nat @ A @ B )
% 7.94/5.76 => ( ( ord_less_nat @ C @ D2 )
% 7.94/5.76 => ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 7.94/5.76 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 7.94/5.76 = ( ( A = C )
% 7.94/5.76 & ( B = D2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_eq_iff
% 7.94/5.76 thf(fact_8794_atLeastLessThan__eq__iff,axiom,
% 7.94/5.76 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.94/5.76 ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.94/5.76 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 7.94/5.76 => ( ( ( set_or8404916559141939852nteger @ A @ B )
% 7.94/5.76 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 7.94/5.76 = ( ( A = C )
% 7.94/5.76 & ( B = D2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_eq_iff
% 7.94/5.76 thf(fact_8795_atLeastLessThan__eq__iff,axiom,
% 7.94/5.76 ! [A: int,B: int,C: int,D2: int] :
% 7.94/5.76 ( ( ord_less_int @ A @ B )
% 7.94/5.76 => ( ( ord_less_int @ C @ D2 )
% 7.94/5.76 => ( ( ( set_or4662586982721622107an_int @ A @ B )
% 7.94/5.76 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 7.94/5.76 = ( ( A = C )
% 7.94/5.76 & ( B = D2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_eq_iff
% 7.94/5.76 thf(fact_8796_atLeastLessThan__inj_I1_J,axiom,
% 7.94/5.76 ! [A: real,B: real,C: real,D2: real] :
% 7.94/5.76 ( ( ( set_or66887138388493659n_real @ A @ B )
% 7.94/5.76 = ( set_or66887138388493659n_real @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_real @ A @ B )
% 7.94/5.76 => ( ( ord_less_real @ C @ D2 )
% 7.94/5.76 => ( A = C ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(1)
% 7.94/5.76 thf(fact_8797_atLeastLessThan__inj_I1_J,axiom,
% 7.94/5.76 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.94/5.76 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 7.94/5.76 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_rat @ A @ B )
% 7.94/5.76 => ( ( ord_less_rat @ C @ D2 )
% 7.94/5.76 => ( A = C ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(1)
% 7.94/5.76 thf(fact_8798_atLeastLessThan__inj_I1_J,axiom,
% 7.94/5.76 ! [A: num,B: num,C: num,D2: num] :
% 7.94/5.76 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 7.94/5.76 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_num @ A @ B )
% 7.94/5.76 => ( ( ord_less_num @ C @ D2 )
% 7.94/5.76 => ( A = C ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(1)
% 7.94/5.76 thf(fact_8799_atLeastLessThan__inj_I1_J,axiom,
% 7.94/5.76 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.94/5.76 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 7.94/5.76 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_nat @ A @ B )
% 7.94/5.76 => ( ( ord_less_nat @ C @ D2 )
% 7.94/5.76 => ( A = C ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(1)
% 7.94/5.76 thf(fact_8800_atLeastLessThan__inj_I1_J,axiom,
% 7.94/5.76 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.94/5.76 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 7.94/5.76 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.94/5.76 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 7.94/5.76 => ( A = C ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(1)
% 7.94/5.76 thf(fact_8801_atLeastLessThan__inj_I1_J,axiom,
% 7.94/5.76 ! [A: int,B: int,C: int,D2: int] :
% 7.94/5.76 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 7.94/5.76 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_int @ A @ B )
% 7.94/5.76 => ( ( ord_less_int @ C @ D2 )
% 7.94/5.76 => ( A = C ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(1)
% 7.94/5.76 thf(fact_8802_atLeastLessThan__inj_I2_J,axiom,
% 7.94/5.76 ! [A: real,B: real,C: real,D2: real] :
% 7.94/5.76 ( ( ( set_or66887138388493659n_real @ A @ B )
% 7.94/5.76 = ( set_or66887138388493659n_real @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_real @ A @ B )
% 7.94/5.76 => ( ( ord_less_real @ C @ D2 )
% 7.94/5.76 => ( B = D2 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(2)
% 7.94/5.76 thf(fact_8803_atLeastLessThan__inj_I2_J,axiom,
% 7.94/5.76 ! [A: rat,B: rat,C: rat,D2: rat] :
% 7.94/5.76 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 7.94/5.76 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_rat @ A @ B )
% 7.94/5.76 => ( ( ord_less_rat @ C @ D2 )
% 7.94/5.76 => ( B = D2 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(2)
% 7.94/5.76 thf(fact_8804_atLeastLessThan__inj_I2_J,axiom,
% 7.94/5.76 ! [A: num,B: num,C: num,D2: num] :
% 7.94/5.76 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 7.94/5.76 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_num @ A @ B )
% 7.94/5.76 => ( ( ord_less_num @ C @ D2 )
% 7.94/5.76 => ( B = D2 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(2)
% 7.94/5.76 thf(fact_8805_atLeastLessThan__inj_I2_J,axiom,
% 7.94/5.76 ! [A: nat,B: nat,C: nat,D2: nat] :
% 7.94/5.76 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 7.94/5.76 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_nat @ A @ B )
% 7.94/5.76 => ( ( ord_less_nat @ C @ D2 )
% 7.94/5.76 => ( B = D2 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(2)
% 7.94/5.76 thf(fact_8806_atLeastLessThan__inj_I2_J,axiom,
% 7.94/5.76 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 7.94/5.76 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 7.94/5.76 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 7.94/5.76 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 7.94/5.76 => ( B = D2 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(2)
% 7.94/5.76 thf(fact_8807_atLeastLessThan__inj_I2_J,axiom,
% 7.94/5.76 ! [A: int,B: int,C: int,D2: int] :
% 7.94/5.76 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 7.94/5.76 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 7.94/5.76 => ( ( ord_less_int @ A @ B )
% 7.94/5.76 => ( ( ord_less_int @ C @ D2 )
% 7.94/5.76 => ( B = D2 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_inj(2)
% 7.94/5.76 thf(fact_8808_pi__neq__zero,axiom,
% 7.94/5.76 pi != zero_zero_real ).
% 7.94/5.76
% 7.94/5.76 % pi_neq_zero
% 7.94/5.76 thf(fact_8809_listI__assn__conv,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBT,A2: vEBT_VEBT > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 7.94/5.76 ( ( N
% 7.94/5.76 = ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.94/5.76 => ( ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) @ A2 @ Xs2 @ Xsi )
% 7.94/5.76 = ( vEBT_L6296928887356842470_VEBTi @ A2 @ Xs2 @ Xsi ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % listI_assn_conv
% 7.94/5.76 thf(fact_8810_list__assn__conv__idx,axiom,
% 7.94/5.76 ( vEBT_L6296928887356842470_VEBTi
% 7.94/5.76 = ( ^ [A6: vEBT_VEBT > vEBT_VEBTi > assn,Xs: list_VEBT_VEBT] : ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ A6 @ Xs ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % list_assn_conv_idx
% 7.94/5.76 thf(fact_8811_infinite__Ico,axiom,
% 7.94/5.76 ! [A: real,B: real] :
% 7.94/5.76 ( ( ord_less_real @ A @ B )
% 7.94/5.76 => ~ ( finite_finite_real @ ( set_or66887138388493659n_real @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % infinite_Ico
% 7.94/5.76 thf(fact_8812_infinite__Ico,axiom,
% 7.94/5.76 ! [A: rat,B: rat] :
% 7.94/5.76 ( ( ord_less_rat @ A @ B )
% 7.94/5.76 => ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % infinite_Ico
% 7.94/5.76 thf(fact_8813_all__nat__less__eq,axiom,
% 7.94/5.76 ! [N: nat,P: nat > $o] :
% 7.94/5.76 ( ( ! [M4: nat] :
% 7.94/5.76 ( ( ord_less_nat @ M4 @ N )
% 7.94/5.76 => ( P @ M4 ) ) )
% 7.94/5.76 = ( ! [X2: nat] :
% 7.94/5.76 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 7.94/5.76 => ( P @ X2 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % all_nat_less_eq
% 7.94/5.76 thf(fact_8814_ex__nat__less__eq,axiom,
% 7.94/5.76 ! [N: nat,P: nat > $o] :
% 7.94/5.76 ( ( ? [M4: nat] :
% 7.94/5.76 ( ( ord_less_nat @ M4 @ N )
% 7.94/5.76 & ( P @ M4 ) ) )
% 7.94/5.76 = ( ? [X2: nat] :
% 7.94/5.76 ( ( member_nat @ X2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 7.94/5.76 & ( P @ X2 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % ex_nat_less_eq
% 7.94/5.76 thf(fact_8815_atLeastLessThanSuc__atLeastAtMost,axiom,
% 7.94/5.76 ! [L: nat,U: nat] :
% 7.94/5.76 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 7.94/5.76 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThanSuc_atLeastAtMost
% 7.94/5.76 thf(fact_8816_atLeastLessThan0,axiom,
% 7.94/5.76 ! [M: nat] :
% 7.94/5.76 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 7.94/5.76 = bot_bot_set_nat ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan0
% 7.94/5.76 thf(fact_8817_pi__not__less__zero,axiom,
% 7.94/5.76 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % pi_not_less_zero
% 7.94/5.76 thf(fact_8818_pi__gt__zero,axiom,
% 7.94/5.76 ord_less_real @ zero_zero_real @ pi ).
% 7.94/5.76
% 7.94/5.76 % pi_gt_zero
% 7.94/5.76 thf(fact_8819_pi__ge__zero,axiom,
% 7.94/5.76 ord_less_eq_real @ zero_zero_real @ pi ).
% 7.94/5.76
% 7.94/5.76 % pi_ge_zero
% 7.94/5.76 thf(fact_8820_listI__assn__conv_H,axiom,
% 7.94/5.76 ! [N: nat,Xs2: list_VEBT_VEBT,A2: vEBT_VEBT > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi,F2: assn] :
% 7.94/5.76 ( ( N
% 7.94/5.76 = ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 7.94/5.76 => ( ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) @ A2 @ Xs2 @ Xsi ) @ F2 )
% 7.94/5.76 = ( times_times_assn @ ( vEBT_L6296928887356842470_VEBTi @ A2 @ Xs2 @ Xsi ) @ F2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % listI_assn_conv'
% 7.94/5.76 thf(fact_8821_prod_Oshift__bounds__Suc__ivl,axiom,
% 7.94/5.76 ! [G: nat > nat,M: nat,N: nat] :
% 7.94/5.76 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 7.94/5.76 = ( groups708209901874060359at_nat
% 7.94/5.76 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.94/5.76 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.shift_bounds_Suc_ivl
% 7.94/5.76 thf(fact_8822_prod_Oshift__bounds__Suc__ivl,axiom,
% 7.94/5.76 ! [G: nat > int,M: nat,N: nat] :
% 7.94/5.76 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 7.94/5.76 = ( groups705719431365010083at_int
% 7.94/5.76 @ ^ [I2: nat] : ( G @ ( suc @ I2 ) )
% 7.94/5.76 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.shift_bounds_Suc_ivl
% 7.94/5.76 thf(fact_8823_prod_Oshift__bounds__nat__ivl,axiom,
% 7.94/5.76 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 7.94/5.76 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 7.94/5.76 = ( groups708209901874060359at_nat
% 7.94/5.76 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ I2 @ K ) )
% 7.94/5.76 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.shift_bounds_nat_ivl
% 7.94/5.76 thf(fact_8824_prod_Oshift__bounds__nat__ivl,axiom,
% 7.94/5.76 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 7.94/5.76 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 7.94/5.76 = ( groups705719431365010083at_int
% 7.94/5.76 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ I2 @ K ) )
% 7.94/5.76 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.shift_bounds_nat_ivl
% 7.94/5.76 thf(fact_8825_prod_Oivl__cong,axiom,
% 7.94/5.76 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > nat,H2: nat > nat] :
% 7.94/5.76 ( ( A = C )
% 7.94/5.76 => ( ( B = D2 )
% 7.94/5.76 => ( ! [X3: nat] :
% 7.94/5.76 ( ( ord_less_eq_nat @ C @ X3 )
% 7.94/5.76 => ( ( ord_less_nat @ X3 @ D2 )
% 7.94/5.76 => ( ( G @ X3 )
% 7.94/5.76 = ( H2 @ X3 ) ) ) )
% 7.94/5.76 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 7.94/5.76 = ( groups708209901874060359at_nat @ H2 @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.ivl_cong
% 7.94/5.76 thf(fact_8826_prod_Oivl__cong,axiom,
% 7.94/5.76 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > int,H2: nat > int] :
% 7.94/5.76 ( ( A = C )
% 7.94/5.76 => ( ( B = D2 )
% 7.94/5.76 => ( ! [X3: nat] :
% 7.94/5.76 ( ( ord_less_eq_nat @ C @ X3 )
% 7.94/5.76 => ( ( ord_less_nat @ X3 @ D2 )
% 7.94/5.76 => ( ( G @ X3 )
% 7.94/5.76 = ( H2 @ X3 ) ) ) )
% 7.94/5.76 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 7.94/5.76 = ( groups705719431365010083at_int @ H2 @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.ivl_cong
% 7.94/5.76 thf(fact_8827_prod_Oivl__cong,axiom,
% 7.94/5.76 ! [A: int,C: int,B: int,D2: int,G: int > int,H2: int > int] :
% 7.94/5.76 ( ( A = C )
% 7.94/5.76 => ( ( B = D2 )
% 7.94/5.76 => ( ! [X3: int] :
% 7.94/5.76 ( ( ord_less_eq_int @ C @ X3 )
% 7.94/5.76 => ( ( ord_less_int @ X3 @ D2 )
% 7.94/5.76 => ( ( G @ X3 )
% 7.94/5.76 = ( H2 @ X3 ) ) ) )
% 7.94/5.76 => ( ( groups1705073143266064639nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 7.94/5.76 = ( groups1705073143266064639nt_int @ H2 @ ( set_or4662586982721622107an_int @ C @ D2 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.ivl_cong
% 7.94/5.76 thf(fact_8828_prod_OatLeastLessThan__concat,axiom,
% 7.94/5.76 ! [M: nat,N: nat,P4: nat,G: nat > assn] :
% 7.94/5.76 ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.76 => ( ( ord_less_eq_nat @ N @ P4 )
% 7.94/5.76 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 7.94/5.76 = ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.atLeastLessThan_concat
% 7.94/5.76 thf(fact_8829_prod_OatLeastLessThan__concat,axiom,
% 7.94/5.76 ! [M: nat,N: nat,P4: nat,G: nat > real] :
% 7.94/5.76 ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.76 => ( ( ord_less_eq_nat @ N @ P4 )
% 7.94/5.76 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 7.94/5.76 = ( groups129246275422532515t_real @ G @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.atLeastLessThan_concat
% 7.94/5.76 thf(fact_8830_prod_OatLeastLessThan__concat,axiom,
% 7.94/5.76 ! [M: nat,N: nat,P4: nat,G: nat > code_integer] :
% 7.94/5.76 ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.76 => ( ( ord_less_eq_nat @ N @ P4 )
% 7.94/5.76 => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 7.94/5.76 = ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.atLeastLessThan_concat
% 7.94/5.76 thf(fact_8831_prod_OatLeastLessThan__concat,axiom,
% 7.94/5.76 ! [M: nat,N: nat,P4: nat,G: nat > complex] :
% 7.94/5.76 ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.76 => ( ( ord_less_eq_nat @ N @ P4 )
% 7.94/5.76 => ( ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups6464643781859351333omplex @ G @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 7.94/5.76 = ( groups6464643781859351333omplex @ G @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.atLeastLessThan_concat
% 7.94/5.76 thf(fact_8832_prod_OatLeastLessThan__concat,axiom,
% 7.94/5.76 ! [M: nat,N: nat,P4: nat,G: nat > nat] :
% 7.94/5.76 ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.76 => ( ( ord_less_eq_nat @ N @ P4 )
% 7.94/5.76 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 7.94/5.76 = ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.atLeastLessThan_concat
% 7.94/5.76 thf(fact_8833_prod_OatLeastLessThan__concat,axiom,
% 7.94/5.76 ! [M: nat,N: nat,P4: nat,G: nat > int] :
% 7.94/5.76 ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.76 => ( ( ord_less_eq_nat @ N @ P4 )
% 7.94/5.76 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 7.94/5.76 = ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod.atLeastLessThan_concat
% 7.94/5.76 thf(fact_8834_atLeast0__lessThan__Suc,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 7.94/5.76 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeast0_lessThan_Suc
% 7.94/5.76 thf(fact_8835_subset__eq__atLeast0__lessThan__finite,axiom,
% 7.94/5.76 ! [N4: set_nat,N: nat] :
% 7.94/5.76 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 7.94/5.76 => ( finite_finite_nat @ N4 ) ) ).
% 7.94/5.76
% 7.94/5.76 % subset_eq_atLeast0_lessThan_finite
% 7.94/5.76 thf(fact_8836_pi__less__4,axiom,
% 7.94/5.76 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % pi_less_4
% 7.94/5.76 thf(fact_8837_pi__ge__two,axiom,
% 7.94/5.76 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 7.94/5.76
% 7.94/5.76 % pi_ge_two
% 7.94/5.76 thf(fact_8838_pi__half__neq__two,axiom,
% 7.94/5.76 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % pi_half_neq_two
% 7.94/5.76 thf(fact_8839_atLeastLessThanSuc,axiom,
% 7.94/5.76 ! [M: nat,N: nat] :
% 7.94/5.76 ( ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.76 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 7.94/5.76 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 7.94/5.76 & ( ~ ( ord_less_eq_nat @ M @ N )
% 7.94/5.76 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 7.94/5.76 = bot_bot_set_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThanSuc
% 7.94/5.76 thf(fact_8840_prod__Suc__Suc__fact,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 7.94/5.76 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_Suc_Suc_fact
% 7.94/5.76 thf(fact_8841_prod__Suc__fact,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 7.94/5.76 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % prod_Suc_fact
% 7.94/5.76 thf(fact_8842_pi__half__neq__zero,axiom,
% 7.94/5.76 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 != zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % pi_half_neq_zero
% 7.94/5.76 thf(fact_8843_pi__half__less__two,axiom,
% 7.94/5.76 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 7.94/5.76
% 7.94/5.76 % pi_half_less_two
% 7.94/5.76 thf(fact_8844_pi__half__le__two,axiom,
% 7.94/5.76 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 7.94/5.76
% 7.94/5.76 % pi_half_le_two
% 7.94/5.76 thf(fact_8845_atLeastLessThan__nat__numeral,axiom,
% 7.94/5.76 ! [M: nat,K: num] :
% 7.94/5.76 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 7.94/5.76 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 7.94/5.76 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 7.94/5.76 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 7.94/5.76 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 7.94/5.76 = bot_bot_set_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThan_nat_numeral
% 7.94/5.76 thf(fact_8846_pi__half__gt__zero,axiom,
% 7.94/5.76 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % pi_half_gt_zero
% 7.94/5.76 thf(fact_8847_pi__half__ge__zero,axiom,
% 7.94/5.76 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % pi_half_ge_zero
% 7.94/5.76 thf(fact_8848_m2pi__less__pi,axiom,
% 7.94/5.76 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 7.94/5.76
% 7.94/5.76 % m2pi_less_pi
% 7.94/5.76 thf(fact_8849_arctan__ubound,axiom,
% 7.94/5.76 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_ubound
% 7.94/5.76 thf(fact_8850_arctan__one,axiom,
% 7.94/5.76 ( ( arctan @ one_one_real )
% 7.94/5.76 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_one
% 7.94/5.76 thf(fact_8851_minus__pi__half__less__zero,axiom,
% 7.94/5.76 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 7.94/5.76
% 7.94/5.76 % minus_pi_half_less_zero
% 7.94/5.76 thf(fact_8852_arctan__bounded,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 7.94/5.76 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_bounded
% 7.94/5.76 thf(fact_8853_arctan__lbound,axiom,
% 7.94/5.76 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_lbound
% 7.94/5.76 thf(fact_8854_machin__Euler,axiom,
% 7.94/5.76 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 7.94/5.76 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % machin_Euler
% 7.94/5.76 thf(fact_8855_machin,axiom,
% 7.94/5.76 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % machin
% 7.94/5.76 thf(fact_8856_arctan__inverse,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( X != zero_zero_real )
% 7.94/5.76 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 7.94/5.76 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_inverse
% 7.94/5.76 thf(fact_8857_sin__cos__npi,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_cos_npi
% 7.94/5.76 thf(fact_8858_sin__pi,axiom,
% 7.94/5.76 ( ( sin_real @ pi )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % sin_pi
% 7.94/5.76 thf(fact_8859_sin__npi,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % sin_npi
% 7.94/5.76 thf(fact_8860_sin__npi2,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % sin_npi2
% 7.94/5.76 thf(fact_8861_sin__npi__int,axiom,
% 7.94/5.76 ! [N: int] :
% 7.94/5.76 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % sin_npi_int
% 7.94/5.76 thf(fact_8862_sin__two__pi,axiom,
% 7.94/5.76 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % sin_two_pi
% 7.94/5.76 thf(fact_8863_sin__pi__half,axiom,
% 7.94/5.76 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % sin_pi_half
% 7.94/5.76 thf(fact_8864_sin__periodic,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 7.94/5.76 = ( sin_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_periodic
% 7.94/5.76 thf(fact_8865_sin__2npi,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % sin_2npi
% 7.94/5.76 thf(fact_8866_sin__2pi__minus,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 7.94/5.76 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_2pi_minus
% 7.94/5.76 thf(fact_8867_sin__int__2pin,axiom,
% 7.94/5.76 ! [N: int] :
% 7.94/5.76 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % sin_int_2pin
% 7.94/5.76 thf(fact_8868_sin__3over2__pi,axiom,
% 7.94/5.76 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 7.94/5.76 = ( uminus_uminus_real @ one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_3over2_pi
% 7.94/5.76 thf(fact_8869_finite__atLeastZeroLessThan__integer,axiom,
% 7.94/5.76 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 7.94/5.76
% 7.94/5.76 % finite_atLeastZeroLessThan_integer
% 7.94/5.76 thf(fact_8870_sin__x__le__x,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_x_le_x
% 7.94/5.76 thf(fact_8871_sin__le__one,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % sin_le_one
% 7.94/5.76 thf(fact_8872_finite__atLeastZeroLessThan__int,axiom,
% 7.94/5.76 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 7.94/5.76
% 7.94/5.76 % finite_atLeastZeroLessThan_int
% 7.94/5.76 thf(fact_8873_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 7.94/5.76 ! [L: code_integer,U: code_integer] :
% 7.94/5.76 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 7.94/5.76 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThanPlusOne_atLeastAtMost_integer
% 7.94/5.76 thf(fact_8874_sin__gt__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ pi )
% 7.94/5.76 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_gt_zero
% 7.94/5.76 thf(fact_8875_sin__x__ge__neg__x,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_x_ge_neg_x
% 7.94/5.76 thf(fact_8876_sin__ge__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ pi )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_ge_zero
% 7.94/5.76 thf(fact_8877_sin__ge__minus__one,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_ge_minus_one
% 7.94/5.76 thf(fact_8878_abs__sin__le__one,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % abs_sin_le_one
% 7.94/5.76 thf(fact_8879_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 7.94/5.76 ! [L: int,U: int] :
% 7.94/5.76 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 7.94/5.76 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeastLessThanPlusOne_atLeastAtMost_int
% 7.94/5.76 thf(fact_8880_sin__eq__0__pi,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ pi )
% 7.94/5.76 => ( ( ( sin_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 => ( X = zero_zero_real ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_eq_0_pi
% 7.94/5.76 thf(fact_8881_divmod__int__def,axiom,
% 7.94/5.76 ( unique5052692396658037445od_int
% 7.94/5.76 = ( ^ [M4: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M4 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M4 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divmod_int_def
% 7.94/5.76 thf(fact_8882_sin__zero__pi__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 7.94/5.76 => ( ( ( sin_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 = ( X = zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_zero_pi_iff
% 7.94/5.76 thf(fact_8883_sin__zero__iff__int2,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( sin_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 = ( ? [I2: int] :
% 7.94/5.76 ( X
% 7.94/5.76 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_zero_iff_int2
% 7.94/5.76 thf(fact_8884_sin__gt__zero__02,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_gt_zero_02
% 7.94/5.76 thf(fact_8885_divmod_H__nat__def,axiom,
% 7.94/5.76 ( unique5055182867167087721od_nat
% 7.94/5.76 = ( ^ [M4: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M4 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M4 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divmod'_nat_def
% 7.94/5.76 thf(fact_8886_sin__pi__divide__n__ge__0,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( N != zero_zero_nat )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_pi_divide_n_ge_0
% 7.94/5.76 thf(fact_8887_sin__gt__zero2,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_gt_zero2
% 7.94/5.76 thf(fact_8888_sin__lt__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ pi @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 7.94/5.76 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_lt_zero
% 7.94/5.76 thf(fact_8889_sin__30,axiom,
% 7.94/5.76 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 7.94/5.76 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_30
% 7.94/5.76 thf(fact_8890_sin__inj__pi,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ( sin_real @ X )
% 7.94/5.76 = ( sin_real @ Y ) )
% 7.94/5.76 => ( X = Y ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_inj_pi
% 7.94/5.76 thf(fact_8891_sin__mono__le__eq,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_mono_le_eq
% 7.94/5.76 thf(fact_8892_sin__monotone__2pi__le,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_monotone_2pi_le
% 7.94/5.76 thf(fact_8893_sin__le__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ pi @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_le_zero
% 7.94/5.76 thf(fact_8894_sin__less__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ zero_zero_real )
% 7.94/5.76 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_less_zero
% 7.94/5.76 thf(fact_8895_sin__monotone__2pi,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_monotone_2pi
% 7.94/5.76 thf(fact_8896_sin__mono__less__eq,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 7.94/5.76 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_mono_less_eq
% 7.94/5.76 thf(fact_8897_sin__total,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ? [X3: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 7.94/5.76 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( sin_real @ X3 )
% 7.94/5.76 = Y )
% 7.94/5.76 & ! [Y4: real] :
% 7.94/5.76 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 7.94/5.76 & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( sin_real @ Y4 )
% 7.94/5.76 = Y ) )
% 7.94/5.76 => ( Y4 = X3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_total
% 7.94/5.76 thf(fact_8898_sin__pi__divide__n__gt__0,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.94/5.76 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_pi_divide_n_gt_0
% 7.94/5.76 thf(fact_8899_sin__zero__iff__int,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( sin_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 = ( ? [I2: int] :
% 7.94/5.76 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I2 )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_zero_iff_int
% 7.94/5.76 thf(fact_8900_sin__zero__lemma,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ( sin_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 => ? [N2: nat] :
% 7.94/5.76 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_zero_lemma
% 7.94/5.76 thf(fact_8901_sin__zero__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( sin_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 = ( ? [N3: nat] :
% 7.94/5.76 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 7.94/5.76 | ? [N3: nat] :
% 7.94/5.76 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_zero_iff
% 7.94/5.76 thf(fact_8902_one__div__minus__numeral,axiom,
% 7.94/5.76 ! [N: num] :
% 7.94/5.76 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.94/5.76 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % one_div_minus_numeral
% 7.94/5.76 thf(fact_8903_minus__one__div__numeral,axiom,
% 7.94/5.76 ! [N: num] :
% 7.94/5.76 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 7.94/5.76 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % minus_one_div_numeral
% 7.94/5.76 thf(fact_8904_summable__arctan__series,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 => ( summable_real
% 7.94/5.76 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % summable_arctan_series
% 7.94/5.76 thf(fact_8905_Divides_Oadjust__div__eq,axiom,
% 7.94/5.76 ! [Q3: int,R2: int] :
% 7.94/5.76 ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.94/5.76 = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Divides.adjust_div_eq
% 7.94/5.76 thf(fact_8906_minus__numeral__div__numeral,axiom,
% 7.94/5.76 ! [M: num,N: num] :
% 7.94/5.76 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 7.94/5.76 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % minus_numeral_div_numeral
% 7.94/5.76 thf(fact_8907_numeral__div__minus__numeral,axiom,
% 7.94/5.76 ! [M: num,N: num] :
% 7.94/5.76 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.94/5.76 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % numeral_div_minus_numeral
% 7.94/5.76 thf(fact_8908_summable__power__series,axiom,
% 7.94/5.76 ! [F: nat > real,Z: real] :
% 7.94/5.76 ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 7.94/5.76 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 7.94/5.76 => ( ( ord_less_real @ Z @ one_one_real )
% 7.94/5.76 => ( summable_real
% 7.94/5.76 @ ^ [I2: nat] : ( times_times_real @ ( F @ I2 ) @ ( power_power_real @ Z @ I2 ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % summable_power_series
% 7.94/5.76 thf(fact_8909_neg__eucl__rel__int__mult__2,axiom,
% 7.94/5.76 ! [B: int,A: int,Q3: int,R2: int] :
% 7.94/5.76 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 7.94/5.76 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.94/5.76 => ( 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 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % neg_eucl_rel_int_mult_2
% 7.94/5.76 thf(fact_8910_pos__eucl__rel__int__mult__2,axiom,
% 7.94/5.76 ! [B: int,A: int,Q3: int,R2: int] :
% 7.94/5.76 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 7.94/5.76 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.94/5.76 => ( 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 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % pos_eucl_rel_int_mult_2
% 7.94/5.76 thf(fact_8911_cos__pi__eq__zero,axiom,
% 7.94/5.76 ! [M: nat] :
% 7.94/5.76 ( ( 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 ) ) ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % cos_pi_eq_zero
% 7.94/5.76 thf(fact_8912_cos__pi,axiom,
% 7.94/5.76 ( ( cos_real @ pi )
% 7.94/5.76 = ( uminus_uminus_real @ one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_pi
% 7.94/5.76 thf(fact_8913_cos__pi__half,axiom,
% 7.94/5.76 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % cos_pi_half
% 7.94/5.76 thf(fact_8914_cos__two__pi,axiom,
% 7.94/5.76 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % cos_two_pi
% 7.94/5.76 thf(fact_8915_cos__periodic,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 7.94/5.76 = ( cos_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_periodic
% 7.94/5.76 thf(fact_8916_cos__2pi__minus,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 7.94/5.76 = ( cos_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_2pi_minus
% 7.94/5.76 thf(fact_8917_cos__npi,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 7.94/5.76 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_npi
% 7.94/5.76 thf(fact_8918_cos__npi2,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 7.94/5.76 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_npi2
% 7.94/5.76 thf(fact_8919_cos__2npi,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % cos_2npi
% 7.94/5.76 thf(fact_8920_cos__int__2pin,axiom,
% 7.94/5.76 ! [N: int] :
% 7.94/5.76 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % cos_int_2pin
% 7.94/5.76 thf(fact_8921_cos__3over2__pi,axiom,
% 7.94/5.76 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % cos_3over2_pi
% 7.94/5.76 thf(fact_8922_cos__npi__int,axiom,
% 7.94/5.76 ! [N: int] :
% 7.94/5.76 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 7.94/5.76 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 7.94/5.76 = one_one_real ) )
% 7.94/5.76 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 7.94/5.76 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 7.94/5.76 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_npi_int
% 7.94/5.76 thf(fact_8923_unique__remainder,axiom,
% 7.94/5.76 ! [A: int,B: int,Q3: int,R2: int,Q7: int,R4: int] :
% 7.94/5.76 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.94/5.76 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q7 @ R4 ) )
% 7.94/5.76 => ( R2 = R4 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % unique_remainder
% 7.94/5.76 thf(fact_8924_unique__quotient,axiom,
% 7.94/5.76 ! [A: int,B: int,Q3: int,R2: int,Q7: int,R4: int] :
% 7.94/5.76 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.94/5.76 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q7 @ R4 ) )
% 7.94/5.76 => ( Q3 = Q7 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % unique_quotient
% 7.94/5.76 thf(fact_8925_cos__le__one,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % cos_le_one
% 7.94/5.76 thf(fact_8926_polar__Ex,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ? [R3: real,A5: real] :
% 7.94/5.76 ( ( X
% 7.94/5.76 = ( times_times_real @ R3 @ ( cos_real @ A5 ) ) )
% 7.94/5.76 & ( Y
% 7.94/5.76 = ( times_times_real @ R3 @ ( sin_real @ A5 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % polar_Ex
% 7.94/5.76 thf(fact_8927_cos__arctan__not__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( cos_real @ ( arctan @ X ) )
% 7.94/5.76 != zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % cos_arctan_not_zero
% 7.94/5.76 thf(fact_8928_cos__monotone__0__pi__le,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ pi )
% 7.94/5.76 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_monotone_0_pi_le
% 7.94/5.76 thf(fact_8929_cos__mono__le__eq,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ pi )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ pi )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_mono_le_eq
% 7.94/5.76 thf(fact_8930_cos__inj__pi,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ pi )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ pi )
% 7.94/5.76 => ( ( ( cos_real @ X )
% 7.94/5.76 = ( cos_real @ Y ) )
% 7.94/5.76 => ( X = Y ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_inj_pi
% 7.94/5.76 thf(fact_8931_cos__ge__minus__one,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_ge_minus_one
% 7.94/5.76 thf(fact_8932_abs__cos__le__one,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % abs_cos_le_one
% 7.94/5.76 thf(fact_8933_eucl__rel__int__by0,axiom,
% 7.94/5.76 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % eucl_rel_int_by0
% 7.94/5.76 thf(fact_8934_mod__int__unique,axiom,
% 7.94/5.76 ! [K: int,L: int,Q3: int,R2: int] :
% 7.94/5.76 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.94/5.76 => ( ( modulo_modulo_int @ K @ L )
% 7.94/5.76 = R2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % mod_int_unique
% 7.94/5.76 thf(fact_8935_div__int__unique,axiom,
% 7.94/5.76 ! [K: int,L: int,Q3: int,R2: int] :
% 7.94/5.76 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.94/5.76 => ( ( divide_divide_int @ K @ L )
% 7.94/5.76 = Q3 ) ) ).
% 7.94/5.76
% 7.94/5.76 % div_int_unique
% 7.94/5.76 thf(fact_8936_cos__two__neq__zero,axiom,
% 7.94/5.76 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 != zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % cos_two_neq_zero
% 7.94/5.76 thf(fact_8937_cos__monotone__0__pi,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ pi )
% 7.94/5.76 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_monotone_0_pi
% 7.94/5.76 thf(fact_8938_cos__mono__less__eq,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ pi )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ pi )
% 7.94/5.76 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 7.94/5.76 = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_mono_less_eq
% 7.94/5.76 thf(fact_8939_cos__monotone__minus__pi__0_H,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.94/5.76 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_monotone_minus_pi_0'
% 7.94/5.76 thf(fact_8940_sin__zero__abs__cos__one,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( sin_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 => ( ( abs_abs_real @ ( cos_real @ X ) )
% 7.94/5.76 = one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_zero_abs_cos_one
% 7.94/5.76 thf(fact_8941_eucl__rel__int__dividesI,axiom,
% 7.94/5.76 ! [L: int,K: int,Q3: int] :
% 7.94/5.76 ( ( L != zero_zero_int )
% 7.94/5.76 => ( ( K
% 7.94/5.76 = ( times_times_int @ Q3 @ L ) )
% 7.94/5.76 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % eucl_rel_int_dividesI
% 7.94/5.76 thf(fact_8942_eucl__rel__int,axiom,
% 7.94/5.76 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % eucl_rel_int
% 7.94/5.76 thf(fact_8943_cos__two__less__zero,axiom,
% 7.94/5.76 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 7.94/5.76
% 7.94/5.76 % cos_two_less_zero
% 7.94/5.76 thf(fact_8944_cos__is__zero,axiom,
% 7.94/5.76 ? [X3: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 7.94/5.76 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 & ( ( cos_real @ X3 )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 & ! [Y4: real] :
% 7.94/5.76 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 7.94/5.76 & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 & ( ( cos_real @ Y4 )
% 7.94/5.76 = zero_zero_real ) )
% 7.94/5.76 => ( Y4 = X3 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_is_zero
% 7.94/5.76 thf(fact_8945_cos__two__le__zero,axiom,
% 7.94/5.76 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 7.94/5.76
% 7.94/5.76 % cos_two_le_zero
% 7.94/5.76 thf(fact_8946_cos__monotone__minus__pi__0,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.94/5.76 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_monotone_minus_pi_0
% 7.94/5.76 thf(fact_8947_cos__total,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ? [X3: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 7.94/5.76 & ( ord_less_eq_real @ X3 @ pi )
% 7.94/5.76 & ( ( cos_real @ X3 )
% 7.94/5.76 = Y )
% 7.94/5.76 & ! [Y4: real] :
% 7.94/5.76 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 7.94/5.76 & ( ord_less_eq_real @ Y4 @ pi )
% 7.94/5.76 & ( ( cos_real @ Y4 )
% 7.94/5.76 = Y ) )
% 7.94/5.76 => ( Y4 = X3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_total
% 7.94/5.76 thf(fact_8948_sincos__principal__value,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ? [Y3: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 7.94/5.76 & ( ord_less_eq_real @ Y3 @ pi )
% 7.94/5.76 & ( ( sin_real @ Y3 )
% 7.94/5.76 = ( sin_real @ X ) )
% 7.94/5.76 & ( ( cos_real @ Y3 )
% 7.94/5.76 = ( cos_real @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sincos_principal_value
% 7.94/5.76 thf(fact_8949_sin__cos__le1,axiom,
% 7.94/5.76 ! [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 ) ).
% 7.94/5.76
% 7.94/5.76 % sin_cos_le1
% 7.94/5.76 thf(fact_8950_cos__double__less__one,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_double_less_one
% 7.94/5.76 thf(fact_8951_cos__gt__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_gt_zero
% 7.94/5.76 thf(fact_8952_cos__60,axiom,
% 7.94/5.76 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 7.94/5.76 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_60
% 7.94/5.76 thf(fact_8953_cos__one__2pi__int,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( cos_real @ X )
% 7.94/5.76 = one_one_real )
% 7.94/5.76 = ( ? [X2: int] :
% 7.94/5.76 ( X
% 7.94/5.76 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_one_2pi_int
% 7.94/5.76 thf(fact_8954_zminus1__lemma,axiom,
% 7.94/5.76 ! [A: int,B: int,Q3: int,R2: int] :
% 7.94/5.76 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.94/5.76 => ( ( B != zero_zero_int )
% 7.94/5.76 => ( 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 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % zminus1_lemma
% 7.94/5.76 thf(fact_8955_cos__gt__zero__pi,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_gt_zero_pi
% 7.94/5.76 thf(fact_8956_cos__ge__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_ge_zero
% 7.94/5.76 thf(fact_8957_cos__one__2pi,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( cos_real @ X )
% 7.94/5.76 = one_one_real )
% 7.94/5.76 = ( ? [X2: nat] :
% 7.94/5.76 ( X
% 7.94/5.76 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 7.94/5.76 | ? [X2: nat] :
% 7.94/5.76 ( X
% 7.94/5.76 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_one_2pi
% 7.94/5.76 thf(fact_8958_eucl__rel__int__iff,axiom,
% 7.94/5.76 ! [K: int,L: int,Q3: int,R2: int] :
% 7.94/5.76 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 7.94/5.76 = ( ( K
% 7.94/5.76 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R2 ) )
% 7.94/5.76 & ( ( ord_less_int @ zero_zero_int @ L )
% 7.94/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 7.94/5.76 & ( ord_less_int @ R2 @ L ) ) )
% 7.94/5.76 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 7.94/5.76 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 7.94/5.76 => ( ( ord_less_int @ L @ R2 )
% 7.94/5.76 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 7.94/5.76 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 7.94/5.76 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % eucl_rel_int_iff
% 7.94/5.76 thf(fact_8959_eucl__rel__int__remainderI,axiom,
% 7.94/5.76 ! [R2: int,L: int,K: int,Q3: int] :
% 7.94/5.76 ( ( ( sgn_sgn_int @ R2 )
% 7.94/5.76 = ( sgn_sgn_int @ L ) )
% 7.94/5.76 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 7.94/5.76 => ( ( K
% 7.94/5.76 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R2 ) )
% 7.94/5.76 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % eucl_rel_int_remainderI
% 7.94/5.76 thf(fact_8960_sincos__total__pi,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = one_one_real )
% 7.94/5.76 => ? [T6: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 7.94/5.76 & ( ord_less_eq_real @ T6 @ pi )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( cos_real @ T6 ) )
% 7.94/5.76 & ( Y
% 7.94/5.76 = ( sin_real @ T6 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sincos_total_pi
% 7.94/5.76 thf(fact_8961_sin__expansion__lemma,axiom,
% 7.94/5.76 ! [X: real,M: nat] :
% 7.94/5.76 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_expansion_lemma
% 7.94/5.76 thf(fact_8962_cos__zero__iff__int,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( cos_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 = ( ? [I2: int] :
% 7.94/5.76 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I2 )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_zero_iff_int
% 7.94/5.76 thf(fact_8963_eucl__rel__int_Osimps,axiom,
% 7.94/5.76 ( eucl_rel_int
% 7.94/5.76 = ( ^ [A12: int,A23: int,A32: product_prod_int_int] :
% 7.94/5.76 ( ? [K3: int] :
% 7.94/5.76 ( ( A12 = K3 )
% 7.94/5.76 & ( A23 = zero_zero_int )
% 7.94/5.76 & ( A32
% 7.94/5.76 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 7.94/5.76 | ? [L2: int,K3: int,Q6: int] :
% 7.94/5.76 ( ( A12 = K3 )
% 7.94/5.76 & ( A23 = L2 )
% 7.94/5.76 & ( A32
% 7.94/5.76 = ( product_Pair_int_int @ Q6 @ zero_zero_int ) )
% 7.94/5.76 & ( L2 != zero_zero_int )
% 7.94/5.76 & ( K3
% 7.94/5.76 = ( times_times_int @ Q6 @ L2 ) ) )
% 7.94/5.76 | ? [R5: int,L2: int,K3: int,Q6: int] :
% 7.94/5.76 ( ( A12 = K3 )
% 7.94/5.76 & ( A23 = L2 )
% 7.94/5.76 & ( A32
% 7.94/5.76 = ( product_Pair_int_int @ Q6 @ R5 ) )
% 7.94/5.76 & ( ( sgn_sgn_int @ R5 )
% 7.94/5.76 = ( sgn_sgn_int @ L2 ) )
% 7.94/5.76 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 7.94/5.76 & ( K3
% 7.94/5.76 = ( plus_plus_int @ ( times_times_int @ Q6 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % eucl_rel_int.simps
% 7.94/5.76 thf(fact_8964_eucl__rel__int_Ocases,axiom,
% 7.94/5.76 ! [A1: int,A22: int,A33: product_prod_int_int] :
% 7.94/5.76 ( ( eucl_rel_int @ A1 @ A22 @ A33 )
% 7.94/5.76 => ( ( ( A22 = zero_zero_int )
% 7.94/5.76 => ( A33
% 7.94/5.76 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 7.94/5.76 => ( ! [Q5: int] :
% 7.94/5.76 ( ( A33
% 7.94/5.76 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 7.94/5.76 => ( ( A22 != zero_zero_int )
% 7.94/5.76 => ( A1
% 7.94/5.76 != ( times_times_int @ Q5 @ A22 ) ) ) )
% 7.94/5.76 => ~ ! [R3: int,Q5: int] :
% 7.94/5.76 ( ( A33
% 7.94/5.76 = ( product_Pair_int_int @ Q5 @ R3 ) )
% 7.94/5.76 => ( ( ( sgn_sgn_int @ R3 )
% 7.94/5.76 = ( sgn_sgn_int @ A22 ) )
% 7.94/5.76 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 7.94/5.76 => ( A1
% 7.94/5.76 != ( plus_plus_int @ ( times_times_int @ Q5 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % eucl_rel_int.cases
% 7.94/5.76 thf(fact_8965_cos__zero__lemma,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ( cos_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 => ? [N2: nat] :
% 7.94/5.76 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_zero_lemma
% 7.94/5.76 thf(fact_8966_cos__zero__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( cos_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 = ( ? [N3: nat] :
% 7.94/5.76 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 7.94/5.76 | ? [N3: nat] :
% 7.94/5.76 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_zero_iff
% 7.94/5.76 thf(fact_8967_cos__expansion__lemma,axiom,
% 7.94/5.76 ! [X: real,M: nat] :
% 7.94/5.76 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_expansion_lemma
% 7.94/5.76 thf(fact_8968_sincos__total__pi__half,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = one_one_real )
% 7.94/5.76 => ? [T6: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 7.94/5.76 & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( cos_real @ T6 ) )
% 7.94/5.76 & ( Y
% 7.94/5.76 = ( sin_real @ T6 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sincos_total_pi_half
% 7.94/5.76 thf(fact_8969_sincos__total__2pi__le,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = one_one_real )
% 7.94/5.76 => ? [T6: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 7.94/5.76 & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 7.94/5.76 & ( X
% 7.94/5.76 = ( cos_real @ T6 ) )
% 7.94/5.76 & ( Y
% 7.94/5.76 = ( sin_real @ T6 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sincos_total_2pi_le
% 7.94/5.76 thf(fact_8970_sincos__total__2pi,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = one_one_real )
% 7.94/5.76 => ~ ! [T6: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 7.94/5.76 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 7.94/5.76 => ( ( X
% 7.94/5.76 = ( cos_real @ T6 ) )
% 7.94/5.76 => ( Y
% 7.94/5.76 != ( sin_real @ T6 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sincos_total_2pi
% 7.94/5.76 thf(fact_8971__C11_C,axiom,
% 7.94/5.76 ! [Xa3: array_VEBT_VEBTi,X: list_VEBT_VEBTi] :
% 7.94/5.76 ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa3 @ X ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( replicate_VEBT_VEBT @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ X ) ) @ ( vEBT_V739175172307565963ildupi @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ na ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa3 @ X ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( replicate_VEBT_VEBT @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ X ) ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ na ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ R5 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % "11"
% 7.94/5.76 thf(fact_8972_sgn__integer__code,axiom,
% 7.94/5.76 ( sgn_sgn_Code_integer
% 7.94/5.76 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sgn_integer_code
% 7.94/5.76 thf(fact_8973_infinite__int__iff__unbounded,axiom,
% 7.94/5.76 ! [S3: set_int] :
% 7.94/5.76 ( ( ~ ( finite_finite_int @ S3 ) )
% 7.94/5.76 = ( ! [M4: int] :
% 7.94/5.76 ? [N3: int] :
% 7.94/5.76 ( ( ord_less_int @ M4 @ ( abs_abs_int @ N3 ) )
% 7.94/5.76 & ( member_int @ N3 @ S3 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % infinite_int_iff_unbounded
% 7.94/5.76 thf(fact_8974_tan__pi,axiom,
% 7.94/5.76 ( ( tan_real @ pi )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % tan_pi
% 7.94/5.76 thf(fact_8975__C3_OIH_C_I4_J,axiom,
% 7.94/5.76 ! [X: nat] :
% 7.94/5.76 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ na ) ) )
% 7.94/5.76 => ( ( X
% 7.94/5.76 = ( divide_divide_nat @ ( suc @ ( suc @ na ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ ( suc @ X ) ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ ( suc @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % "3.IH"(4)
% 7.94/5.76 thf(fact_8976__C3_OIH_C_I3_J,axiom,
% 7.94/5.76 ! [X: nat] :
% 7.94/5.76 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ na ) ) )
% 7.94/5.76 => ( ( X
% 7.94/5.76 = ( divide_divide_nat @ ( suc @ ( suc @ na ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % "3.IH"(3)
% 7.94/5.76 thf(fact_8977__C3_OIH_C_I1_J,axiom,
% 7.94/5.76 ! [X: nat] :
% 7.94/5.76 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ na ) ) )
% 7.94/5.76 => ( ( X
% 7.94/5.76 = ( divide_divide_nat @ ( suc @ ( suc @ na ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % "3.IH"(1)
% 7.94/5.76 thf(fact_8978_tan__npi,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % tan_npi
% 7.94/5.76 thf(fact_8979_tan__periodic__n,axiom,
% 7.94/5.76 ! [X: real,N: num] :
% 7.94/5.76 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 7.94/5.76 = ( tan_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_periodic_n
% 7.94/5.76 thf(fact_8980_tan__periodic__nat,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 7.94/5.76 = ( tan_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_periodic_nat
% 7.94/5.76 thf(fact_8981_tan__periodic__int,axiom,
% 7.94/5.76 ! [X: real,I: int] :
% 7.94/5.76 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 7.94/5.76 = ( tan_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_periodic_int
% 7.94/5.76 thf(fact_8982_tan__periodic,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 7.94/5.76 = ( tan_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_periodic
% 7.94/5.76 thf(fact_8983_zero__natural_Orsp,axiom,
% 7.94/5.76 zero_zero_nat = zero_zero_nat ).
% 7.94/5.76
% 7.94/5.76 % zero_natural.rsp
% 7.94/5.76 thf(fact_8984_one__natural_Orsp,axiom,
% 7.94/5.76 one_one_nat = one_one_nat ).
% 7.94/5.76
% 7.94/5.76 % one_natural.rsp
% 7.94/5.76 thf(fact_8985_zero__integer_Orsp,axiom,
% 7.94/5.76 zero_zero_int = zero_zero_int ).
% 7.94/5.76
% 7.94/5.76 % zero_integer.rsp
% 7.94/5.76 thf(fact_8986_one__integer_Orsp,axiom,
% 7.94/5.76 one_one_int = one_one_int ).
% 7.94/5.76
% 7.94/5.76 % one_integer.rsp
% 7.94/5.76 thf(fact_8987_less__eq__integer__code_I1_J,axiom,
% 7.94/5.76 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 7.94/5.76
% 7.94/5.76 % less_eq_integer_code(1)
% 7.94/5.76 thf(fact_8988_uminus__integer__code_I1_J,axiom,
% 7.94/5.76 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 7.94/5.76 = zero_z3403309356797280102nteger ) ).
% 7.94/5.76
% 7.94/5.76 % uminus_integer_code(1)
% 7.94/5.76 thf(fact_8989_times__integer__code_I2_J,axiom,
% 7.94/5.76 ! [L: code_integer] :
% 7.94/5.76 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 7.94/5.76 = zero_z3403309356797280102nteger ) ).
% 7.94/5.76
% 7.94/5.76 % times_integer_code(2)
% 7.94/5.76 thf(fact_8990_times__integer__code_I1_J,axiom,
% 7.94/5.76 ! [K: code_integer] :
% 7.94/5.76 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 7.94/5.76 = zero_z3403309356797280102nteger ) ).
% 7.94/5.76
% 7.94/5.76 % times_integer_code(1)
% 7.94/5.76 thf(fact_8991_tan__45,axiom,
% 7.94/5.76 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % tan_45
% 7.94/5.76 thf(fact_8992_lemma__tan__total,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ Y )
% 7.94/5.76 => ? [X3: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X3 )
% 7.94/5.76 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ord_less_real @ Y @ ( tan_real @ X3 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % lemma_tan_total
% 7.94/5.76 thf(fact_8993_tan__gt__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_gt_zero
% 7.94/5.76 thf(fact_8994_lemma__tan__total1,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ? [X3: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 7.94/5.76 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( tan_real @ X3 )
% 7.94/5.76 = Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % lemma_tan_total1
% 7.94/5.76 thf(fact_8995_tan__mono__lt__eq,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 7.94/5.76 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_mono_lt_eq
% 7.94/5.76 thf(fact_8996_tan__monotone_H,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ Y @ X )
% 7.94/5.76 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_monotone'
% 7.94/5.76 thf(fact_8997_tan__monotone,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_monotone
% 7.94/5.76 thf(fact_8998_tan__total,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ? [X3: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 7.94/5.76 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( tan_real @ X3 )
% 7.94/5.76 = Y )
% 7.94/5.76 & ! [Y4: real] :
% 7.94/5.76 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 7.94/5.76 & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( tan_real @ Y4 )
% 7.94/5.76 = Y ) )
% 7.94/5.76 => ( Y4 = X3 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_total
% 7.94/5.76 thf(fact_8999_tan__minus__45,axiom,
% 7.94/5.76 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 7.94/5.76 = ( uminus_uminus_real @ one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_minus_45
% 7.94/5.76 thf(fact_9000_tan__inverse,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 7.94/5.76 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_inverse
% 7.94/5.76 thf(fact_9001_infinite__nat__iff__unbounded,axiom,
% 7.94/5.76 ! [S3: set_nat] :
% 7.94/5.76 ( ( ~ ( finite_finite_nat @ S3 ) )
% 7.94/5.76 = ( ! [M4: nat] :
% 7.94/5.76 ? [N3: nat] :
% 7.94/5.76 ( ( ord_less_nat @ M4 @ N3 )
% 7.94/5.76 & ( member_nat @ N3 @ S3 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % infinite_nat_iff_unbounded
% 7.94/5.76 thf(fact_9002_unbounded__k__infinite,axiom,
% 7.94/5.76 ! [K: nat,S3: set_nat] :
% 7.94/5.76 ( ! [M2: nat] :
% 7.94/5.76 ( ( ord_less_nat @ K @ M2 )
% 7.94/5.76 => ? [N9: nat] :
% 7.94/5.76 ( ( ord_less_nat @ M2 @ N9 )
% 7.94/5.76 & ( member_nat @ N9 @ S3 ) ) )
% 7.94/5.76 => ~ ( finite_finite_nat @ S3 ) ) ).
% 7.94/5.76
% 7.94/5.76 % unbounded_k_infinite
% 7.94/5.76 thf(fact_9003_tan__total__pos,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ? [X3: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 7.94/5.76 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( tan_real @ X3 )
% 7.94/5.76 = Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_total_pos
% 7.94/5.76 thf(fact_9004_tan__pos__pi2__le,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_pos_pi2_le
% 7.94/5.76 thf(fact_9005_tan__less__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ zero_zero_real )
% 7.94/5.76 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_less_zero
% 7.94/5.76 thf(fact_9006_tan__mono__le,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_mono_le
% 7.94/5.76 thf(fact_9007_tan__mono__le__eq,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_mono_le_eq
% 7.94/5.76 thf(fact_9008_tan__bound__pi2,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_bound_pi2
% 7.94/5.76 thf(fact_9009_arctan,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 7.94/5.76 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( tan_real @ ( arctan @ Y ) )
% 7.94/5.76 = Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan
% 7.94/5.76 thf(fact_9010_arctan__tan,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( arctan @ ( tan_real @ X ) )
% 7.94/5.76 = X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_tan
% 7.94/5.76 thf(fact_9011_arctan__unique,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ( tan_real @ X )
% 7.94/5.76 = Y )
% 7.94/5.76 => ( ( arctan @ Y )
% 7.94/5.76 = X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_unique
% 7.94/5.76 thf(fact_9012_abs__integer__code,axiom,
% 7.94/5.76 ( abs_abs_Code_integer
% 7.94/5.76 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % abs_integer_code
% 7.94/5.76 thf(fact_9013_less__integer__code_I1_J,axiom,
% 7.94/5.76 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 7.94/5.76
% 7.94/5.76 % less_integer_code(1)
% 7.94/5.76 thf(fact_9014_plus__integer__code_I1_J,axiom,
% 7.94/5.76 ! [K: code_integer] :
% 7.94/5.76 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 7.94/5.76 = K ) ).
% 7.94/5.76
% 7.94/5.76 % plus_integer_code(1)
% 7.94/5.76 thf(fact_9015_plus__integer__code_I2_J,axiom,
% 7.94/5.76 ! [L: code_integer] :
% 7.94/5.76 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 7.94/5.76 = L ) ).
% 7.94/5.76
% 7.94/5.76 % plus_integer_code(2)
% 7.94/5.76 thf(fact_9016_minus__integer__code_I2_J,axiom,
% 7.94/5.76 ! [L: code_integer] :
% 7.94/5.76 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 7.94/5.76 = ( uminus1351360451143612070nteger @ L ) ) ).
% 7.94/5.76
% 7.94/5.76 % minus_integer_code(2)
% 7.94/5.76 thf(fact_9017_minus__integer__code_I1_J,axiom,
% 7.94/5.76 ! [K: code_integer] :
% 7.94/5.76 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 7.94/5.76 = K ) ).
% 7.94/5.76
% 7.94/5.76 % minus_integer_code(1)
% 7.94/5.76 thf(fact_9018_tan__total__pi4,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 => ? [Z3: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 7.94/5.76 & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 & ( ( tan_real @ Z3 )
% 7.94/5.76 = X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_total_pi4
% 7.94/5.76 thf(fact_9019_T__vebt__buildupi,axiom,
% 7.94/5.76 ! [N: nat,H2: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ ( vEBT_V739175172307565963ildupi @ N ) @ H2 ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % T_vebt_buildupi
% 7.94/5.76 thf(fact_9020_highi__h,axiom,
% 7.94/5.76 ! [X: nat,N: nat] :
% 7.94/5.76 ( hoare_3067605981109127869le_nat @ one_one_assn @ ( vEBT_VEBT_highi @ X @ N )
% 7.94/5.76 @ ^ [R5: nat] :
% 7.94/5.76 ( pure_assn
% 7.94/5.76 @ ( R5
% 7.94/5.76 = ( vEBT_VEBT_high @ X @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % highi_h
% 7.94/5.76 thf(fact_9021_lowi__h,axiom,
% 7.94/5.76 ! [X: nat,N: nat] :
% 7.94/5.76 ( hoare_3067605981109127869le_nat @ one_one_assn @ ( vEBT_VEBT_lowi @ X @ N )
% 7.94/5.76 @ ^ [R5: nat] :
% 7.94/5.76 ( pure_assn
% 7.94/5.76 @ ( R5
% 7.94/5.76 = ( vEBT_VEBT_low @ X @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % lowi_h
% 7.94/5.76 thf(fact_9022_integer__of__int__code,axiom,
% 7.94/5.76 ( code_integer_of_int
% 7.94/5.76 = ( ^ [K3: int] :
% 7.94/5.76 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 7.94/5.76 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 7.94/5.76 @ ( if_Code_integer
% 7.94/5.76 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.94/5.76 = zero_zero_int )
% 7.94/5.76 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % integer_of_int_code
% 7.94/5.76 thf(fact_9023_sin__tan,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( sin_real @ X )
% 7.94/5.76 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_tan
% 7.94/5.76 thf(fact_9024_cos__tan,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( cos_real @ X )
% 7.94/5.76 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_tan
% 7.94/5.76 thf(fact_9025_real__sqrt__eq__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ( sqrt @ X )
% 7.94/5.76 = ( sqrt @ Y ) )
% 7.94/5.76 = ( X = Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_eq_iff
% 7.94/5.76 thf(fact_9026_real__sqrt__eq__zero__cancel__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( sqrt @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 = ( X = zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_eq_zero_cancel_iff
% 7.94/5.76 thf(fact_9027_real__sqrt__zero,axiom,
% 7.94/5.76 ( ( sqrt @ zero_zero_real )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_zero
% 7.94/5.76 thf(fact_9028_real__sqrt__less__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 7.94/5.76 = ( ord_less_real @ X @ Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_less_iff
% 7.94/5.76 thf(fact_9029_real__sqrt__le__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ X @ Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_le_iff
% 7.94/5.76 thf(fact_9030_real__sqrt__one,axiom,
% 7.94/5.76 ( ( sqrt @ one_one_real )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_one
% 7.94/5.76 thf(fact_9031_real__sqrt__eq__1__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( sqrt @ X )
% 7.94/5.76 = one_one_real )
% 7.94/5.76 = ( X = one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_eq_1_iff
% 7.94/5.76 thf(fact_9032_real__sqrt__gt__0__iff,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 7.94/5.76 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_gt_0_iff
% 7.94/5.76 thf(fact_9033_real__sqrt__lt__0__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 7.94/5.76 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_lt_0_iff
% 7.94/5.76 thf(fact_9034_real__sqrt__ge__0__iff,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_ge_0_iff
% 7.94/5.76 thf(fact_9035_real__sqrt__le__0__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 7.94/5.76 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_le_0_iff
% 7.94/5.76 thf(fact_9036_real__sqrt__gt__1__iff,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 7.94/5.76 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_gt_1_iff
% 7.94/5.76 thf(fact_9037_real__sqrt__lt__1__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 7.94/5.76 = ( ord_less_real @ X @ one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_lt_1_iff
% 7.94/5.76 thf(fact_9038_real__sqrt__ge__1__iff,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_ge_1_iff
% 7.94/5.76 thf(fact_9039_real__sqrt__le__1__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 7.94/5.76 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_le_1_iff
% 7.94/5.76 thf(fact_9040_real__sqrt__mult__self,axiom,
% 7.94/5.76 ! [A: real] :
% 7.94/5.76 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 7.94/5.76 = ( abs_abs_real @ A ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_mult_self
% 7.94/5.76 thf(fact_9041_real__sqrt__abs2,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 7.94/5.76 = ( abs_abs_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_abs2
% 7.94/5.76 thf(fact_9042_real__sqrt__four,axiom,
% 7.94/5.76 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_four
% 7.94/5.76 thf(fact_9043_real__sqrt__abs,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = ( abs_abs_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_abs
% 7.94/5.76 thf(fact_9044_real__sqrt__pow2,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.94/5.76 = X ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_pow2
% 7.94/5.76 thf(fact_9045_real__sqrt__pow2__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.94/5.76 = X )
% 7.94/5.76 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_pow2_iff
% 7.94/5.76 thf(fact_9046_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 7.94/5.76 ! [X: real,Y: real,Xa3: real,Ya: real] :
% 7.94/5.76 ( ( 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 @ Xa3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.94/5.76 = ( 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 @ Xa3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_sum_squares_mult_squared_eq
% 7.94/5.76 thf(fact_9047_real__sqrt__le__mono,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ X @ Y )
% 7.94/5.76 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_le_mono
% 7.94/5.76 thf(fact_9048_real__sqrt__mult,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 7.94/5.76 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_mult
% 7.94/5.76 thf(fact_9049_real__sqrt__less__mono,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ X @ Y )
% 7.94/5.76 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_less_mono
% 7.94/5.76 thf(fact_9050_real__sqrt__divide,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( sqrt @ ( divide_divide_real @ X @ Y ) )
% 7.94/5.76 = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_divide
% 7.94/5.76 thf(fact_9051_real__sqrt__power,axiom,
% 7.94/5.76 ! [X: real,K: nat] :
% 7.94/5.76 ( ( sqrt @ ( power_power_real @ X @ K ) )
% 7.94/5.76 = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_power
% 7.94/5.76 thf(fact_9052_divmod__integer_H__def,axiom,
% 7.94/5.76 ( unique3479559517661332726nteger
% 7.94/5.76 = ( ^ [M4: num,N3: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M4 ) @ ( numera6620942414471956472nteger @ N3 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M4 ) @ ( numera6620942414471956472nteger @ N3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divmod_integer'_def
% 7.94/5.76 thf(fact_9053_real__sqrt__minus,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 7.94/5.76 = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_minus
% 7.94/5.76 thf(fact_9054_Code__Numeral_Oset__bit__integer_Oabs__eq,axiom,
% 7.94/5.76 ! [Xa3: nat,X: int] :
% 7.94/5.76 ( ( bit_se2793503036327961859nteger @ Xa3 @ ( code_integer_of_int @ X ) )
% 7.94/5.76 = ( code_integer_of_int @ ( bit_se7879613467334960850it_int @ Xa3 @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Code_Numeral.set_bit_integer.abs_eq
% 7.94/5.76 thf(fact_9055_divide__integer_Oabs__eq,axiom,
% 7.94/5.76 ! [Xa3: int,X: int] :
% 7.94/5.76 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa3 ) @ ( code_integer_of_int @ X ) )
% 7.94/5.76 = ( code_integer_of_int @ ( divide_divide_int @ Xa3 @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divide_integer.abs_eq
% 7.94/5.76 thf(fact_9056_modulo__integer_Oabs__eq,axiom,
% 7.94/5.76 ! [Xa3: int,X: int] :
% 7.94/5.76 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa3 ) @ ( code_integer_of_int @ X ) )
% 7.94/5.76 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa3 @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % modulo_integer.abs_eq
% 7.94/5.76 thf(fact_9057_real__sqrt__gt__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_gt_zero
% 7.94/5.76 thf(fact_9058_real__sqrt__ge__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_ge_zero
% 7.94/5.76 thf(fact_9059_real__sqrt__eq__zero__cancel,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ( sqrt @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 => ( X = zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_eq_zero_cancel
% 7.94/5.76 thf(fact_9060_real__sqrt__ge__one,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ one_one_real @ X )
% 7.94/5.76 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_ge_one
% 7.94/5.76 thf(fact_9061_zero__integer__def,axiom,
% 7.94/5.76 ( zero_z3403309356797280102nteger
% 7.94/5.76 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 7.94/5.76
% 7.94/5.76 % zero_integer_def
% 7.94/5.76 thf(fact_9062_less__integer_Oabs__eq,axiom,
% 7.94/5.76 ! [Xa3: int,X: int] :
% 7.94/5.76 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa3 ) @ ( code_integer_of_int @ X ) )
% 7.94/5.76 = ( ord_less_int @ Xa3 @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % less_integer.abs_eq
% 7.94/5.76 thf(fact_9063_one__integer__def,axiom,
% 7.94/5.76 ( one_one_Code_integer
% 7.94/5.76 = ( code_integer_of_int @ one_one_int ) ) ).
% 7.94/5.76
% 7.94/5.76 % one_integer_def
% 7.94/5.76 thf(fact_9064_real__div__sqrt,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 7.94/5.76 = ( sqrt @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_div_sqrt
% 7.94/5.76 thf(fact_9065_sqrt__add__le__add__sqrt,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sqrt_add_le_add_sqrt
% 7.94/5.76 thf(fact_9066_le__real__sqrt__sumsq,axiom,
% 7.94/5.76 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % le_real_sqrt_sumsq
% 7.94/5.76 thf(fact_9067_sqrt2__less__2,axiom,
% 7.94/5.76 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 7.94/5.76
% 7.94/5.76 % sqrt2_less_2
% 7.94/5.76 thf(fact_9068_real__less__rsqrt,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 7.94/5.76 => ( ord_less_real @ X @ ( sqrt @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_less_rsqrt
% 7.94/5.76 thf(fact_9069_sqrt__le__D,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 7.94/5.76 => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sqrt_le_D
% 7.94/5.76 thf(fact_9070_real__le__rsqrt,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 7.94/5.76 => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_le_rsqrt
% 7.94/5.76 thf(fact_9071_real__le__lsqrt,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_le_lsqrt
% 7.94/5.76 thf(fact_9072_real__sqrt__unique,axiom,
% 7.94/5.76 ! [Y: real,X: real] :
% 7.94/5.76 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.94/5.76 = X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( sqrt @ X )
% 7.94/5.76 = Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_unique
% 7.94/5.76 thf(fact_9073_lemma__real__divide__sqrt__less,axiom,
% 7.94/5.76 ! [U: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ U )
% 7.94/5.76 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 7.94/5.76
% 7.94/5.76 % lemma_real_divide_sqrt_less
% 7.94/5.76 thf(fact_9074_real__sqrt__sum__squares__eq__cancel,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 = X )
% 7.94/5.76 => ( Y = zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_sum_squares_eq_cancel
% 7.94/5.76 thf(fact_9075_real__sqrt__sum__squares__eq__cancel2,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 = Y )
% 7.94/5.76 => ( X = zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_sum_squares_eq_cancel2
% 7.94/5.76 thf(fact_9076_real__sqrt__sum__squares__ge1,axiom,
% 7.94/5.76 ! [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 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_sum_squares_ge1
% 7.94/5.76 thf(fact_9077_real__sqrt__sum__squares__ge2,axiom,
% 7.94/5.76 ! [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 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_sum_squares_ge2
% 7.94/5.76 thf(fact_9078_real__sqrt__sum__squares__triangle__ineq,axiom,
% 7.94/5.76 ! [A: real,C: real,B: real,D2: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_sum_squares_triangle_ineq
% 7.94/5.76 thf(fact_9079_sqrt__ge__absD,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 7.94/5.76 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % sqrt_ge_absD
% 7.94/5.76 thf(fact_9080_cos__45,axiom,
% 7.94/5.76 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_45
% 7.94/5.76 thf(fact_9081_sin__45,axiom,
% 7.94/5.76 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_45
% 7.94/5.76 thf(fact_9082_tan__60,axiom,
% 7.94/5.76 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 7.94/5.76 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_60
% 7.94/5.76 thf(fact_9083_real__less__lsqrt,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_less_lsqrt
% 7.94/5.76 thf(fact_9084_sqrt__sum__squares__le__sum,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( 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 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sqrt_sum_squares_le_sum
% 7.94/5.76 thf(fact_9085_sqrt__even__pow2,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.94/5.76 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 7.94/5.76 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sqrt_even_pow2
% 7.94/5.76 thf(fact_9086_sqrt__sum__squares__le__sum__abs,axiom,
% 7.94/5.76 ! [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 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sqrt_sum_squares_le_sum_abs
% 7.94/5.76 thf(fact_9087_real__sqrt__ge__abs2,axiom,
% 7.94/5.76 ! [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 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_ge_abs2
% 7.94/5.76 thf(fact_9088_real__sqrt__ge__abs1,axiom,
% 7.94/5.76 ! [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 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_ge_abs1
% 7.94/5.76 thf(fact_9089_ln__sqrt,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 7.94/5.76 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % ln_sqrt
% 7.94/5.76 thf(fact_9090_cos__30,axiom,
% 7.94/5.76 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 7.94/5.76 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_30
% 7.94/5.76 thf(fact_9091_sin__60,axiom,
% 7.94/5.76 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 7.94/5.76 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_60
% 7.94/5.76 thf(fact_9092_arsinh__real__def,axiom,
% 7.94/5.76 ( arsinh_real
% 7.94/5.76 = ( ^ [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 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arsinh_real_def
% 7.94/5.76 thf(fact_9093_real__sqrt__power__even,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 7.94/5.76 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_power_even
% 7.94/5.76 thf(fact_9094_arsinh__real__aux,axiom,
% 7.94/5.76 ! [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 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arsinh_real_aux
% 7.94/5.76 thf(fact_9095_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 7.94/5.76 ! [X: real,Y: real,Xa3: 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 @ Xa3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_sum_squares_mult_ge_zero
% 7.94/5.76 thf(fact_9096_arith__geo__mean__sqrt,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arith_geo_mean_sqrt
% 7.94/5.76 thf(fact_9097_powr__half__sqrt,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = ( sqrt @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % powr_half_sqrt
% 7.94/5.76 thf(fact_9098_tan__30,axiom,
% 7.94/5.76 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 7.94/5.76 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_30
% 7.94/5.76 thf(fact_9099_cos__x__y__le__one,axiom,
% 7.94/5.76 ! [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 ) ).
% 7.94/5.76
% 7.94/5.76 % cos_x_y_le_one
% 7.94/5.76 thf(fact_9100_real__sqrt__sum__squares__less,axiom,
% 7.94/5.76 ! [X: real,U: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 => ( 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 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_sum_squares_less
% 7.94/5.76 thf(fact_9101_arcosh__real__def,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ one_one_real @ X )
% 7.94/5.76 => ( ( arcosh_real @ X )
% 7.94/5.76 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcosh_real_def
% 7.94/5.76 thf(fact_9102_cos__arctan,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( cos_real @ ( arctan @ X ) )
% 7.94/5.76 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_arctan
% 7.94/5.76 thf(fact_9103_sin__arctan,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( sin_real @ ( arctan @ X ) )
% 7.94/5.76 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_arctan
% 7.94/5.76 thf(fact_9104_sqrt__sum__squares__half__less,axiom,
% 7.94/5.76 ! [X: real,U: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( 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 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sqrt_sum_squares_half_less
% 7.94/5.76 thf(fact_9105_sin__cos__sqrt,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 7.94/5.76 => ( ( sin_real @ X )
% 7.94/5.76 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_cos_sqrt
% 7.94/5.76 thf(fact_9106_arctan__half,axiom,
% 7.94/5.76 ( arctan
% 7.94/5.76 = ( ^ [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 ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_half
% 7.94/5.76 thf(fact_9107_sin__paired,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( sums_real
% 7.94/5.76 @ ^ [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 ) ) )
% 7.94/5.76 @ ( sin_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_paired
% 7.94/5.76 thf(fact_9108_and__int_Opelims,axiom,
% 7.94/5.76 ! [X: int,Xa3: int,Y: int] :
% 7.94/5.76 ( ( ( bit_se725231765392027082nd_int @ X @ Xa3 )
% 7.94/5.76 = Y )
% 7.94/5.76 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa3 ) )
% 7.94/5.76 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 7.94/5.76 & ( member_int @ Xa3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 7.94/5.76 => ( Y
% 7.94/5.76 = ( uminus_uminus_int
% 7.94/5.76 @ ( zero_n2684676970156552555ol_int
% 7.94/5.76 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 7.94/5.76 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa3 ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 7.94/5.76 & ( member_int @ Xa3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 7.94/5.76 => ( Y
% 7.94/5.76 = ( plus_plus_int
% 7.94/5.76 @ ( zero_n2684676970156552555ol_int
% 7.94/5.76 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 7.94/5.76 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa3 ) ) )
% 7.94/5.76 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 7.94/5.76 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % and_int.pelims
% 7.94/5.76 thf(fact_9109_and__int_Opsimps,axiom,
% 7.94/5.76 ! [K: int,L: int] :
% 7.94/5.76 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 7.94/5.76 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 7.94/5.76 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 7.94/5.76 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 7.94/5.76 = ( uminus_uminus_int
% 7.94/5.76 @ ( zero_n2684676970156552555ol_int
% 7.94/5.76 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 7.94/5.76 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 7.94/5.76 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 7.94/5.76 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 7.94/5.76 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 7.94/5.76 = ( plus_plus_int
% 7.94/5.76 @ ( zero_n2684676970156552555ol_int
% 7.94/5.76 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 7.94/5.76 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 7.94/5.76 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % and_int.psimps
% 7.94/5.76 thf(fact_9110_power__half__series,axiom,
% 7.94/5.76 ( sums_real
% 7.94/5.76 @ ^ [N3: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N3 ) )
% 7.94/5.76 @ one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % power_half_series
% 7.94/5.76 thf(fact_9111_sums__if_H,axiom,
% 7.94/5.76 ! [G: nat > real,X: real] :
% 7.94/5.76 ( ( sums_real @ G @ X )
% 7.94/5.76 => ( sums_real
% 7.94/5.76 @ ^ [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 ) ) ) ) )
% 7.94/5.76 @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % sums_if'
% 7.94/5.76 thf(fact_9112_sums__if,axiom,
% 7.94/5.76 ! [G: nat > real,X: real,F: nat > real,Y: real] :
% 7.94/5.76 ( ( sums_real @ G @ X )
% 7.94/5.76 => ( ( sums_real @ F @ Y )
% 7.94/5.76 => ( sums_real
% 7.94/5.76 @ ^ [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 ) ) ) ) )
% 7.94/5.76 @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sums_if
% 7.94/5.76 thf(fact_9113_and__int_Opinduct,axiom,
% 7.94/5.76 ! [A0: int,A1: int,P: int > int > $o] :
% 7.94/5.76 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 7.94/5.76 => ( ! [K2: int,L4: int] :
% 7.94/5.76 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 7.94/5.76 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 7.94/5.76 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 7.94/5.76 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 => ( P @ K2 @ L4 ) ) )
% 7.94/5.76 => ( P @ A0 @ A1 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % and_int.pinduct
% 7.94/5.76 thf(fact_9114_cos__paired,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( sums_real
% 7.94/5.76 @ ^ [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 ) ) )
% 7.94/5.76 @ ( cos_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_paired
% 7.94/5.76 thf(fact_9115_upto_Opinduct,axiom,
% 7.94/5.76 ! [A0: int,A1: int,P: int > int > $o] :
% 7.94/5.76 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 7.94/5.76 => ( ! [I3: int,J3: int] :
% 7.94/5.76 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J3 ) )
% 7.94/5.76 => ( ( ( ord_less_eq_int @ I3 @ J3 )
% 7.94/5.76 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) )
% 7.94/5.76 => ( P @ I3 @ J3 ) ) )
% 7.94/5.76 => ( P @ A0 @ A1 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % upto.pinduct
% 7.94/5.76 thf(fact_9116_cos__arcsin,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.94/5.76 => ( ( cos_real @ ( arcsin @ X ) )
% 7.94/5.76 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_arcsin
% 7.94/5.76 thf(fact_9117_arcsin__0,axiom,
% 7.94/5.76 ( ( arcsin @ zero_zero_real )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_0
% 7.94/5.76 thf(fact_9118_sin__arcsin,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ( sin_real @ ( arcsin @ Y ) )
% 7.94/5.76 = Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_arcsin
% 7.94/5.76 thf(fact_9119_arcsin__1,axiom,
% 7.94/5.76 ( ( arcsin @ one_one_real )
% 7.94/5.76 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_1
% 7.94/5.76 thf(fact_9120_arcsin__minus__1,axiom,
% 7.94/5.76 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 7.94/5.76 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_minus_1
% 7.94/5.76 thf(fact_9121_arcsin__minus,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.94/5.76 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 7.94/5.76 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_minus
% 7.94/5.76 thf(fact_9122_arcsin__le__arcsin,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_le_arcsin
% 7.94/5.76 thf(fact_9123_arcsin__le__mono,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_le_mono
% 7.94/5.76 thf(fact_9124_arcsin__eq__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 7.94/5.76 => ( ( ( arcsin @ X )
% 7.94/5.76 = ( arcsin @ Y ) )
% 7.94/5.76 = ( X = Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_eq_iff
% 7.94/5.76 thf(fact_9125_arcsin__less__arcsin,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_less_arcsin
% 7.94/5.76 thf(fact_9126_arcsin__less__mono,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 7.94/5.76 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 7.94/5.76 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_less_mono
% 7.94/5.76 thf(fact_9127_set__encode__def,axiom,
% 7.94/5.76 ( nat_set_encode
% 7.94/5.76 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % set_encode_def
% 7.94/5.76 thf(fact_9128_cos__arcsin__nonzero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ one_one_real )
% 7.94/5.76 => ( ( cos_real @ ( arcsin @ X ) )
% 7.94/5.76 != zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_arcsin_nonzero
% 7.94/5.76 thf(fact_9129_mask__eq__sum__exp__nat,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 7.94/5.76 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.94/5.76 @ ( collect_nat
% 7.94/5.76 @ ^ [Q6: nat] : ( ord_less_nat @ Q6 @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % mask_eq_sum_exp_nat
% 7.94/5.76 thf(fact_9130_gauss__sum__nat,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [X2: nat] : X2
% 7.94/5.76 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 7.94/5.76 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % gauss_sum_nat
% 7.94/5.76 thf(fact_9131_sum__power2,axiom,
% 7.94/5.76 ! [K: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 7.94/5.76 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 7.94/5.76
% 7.94/5.76 % sum_power2
% 7.94/5.76 thf(fact_9132_Sum__Ico__nat,axiom,
% 7.94/5.76 ! [M: nat,N: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [X2: nat] : X2
% 7.94/5.76 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 7.94/5.76 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Sum_Ico_nat
% 7.94/5.76 thf(fact_9133_arith__series__nat,axiom,
% 7.94/5.76 ! [A: nat,D2: nat,N: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I2 @ D2 ) )
% 7.94/5.76 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 7.94/5.76 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arith_series_nat
% 7.94/5.76 thf(fact_9134_Sum__Icc__nat,axiom,
% 7.94/5.76 ! [M: nat,N: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [X2: nat] : X2
% 7.94/5.76 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 7.94/5.76 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Sum_Icc_nat
% 7.94/5.76 thf(fact_9135_arcsin__lt__bounded,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ one_one_real )
% 7.94/5.76 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 7.94/5.76 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_lt_bounded
% 7.94/5.76 thf(fact_9136_arcsin__lbound,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_lbound
% 7.94/5.76 thf(fact_9137_arcsin__ubound,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_ubound
% 7.94/5.76 thf(fact_9138_arcsin__bounded,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 7.94/5.76 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_bounded
% 7.94/5.76 thf(fact_9139_arcsin__sin,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( arcsin @ ( sin_real @ X ) )
% 7.94/5.76 = X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_sin
% 7.94/5.76 thf(fact_9140_arcsin,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 7.94/5.76 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( sin_real @ ( arcsin @ Y ) )
% 7.94/5.76 = Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin
% 7.94/5.76 thf(fact_9141_arcsin__pi,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 7.94/5.76 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 7.94/5.76 & ( ( sin_real @ ( arcsin @ Y ) )
% 7.94/5.76 = Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_pi
% 7.94/5.76 thf(fact_9142_arcsin__le__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 7.94/5.76 = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_le_iff
% 7.94/5.76 thf(fact_9143_le__arcsin__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 7.94/5.76 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % le_arcsin_iff
% 7.94/5.76 thf(fact_9144_Chebyshev__sum__upper__nat,axiom,
% 7.94/5.76 ! [N: nat,A: nat > nat,B: nat > nat] :
% 7.94/5.76 ( ! [I3: nat,J3: nat] :
% 7.94/5.76 ( ( ord_less_eq_nat @ I3 @ J3 )
% 7.94/5.76 => ( ( ord_less_nat @ J3 @ N )
% 7.94/5.76 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J3 ) ) ) )
% 7.94/5.76 => ( ! [I3: nat,J3: nat] :
% 7.94/5.76 ( ( ord_less_eq_nat @ I3 @ J3 )
% 7.94/5.76 => ( ( ord_less_nat @ J3 @ N )
% 7.94/5.76 => ( ord_less_eq_nat @ ( B @ J3 ) @ ( B @ I3 ) ) ) )
% 7.94/5.76 => ( ord_less_eq_nat
% 7.94/5.76 @ ( times_times_nat @ N
% 7.94/5.76 @ ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [I2: nat] : ( times_times_nat @ ( A @ I2 ) @ ( B @ I2 ) )
% 7.94/5.76 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 7.94/5.76 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Chebyshev_sum_upper_nat
% 7.94/5.76 thf(fact_9145_Maclaurin__cos__expansion2,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ? [T6: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ T6 )
% 7.94/5.76 & ( ord_less_real @ T6 @ X )
% 7.94/5.76 & ( ( cos_real @ X )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( cos_coeff @ M4 ) @ ( power_power_real @ X @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_cos_expansion2
% 7.94/5.76 thf(fact_9146_Maclaurin__minus__cos__expansion,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_real @ X @ zero_zero_real )
% 7.94/5.76 => ? [T6: real] :
% 7.94/5.76 ( ( ord_less_real @ X @ T6 )
% 7.94/5.76 & ( ord_less_real @ T6 @ zero_zero_real )
% 7.94/5.76 & ( ( cos_real @ X )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( cos_coeff @ M4 ) @ ( power_power_real @ X @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_minus_cos_expansion
% 7.94/5.76 thf(fact_9147_lessThan__0,axiom,
% 7.94/5.76 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 7.94/5.76 = bot_bot_set_nat ) ).
% 7.94/5.76
% 7.94/5.76 % lessThan_0
% 7.94/5.76 thf(fact_9148_sumr__cos__zero__one,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( cos_coeff @ M4 ) @ ( power_power_real @ zero_zero_real @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % sumr_cos_zero_one
% 7.94/5.76 thf(fact_9149_lessThan__atLeast0,axiom,
% 7.94/5.76 ( set_ord_lessThan_nat
% 7.94/5.76 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 7.94/5.76
% 7.94/5.76 % lessThan_atLeast0
% 7.94/5.76 thf(fact_9150_lessThan__empty__iff,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( ( set_ord_lessThan_nat @ N )
% 7.94/5.76 = bot_bot_set_nat )
% 7.94/5.76 = ( N = zero_zero_nat ) ) ).
% 7.94/5.76
% 7.94/5.76 % lessThan_empty_iff
% 7.94/5.76 thf(fact_9151_lessThan__Suc,axiom,
% 7.94/5.76 ! [K: nat] :
% 7.94/5.76 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 7.94/5.76 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % lessThan_Suc
% 7.94/5.76 thf(fact_9152_lessThan__nat__numeral,axiom,
% 7.94/5.76 ! [K: num] :
% 7.94/5.76 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 7.94/5.76 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % lessThan_nat_numeral
% 7.94/5.76 thf(fact_9153_sum__roots__unity,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( ord_less_nat @ one_one_nat @ N )
% 7.94/5.76 => ( ( groups7754918857620584856omplex
% 7.94/5.76 @ ^ [X2: complex] : X2
% 7.94/5.76 @ ( collect_complex
% 7.94/5.76 @ ^ [Z6: complex] :
% 7.94/5.76 ( ( power_power_complex @ Z6 @ N )
% 7.94/5.76 = one_one_complex ) ) )
% 7.94/5.76 = zero_zero_complex ) ) ).
% 7.94/5.76
% 7.94/5.76 % sum_roots_unity
% 7.94/5.76 thf(fact_9154_sum__nth__roots,axiom,
% 7.94/5.76 ! [N: nat,C: complex] :
% 7.94/5.76 ( ( ord_less_nat @ one_one_nat @ N )
% 7.94/5.76 => ( ( groups7754918857620584856omplex
% 7.94/5.76 @ ^ [X2: complex] : X2
% 7.94/5.76 @ ( collect_complex
% 7.94/5.76 @ ^ [Z6: complex] :
% 7.94/5.76 ( ( power_power_complex @ Z6 @ N )
% 7.94/5.76 = C ) ) )
% 7.94/5.76 = zero_zero_complex ) ) ).
% 7.94/5.76
% 7.94/5.76 % sum_nth_roots
% 7.94/5.76 thf(fact_9155_atLeast1__lessThan__eq__remove0,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.94/5.76 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeast1_lessThan_eq_remove0
% 7.94/5.76 thf(fact_9156_Maclaurin__lemma,axiom,
% 7.94/5.76 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ H2 )
% 7.94/5.76 => ? [B9: real] :
% 7.94/5.76 ( ( F @ H2 )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M4 ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ H2 @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ B9 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_lemma
% 7.94/5.76 thf(fact_9157_sum__split__even__odd,axiom,
% 7.94/5.76 ! [F: nat > real,G: nat > real,N: nat] :
% 7.94/5.76 ( ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [I2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) @ ( F @ I2 ) @ ( G @ I2 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [I2: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) @ one_one_nat ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sum_split_even_odd
% 7.94/5.76 thf(fact_9158_Maclaurin__exp__le,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ? [T6: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 7.94/5.76 & ( ( exp_real @ X )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( divide_divide_real @ ( power_power_real @ X @ M4 ) @ ( semiri2265585572941072030t_real @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_exp_le
% 7.94/5.76 thf(fact_9159_Sum__Icc__int,axiom,
% 7.94/5.76 ! [M: int,N: int] :
% 7.94/5.76 ( ( ord_less_eq_int @ M @ N )
% 7.94/5.76 => ( ( groups4538972089207619220nt_int
% 7.94/5.76 @ ^ [X2: int] : X2
% 7.94/5.76 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 7.94/5.76 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Sum_Icc_int
% 7.94/5.76 thf(fact_9160_sum__pos__lt__pair,axiom,
% 7.94/5.76 ! [F: nat > real,K: nat] :
% 7.94/5.76 ( ( summable_real @ F )
% 7.94/5.76 => ( ! [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 ) ) ) ) )
% 7.94/5.76 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sum_pos_lt_pair
% 7.94/5.76 thf(fact_9161_Maclaurin__exp__lt,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ( ( X != zero_zero_real )
% 7.94/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ? [T6: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 7.94/5.76 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 7.94/5.76 & ( ( exp_real @ X )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( divide_divide_real @ ( power_power_real @ X @ M4 ) @ ( semiri2265585572941072030t_real @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_exp_lt
% 7.94/5.76 thf(fact_9162_Maclaurin__sin__expansion,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ? [T6: real] :
% 7.94/5.76 ( ( sin_real @ X )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( sin_coeff @ M4 ) @ ( power_power_real @ X @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_sin_expansion
% 7.94/5.76 thf(fact_9163_Maclaurin__sin__expansion2,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ? [T6: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 7.94/5.76 & ( ( sin_real @ X )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( sin_coeff @ M4 ) @ ( power_power_real @ X @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_sin_expansion2
% 7.94/5.76 thf(fact_9164_Maclaurin__cos__expansion,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ? [T6: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 7.94/5.76 & ( ( cos_real @ X )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( cos_coeff @ M4 ) @ ( power_power_real @ X @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_cos_expansion
% 7.94/5.76 thf(fact_9165_Maclaurin__sin__expansion4,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ? [T6: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ T6 )
% 7.94/5.76 & ( ord_less_eq_real @ T6 @ X )
% 7.94/5.76 & ( ( sin_real @ X )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( sin_coeff @ M4 ) @ ( power_power_real @ X @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_sin_expansion4
% 7.94/5.76 thf(fact_9166_Maclaurin__sin__expansion3,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ? [T6: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ T6 )
% 7.94/5.76 & ( ord_less_real @ T6 @ X )
% 7.94/5.76 & ( ( sin_real @ X )
% 7.94/5.76 = ( plus_plus_real
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( sin_coeff @ M4 ) @ ( power_power_real @ X @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) )
% 7.94/5.76 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_sin_expansion3
% 7.94/5.76 thf(fact_9167_sin__arccos__abs,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 7.94/5.76 => ( ( sin_real @ ( arccos @ Y ) )
% 7.94/5.76 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_arccos_abs
% 7.94/5.76 thf(fact_9168_sin__arccos,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.94/5.76 => ( ( sin_real @ ( arccos @ X ) )
% 7.94/5.76 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_arccos
% 7.94/5.76 thf(fact_9169_arccos__1,axiom,
% 7.94/5.76 ( ( arccos @ one_one_real )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_1
% 7.94/5.76 thf(fact_9170_arccos__minus__1,axiom,
% 7.94/5.76 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 7.94/5.76 = pi ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_minus_1
% 7.94/5.76 thf(fact_9171_atMost__0,axiom,
% 7.94/5.76 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 7.94/5.76 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 7.94/5.76
% 7.94/5.76 % atMost_0
% 7.94/5.76 thf(fact_9172_cos__arccos,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ( cos_real @ ( arccos @ Y ) )
% 7.94/5.76 = Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_arccos
% 7.94/5.76 thf(fact_9173_arccos__0,axiom,
% 7.94/5.76 ( ( arccos @ zero_zero_real )
% 7.94/5.76 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_0
% 7.94/5.76 thf(fact_9174_atMost__atLeast0,axiom,
% 7.94/5.76 ( set_ord_atMost_nat
% 7.94/5.76 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 7.94/5.76
% 7.94/5.76 % atMost_atLeast0
% 7.94/5.76 thf(fact_9175_lessThan__Suc__atMost,axiom,
% 7.94/5.76 ! [K: nat] :
% 7.94/5.76 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 7.94/5.76 = ( set_ord_atMost_nat @ K ) ) ).
% 7.94/5.76
% 7.94/5.76 % lessThan_Suc_atMost
% 7.94/5.76 thf(fact_9176_atMost__Suc,axiom,
% 7.94/5.76 ! [K: nat] :
% 7.94/5.76 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 7.94/5.76 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atMost_Suc
% 7.94/5.76 thf(fact_9177_atMost__nat__numeral,axiom,
% 7.94/5.76 ! [K: num] :
% 7.94/5.76 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 7.94/5.76 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atMost_nat_numeral
% 7.94/5.76 thf(fact_9178_arccos__le__arccos,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_le_arccos
% 7.94/5.76 thf(fact_9179_sum__choose__upper,axiom,
% 7.94/5.76 ! [M: nat,N: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 7.94/5.76 @ ( set_ord_atMost_nat @ N ) )
% 7.94/5.76 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sum_choose_upper
% 7.94/5.76 thf(fact_9180_arccos__le__mono,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_le_mono
% 7.94/5.76 thf(fact_9181_arccos__eq__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 7.94/5.76 => ( ( ( arccos @ X )
% 7.94/5.76 = ( arccos @ Y ) )
% 7.94/5.76 = ( X = Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_eq_iff
% 7.94/5.76 thf(fact_9182_sum__choose__lower,axiom,
% 7.94/5.76 ! [R2: nat,N: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 7.94/5.76 @ ( set_ord_atMost_nat @ N ) )
% 7.94/5.76 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N ) ) @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % sum_choose_lower
% 7.94/5.76 thf(fact_9183_choose__rising__sum_I2_J,axiom,
% 7.94/5.76 ! [N: nat,M: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N @ J2 ) @ N )
% 7.94/5.76 @ ( set_ord_atMost_nat @ M ) )
% 7.94/5.76 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 7.94/5.76
% 7.94/5.76 % choose_rising_sum(2)
% 7.94/5.76 thf(fact_9184_choose__rising__sum_I1_J,axiom,
% 7.94/5.76 ! [N: nat,M: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [J2: nat] : ( binomial @ ( plus_plus_nat @ N @ J2 ) @ N )
% 7.94/5.76 @ ( set_ord_atMost_nat @ M ) )
% 7.94/5.76 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % choose_rising_sum(1)
% 7.94/5.76 thf(fact_9185_arccos__lbound,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_lbound
% 7.94/5.76 thf(fact_9186_arccos__less__arccos,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_less_arccos
% 7.94/5.76 thf(fact_9187_arccos__less__mono,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 7.94/5.76 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 7.94/5.76 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_less_mono
% 7.94/5.76 thf(fact_9188_arccos__ubound,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_ubound
% 7.94/5.76 thf(fact_9189_arccos__cos,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ pi )
% 7.94/5.76 => ( ( arccos @ ( cos_real @ X ) )
% 7.94/5.76 = X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_cos
% 7.94/5.76 thf(fact_9190_cos__arccos__abs,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 7.94/5.76 => ( ( cos_real @ ( arccos @ Y ) )
% 7.94/5.76 = Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % cos_arccos_abs
% 7.94/5.76 thf(fact_9191_sum__choose__diagonal,axiom,
% 7.94/5.76 ! [M: nat,N: nat] :
% 7.94/5.76 ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.76 => ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 7.94/5.76 @ ( set_ord_atMost_nat @ M ) )
% 7.94/5.76 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sum_choose_diagonal
% 7.94/5.76 thf(fact_9192_vandermonde,axiom,
% 7.94/5.76 ! [M: nat,N: nat,R2: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 7.94/5.76 @ ( set_ord_atMost_nat @ R2 ) )
% 7.94/5.76 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % vandermonde
% 7.94/5.76 thf(fact_9193_arccos__lt__bounded,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_real @ Y @ one_one_real )
% 7.94/5.76 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 7.94/5.76 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_lt_bounded
% 7.94/5.76 thf(fact_9194_arccos__bounded,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 7.94/5.76 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_bounded
% 7.94/5.76 thf(fact_9195_sin__arccos__nonzero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ one_one_real )
% 7.94/5.76 => ( ( sin_real @ ( arccos @ X ) )
% 7.94/5.76 != zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sin_arccos_nonzero
% 7.94/5.76 thf(fact_9196_arccos__cos2,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 7.94/5.76 => ( ( arccos @ ( cos_real @ X ) )
% 7.94/5.76 = ( uminus_uminus_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_cos2
% 7.94/5.76 thf(fact_9197_arccos__minus,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.94/5.76 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 7.94/5.76 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_minus
% 7.94/5.76 thf(fact_9198_atLeast1__atMost__eq__remove0,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.94/5.76 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % atLeast1_atMost_eq_remove0
% 7.94/5.76 thf(fact_9199_choose__row__sum,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 7.94/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % choose_row_sum
% 7.94/5.76 thf(fact_9200_binomial,axiom,
% 7.94/5.76 ! [A: nat,B: nat,N: nat] :
% 7.94/5.76 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 7.94/5.76 = ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 7.94/5.76 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % binomial
% 7.94/5.76 thf(fact_9201_arccos,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 7.94/5.76 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 7.94/5.76 & ( ( cos_real @ ( arccos @ Y ) )
% 7.94/5.76 = Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos
% 7.94/5.76 thf(fact_9202_arccos__minus__abs,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 7.94/5.76 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 7.94/5.76 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_minus_abs
% 7.94/5.76 thf(fact_9203_polynomial__product__nat,axiom,
% 7.94/5.76 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 7.94/5.76 ( ! [I3: nat] :
% 7.94/5.76 ( ( ord_less_nat @ M @ I3 )
% 7.94/5.76 => ( ( A @ I3 )
% 7.94/5.76 = zero_zero_nat ) )
% 7.94/5.76 => ( ! [J3: nat] :
% 7.94/5.76 ( ( ord_less_nat @ N @ J3 )
% 7.94/5.76 => ( ( B @ J3 )
% 7.94/5.76 = zero_zero_nat ) )
% 7.94/5.76 => ( ( times_times_nat
% 7.94/5.76 @ ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [I2: nat] : ( times_times_nat @ ( A @ I2 ) @ ( power_power_nat @ X @ I2 ) )
% 7.94/5.76 @ ( set_ord_atMost_nat @ M ) )
% 7.94/5.76 @ ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [J2: nat] : ( times_times_nat @ ( B @ J2 ) @ ( power_power_nat @ X @ J2 ) )
% 7.94/5.76 @ ( set_ord_atMost_nat @ N ) ) )
% 7.94/5.76 = ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [R5: nat] :
% 7.94/5.76 ( times_times_nat
% 7.94/5.76 @ ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 7.94/5.76 @ ( set_ord_atMost_nat @ R5 ) )
% 7.94/5.76 @ ( power_power_nat @ X @ R5 ) )
% 7.94/5.76 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % polynomial_product_nat
% 7.94/5.76 thf(fact_9204_choose__square__sum,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.94/5.76 @ ( set_ord_atMost_nat @ N ) )
% 7.94/5.76 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % choose_square_sum
% 7.94/5.76 thf(fact_9205_arccos__le__pi2,axiom,
% 7.94/5.76 ! [Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 7.94/5.76 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_le_pi2
% 7.94/5.76 thf(fact_9206_binomial__r__part__sum,axiom,
% 7.94/5.76 ! [M: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 7.94/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % binomial_r_part_sum
% 7.94/5.76 thf(fact_9207_choose__linear__sum,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( groups3542108847815614940at_nat
% 7.94/5.76 @ ^ [I2: nat] : ( times_times_nat @ I2 @ ( binomial @ N @ I2 ) )
% 7.94/5.76 @ ( set_ord_atMost_nat @ N ) )
% 7.94/5.76 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % choose_linear_sum
% 7.94/5.76 thf(fact_9208_arccos__cos__eq__abs__2pi,axiom,
% 7.94/5.76 ! [Theta: real] :
% 7.94/5.76 ~ ! [K2: int] :
% 7.94/5.76 ( ( arccos @ ( cos_real @ Theta ) )
% 7.94/5.76 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_cos_eq_abs_2pi
% 7.94/5.76 thf(fact_9209_of__nat__id,axiom,
% 7.94/5.76 ( semiri1316708129612266289at_nat
% 7.94/5.76 = ( ^ [N3: nat] : N3 ) ) ).
% 7.94/5.76
% 7.94/5.76 % of_nat_id
% 7.94/5.76 thf(fact_9210_real__scaleR__def,axiom,
% 7.94/5.76 real_V1485227260804924795R_real = times_times_real ).
% 7.94/5.76
% 7.94/5.76 % real_scaleR_def
% 7.94/5.76 thf(fact_9211_Maclaurin__sin__bound,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ( ord_less_eq_real
% 7.94/5.76 @ ( abs_abs_real
% 7.94/5.76 @ ( minus_minus_real @ ( sin_real @ X )
% 7.94/5.76 @ ( groups6591440286371151544t_real
% 7.94/5.76 @ ^ [M4: nat] : ( times_times_real @ ( sin_coeff @ M4 ) @ ( power_power_real @ X @ M4 ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 7.94/5.76 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Maclaurin_sin_bound
% 7.94/5.76 thf(fact_9212_real__sqrt__inverse,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 7.94/5.76 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_sqrt_inverse
% 7.94/5.76 thf(fact_9213_divide__real__def,axiom,
% 7.94/5.76 ( divide_divide_real
% 7.94/5.76 = ( ^ [X2: real,Y6: real] : ( times_times_real @ X2 @ ( inverse_inverse_real @ Y6 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divide_real_def
% 7.94/5.76 thf(fact_9214_inverse__powr,axiom,
% 7.94/5.76 ! [Y: real,A: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 7.94/5.76 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % inverse_powr
% 7.94/5.76 thf(fact_9215_forall__pos__mono__1,axiom,
% 7.94/5.76 ! [P: real > $o,E: real] :
% 7.94/5.76 ( ! [D3: real,E2: real] :
% 7.94/5.76 ( ( ord_less_real @ D3 @ E2 )
% 7.94/5.76 => ( ( P @ D3 )
% 7.94/5.76 => ( P @ E2 ) ) )
% 7.94/5.76 => ( ! [N2: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ zero_zero_real @ E )
% 7.94/5.76 => ( P @ E ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % forall_pos_mono_1
% 7.94/5.76 thf(fact_9216_forall__pos__mono,axiom,
% 7.94/5.76 ! [P: real > $o,E: real] :
% 7.94/5.76 ( ! [D3: real,E2: real] :
% 7.94/5.76 ( ( ord_less_real @ D3 @ E2 )
% 7.94/5.76 => ( ( P @ D3 )
% 7.94/5.76 => ( P @ E2 ) ) )
% 7.94/5.76 => ( ! [N2: nat] :
% 7.94/5.76 ( ( N2 != zero_zero_nat )
% 7.94/5.76 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) )
% 7.94/5.76 => ( ( ord_less_real @ zero_zero_real @ E )
% 7.94/5.76 => ( P @ E ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % forall_pos_mono
% 7.94/5.76 thf(fact_9217_real__arch__inverse,axiom,
% 7.94/5.76 ! [E: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ E )
% 7.94/5.76 = ( ? [N3: nat] :
% 7.94/5.76 ( ( N3 != zero_zero_nat )
% 7.94/5.76 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 7.94/5.76 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ E ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_arch_inverse
% 7.94/5.76 thf(fact_9218_sqrt__divide__self__eq,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 7.94/5.76 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sqrt_divide_self_eq
% 7.94/5.76 thf(fact_9219_ln__inverse,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 7.94/5.76 = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % ln_inverse
% 7.94/5.76 thf(fact_9220_log__inverse,axiom,
% 7.94/5.76 ! [A: real,X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 7.94/5.76 => ( ( A != one_one_real )
% 7.94/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 7.94/5.76 = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % log_inverse
% 7.94/5.76 thf(fact_9221_exp__plus__inverse__exp,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % exp_plus_inverse_exp
% 7.94/5.76 thf(fact_9222_plus__inverse__ge__2,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % plus_inverse_ge_2
% 7.94/5.76 thf(fact_9223_real__inv__sqrt__pow2,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.94/5.76 = ( inverse_inverse_real @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_inv_sqrt_pow2
% 7.94/5.76 thf(fact_9224_tan__cot,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 7.94/5.76 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_cot
% 7.94/5.76 thf(fact_9225_real__le__x__sinh,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( 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 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_le_x_sinh
% 7.94/5.76 thf(fact_9226_real__le__abs__sinh,axiom,
% 7.94/5.76 ! [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 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_le_abs_sinh
% 7.94/5.76 thf(fact_9227_powr__real__of__int,axiom,
% 7.94/5.76 ! [X: real,N: int] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 7.94/5.76 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 7.94/5.76 = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 7.94/5.76 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 7.94/5.76 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 7.94/5.76 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % powr_real_of_int
% 7.94/5.76 thf(fact_9228_complex__unimodular__polar,axiom,
% 7.94/5.76 ! [Z: complex] :
% 7.94/5.76 ( ( ( real_V1022390504157884413omplex @ Z )
% 7.94/5.76 = one_one_real )
% 7.94/5.76 => ~ ! [T6: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 7.94/5.76 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 7.94/5.76 => ( Z
% 7.94/5.76 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_unimodular_polar
% 7.94/5.76 thf(fact_9229_sinh__real__zero__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ( sinh_real @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 = ( X = zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % sinh_real_zero_iff
% 7.94/5.76 thf(fact_9230_sinh__real__less__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 7.94/5.76 = ( ord_less_real @ X @ Y ) ) ).
% 7.94/5.76
% 7.94/5.76 % sinh_real_less_iff
% 7.94/5.76 thf(fact_9231_sinh__real__neg__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 7.94/5.76 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % sinh_real_neg_iff
% 7.94/5.76 thf(fact_9232_sinh__real__pos__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 7.94/5.76 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % sinh_real_pos_iff
% 7.94/5.76 thf(fact_9233_sinh__real__nonneg__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 7.94/5.76 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % sinh_real_nonneg_iff
% 7.94/5.76 thf(fact_9234_sinh__real__nonpos__iff,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 7.94/5.76 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % sinh_real_nonpos_iff
% 7.94/5.76 thf(fact_9235_norm__cos__sin,axiom,
% 7.94/5.76 ! [T: real] :
% 7.94/5.76 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % norm_cos_sin
% 7.94/5.76 thf(fact_9236_complex__scaleR,axiom,
% 7.94/5.76 ! [R2: real,A: real,B: real] :
% 7.94/5.76 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 7.94/5.76 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_scaleR
% 7.94/5.76 thf(fact_9237_cosh__real__nonzero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( cosh_real @ X )
% 7.94/5.76 != zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_real_nonzero
% 7.94/5.76 thf(fact_9238_complex__of__real__def,axiom,
% 7.94/5.76 ( real_V4546457046886955230omplex
% 7.94/5.76 = ( ^ [R5: real] : ( complex2 @ R5 @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_of_real_def
% 7.94/5.76 thf(fact_9239_complex__of__real__code,axiom,
% 7.94/5.76 ( real_V4546457046886955230omplex
% 7.94/5.76 = ( ^ [X2: real] : ( complex2 @ X2 @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_of_real_code
% 7.94/5.76 thf(fact_9240_complex__eq__cancel__iff2,axiom,
% 7.94/5.76 ! [X: real,Y: real,Xa3: real] :
% 7.94/5.76 ( ( ( complex2 @ X @ Y )
% 7.94/5.76 = ( real_V4546457046886955230omplex @ Xa3 ) )
% 7.94/5.76 = ( ( X = Xa3 )
% 7.94/5.76 & ( Y = zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_eq_cancel_iff2
% 7.94/5.76 thf(fact_9241_sinh__less__cosh__real,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % sinh_less_cosh_real
% 7.94/5.76 thf(fact_9242_complex__of__real__mult__Complex,axiom,
% 7.94/5.76 ! [R2: real,X: real,Y: real] :
% 7.94/5.76 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y ) )
% 7.94/5.76 = ( complex2 @ ( times_times_real @ R2 @ X ) @ ( times_times_real @ R2 @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_of_real_mult_Complex
% 7.94/5.76 thf(fact_9243_Complex__mult__complex__of__real,axiom,
% 7.94/5.76 ! [X: real,Y: real,R2: real] :
% 7.94/5.76 ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 7.94/5.76 = ( complex2 @ ( times_times_real @ X @ R2 ) @ ( times_times_real @ Y @ R2 ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Complex_mult_complex_of_real
% 7.94/5.76 thf(fact_9244_Complex__eq__numeral,axiom,
% 7.94/5.76 ! [A: real,B: real,W: num] :
% 7.94/5.76 ( ( ( complex2 @ A @ B )
% 7.94/5.76 = ( numera6690914467698888265omplex @ W ) )
% 7.94/5.76 = ( ( A
% 7.94/5.76 = ( numeral_numeral_real @ W ) )
% 7.94/5.76 & ( B = zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Complex_eq_numeral
% 7.94/5.76 thf(fact_9245_cosh__real__pos,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_real_pos
% 7.94/5.76 thf(fact_9246_cosh__real__nonpos__le__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_real_nonpos_le_iff
% 7.94/5.76 thf(fact_9247_cosh__real__nonneg__le__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_real_nonneg_le_iff
% 7.94/5.76 thf(fact_9248_cosh__real__nonneg,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_real_nonneg
% 7.94/5.76 thf(fact_9249_cosh__real__ge__1,axiom,
% 7.94/5.76 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_real_ge_1
% 7.94/5.76 thf(fact_9250_Complex__eq__0,axiom,
% 7.94/5.76 ! [A: real,B: real] :
% 7.94/5.76 ( ( ( complex2 @ A @ B )
% 7.94/5.76 = zero_zero_complex )
% 7.94/5.76 = ( ( A = zero_zero_real )
% 7.94/5.76 & ( B = zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Complex_eq_0
% 7.94/5.76 thf(fact_9251_zero__complex_Ocode,axiom,
% 7.94/5.76 ( zero_zero_complex
% 7.94/5.76 = ( complex2 @ zero_zero_real @ zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % zero_complex.code
% 7.94/5.76 thf(fact_9252_cosh__real__strict__mono,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ Y )
% 7.94/5.76 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_real_strict_mono
% 7.94/5.76 thf(fact_9253_cosh__real__nonneg__less__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.76 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 7.94/5.76 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_real_nonneg_less_iff
% 7.94/5.76 thf(fact_9254_cosh__real__nonpos__less__iff,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.94/5.76 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 7.94/5.76 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 7.94/5.76 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_real_nonpos_less_iff
% 7.94/5.76 thf(fact_9255_Complex__eq__neg__numeral,axiom,
% 7.94/5.76 ! [A: real,B: real,W: num] :
% 7.94/5.76 ( ( ( complex2 @ A @ B )
% 7.94/5.76 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 7.94/5.76 = ( ( A
% 7.94/5.76 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 7.94/5.76 & ( B = zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Complex_eq_neg_numeral
% 7.94/5.76 thf(fact_9256_complex__mult,axiom,
% 7.94/5.76 ! [A: real,B: real,C: real,D2: real] :
% 7.94/5.76 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D2 ) )
% 7.94/5.76 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D2 ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D2 ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_mult
% 7.94/5.76 thf(fact_9257_one__complex_Ocode,axiom,
% 7.94/5.76 ( one_one_complex
% 7.94/5.76 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % one_complex.code
% 7.94/5.76 thf(fact_9258_Complex__eq__1,axiom,
% 7.94/5.76 ! [A: real,B: real] :
% 7.94/5.76 ( ( ( complex2 @ A @ B )
% 7.94/5.76 = one_one_complex )
% 7.94/5.76 = ( ( A = one_one_real )
% 7.94/5.76 & ( B = zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Complex_eq_1
% 7.94/5.76 thf(fact_9259_complex__inverse,axiom,
% 7.94/5.76 ! [A: real,B: real] :
% 7.94/5.76 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 7.94/5.76 = ( 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 ) ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_inverse
% 7.94/5.76 thf(fact_9260_arcosh__cosh__real,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 7.94/5.76 = X ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcosh_cosh_real
% 7.94/5.76 thf(fact_9261_Complex__eq__neg__1,axiom,
% 7.94/5.76 ! [A: real,B: real] :
% 7.94/5.76 ( ( ( complex2 @ A @ B )
% 7.94/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 7.94/5.76 = ( ( A
% 7.94/5.76 = ( uminus_uminus_real @ one_one_real ) )
% 7.94/5.76 & ( B = zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Complex_eq_neg_1
% 7.94/5.76 thf(fact_9262_complex__norm,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y ) )
% 7.94/5.76 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_norm
% 7.94/5.76 thf(fact_9263_cosh__ln__real,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 7.94/5.76 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cosh_ln_real
% 7.94/5.76 thf(fact_9264_sinh__ln__real,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 7.94/5.76 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % sinh_ln_real
% 7.94/5.76 thf(fact_9265_cot__less__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ zero_zero_real )
% 7.94/5.76 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cot_less_zero
% 7.94/5.76 thf(fact_9266_cot__pi,axiom,
% 7.94/5.76 ( ( cot_real @ pi )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % cot_pi
% 7.94/5.76 thf(fact_9267_cot__npi,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % cot_npi
% 7.94/5.76 thf(fact_9268_cot__periodic,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 7.94/5.76 = ( cot_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % cot_periodic
% 7.94/5.76 thf(fact_9269_cot__gt__zero,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cot_gt_zero
% 7.94/5.76 thf(fact_9270_tan__cot_H,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 7.94/5.76 = ( cot_real @ X ) ) ).
% 7.94/5.76
% 7.94/5.76 % tan_cot'
% 7.94/5.76 thf(fact_9271_exp__two__pi__i_H,axiom,
% 7.94/5.76 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 = one_one_complex ) ).
% 7.94/5.76
% 7.94/5.76 % exp_two_pi_i'
% 7.94/5.76 thf(fact_9272_exp__two__pi__i,axiom,
% 7.94/5.76 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 7.94/5.76 = one_one_complex ) ).
% 7.94/5.76
% 7.94/5.76 % exp_two_pi_i
% 7.94/5.76 thf(fact_9273_VEBTi_Osize_I3_J,axiom,
% 7.94/5.76 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( size_size_VEBT_VEBTi @ ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 ) )
% 7.94/5.76 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_a6397454172108246045_VEBTi @ size_size_VEBT_VEBTi @ X13 ) @ ( size_size_VEBT_VEBTi @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBTi.size(3)
% 7.94/5.76 thf(fact_9274_mask__nat__positive__iff,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 7.94/5.76 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % mask_nat_positive_iff
% 7.94/5.76 thf(fact_9275_norm__ii,axiom,
% 7.94/5.76 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % norm_ii
% 7.94/5.76 thf(fact_9276_i__squared,axiom,
% 7.94/5.76 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 7.94/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.94/5.76
% 7.94/5.76 % i_squared
% 7.94/5.76 thf(fact_9277_power2__i,axiom,
% 7.94/5.76 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.94/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.94/5.76
% 7.94/5.76 % power2_i
% 7.94/5.76 thf(fact_9278_exp__pi__i,axiom,
% 7.94/5.76 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 7.94/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.94/5.76
% 7.94/5.76 % exp_pi_i
% 7.94/5.76 thf(fact_9279_exp__pi__i_H,axiom,
% 7.94/5.76 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 7.94/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.94/5.76
% 7.94/5.76 % exp_pi_i'
% 7.94/5.76 thf(fact_9280_i__even__power,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % i_even_power
% 7.94/5.76 thf(fact_9281_less__eq__mask,axiom,
% 7.94/5.76 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % less_eq_mask
% 7.94/5.76 thf(fact_9282_nat__mask__eq,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 7.94/5.76 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % nat_mask_eq
% 7.94/5.76 thf(fact_9283_complex__i__not__one,axiom,
% 7.94/5.76 imaginary_unit != one_one_complex ).
% 7.94/5.76
% 7.94/5.76 % complex_i_not_one
% 7.94/5.76 thf(fact_9284_complex__i__not__zero,axiom,
% 7.94/5.76 imaginary_unit != zero_zero_complex ).
% 7.94/5.76
% 7.94/5.76 % complex_i_not_zero
% 7.94/5.76 thf(fact_9285_mask__nonnegative__int,axiom,
% 7.94/5.76 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % mask_nonnegative_int
% 7.94/5.76 thf(fact_9286_not__mask__negative__int,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 7.94/5.76
% 7.94/5.76 % not_mask_negative_int
% 7.94/5.76 thf(fact_9287_less__mask,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.94/5.76 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % less_mask
% 7.94/5.76 thf(fact_9288_Complex__eq__i,axiom,
% 7.94/5.76 ! [X: real,Y: real] :
% 7.94/5.76 ( ( ( complex2 @ X @ Y )
% 7.94/5.76 = imaginary_unit )
% 7.94/5.76 = ( ( X = zero_zero_real )
% 7.94/5.76 & ( Y = one_one_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Complex_eq_i
% 7.94/5.76 thf(fact_9289_imaginary__unit_Ocode,axiom,
% 7.94/5.76 ( imaginary_unit
% 7.94/5.76 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % imaginary_unit.code
% 7.94/5.76 thf(fact_9290_take__bit__eq__mask__iff,axiom,
% 7.94/5.76 ! [N: nat,K: int] :
% 7.94/5.76 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 7.94/5.76 = ( bit_se2000444600071755411sk_int @ N ) )
% 7.94/5.76 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 7.94/5.76 = zero_zero_int ) ) ).
% 7.94/5.76
% 7.94/5.76 % take_bit_eq_mask_iff
% 7.94/5.76 thf(fact_9291_i__complex__of__real,axiom,
% 7.94/5.76 ! [R2: real] :
% 7.94/5.76 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 7.94/5.76 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % i_complex_of_real
% 7.94/5.76 thf(fact_9292_complex__of__real__i,axiom,
% 7.94/5.76 ! [R2: real] :
% 7.94/5.76 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 7.94/5.76 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 7.94/5.76
% 7.94/5.76 % complex_of_real_i
% 7.94/5.76 thf(fact_9293_Suc__mask__eq__exp,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 7.94/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % Suc_mask_eq_exp
% 7.94/5.76 thf(fact_9294_mask__nat__less__exp,axiom,
% 7.94/5.76 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % mask_nat_less_exp
% 7.94/5.76 thf(fact_9295_mask__half__int,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.94/5.76 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % mask_half_int
% 7.94/5.76 thf(fact_9296_mask__int__def,axiom,
% 7.94/5.76 ( bit_se2000444600071755411sk_int
% 7.94/5.76 = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % mask_int_def
% 7.94/5.76 thf(fact_9297_mask__nat__def,axiom,
% 7.94/5.76 ( bit_se2002935070580805687sk_nat
% 7.94/5.76 = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % mask_nat_def
% 7.94/5.76 thf(fact_9298_cmod__unit__one,axiom,
% 7.94/5.76 ! [A: real] :
% 7.94/5.76 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % cmod_unit_one
% 7.94/5.76 thf(fact_9299_take__bit__eq__mask__iff__exp__dvd,axiom,
% 7.94/5.76 ! [N: nat,K: int] :
% 7.94/5.76 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 7.94/5.76 = ( bit_se2000444600071755411sk_int @ N ) )
% 7.94/5.76 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % take_bit_eq_mask_iff_exp_dvd
% 7.94/5.76 thf(fact_9300_VEBTi_Osize__gen_I1_J,axiom,
% 7.94/5.76 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi] :
% 7.94/5.76 ( ( vEBT_size_VEBTi @ ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 ) )
% 7.94/5.76 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_a6397454172108246045_VEBTi @ vEBT_size_VEBTi @ X13 ) @ ( vEBT_size_VEBTi @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % VEBTi.size_gen(1)
% 7.94/5.76 thf(fact_9301_Arg__minus__ii,axiom,
% 7.94/5.76 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 7.94/5.76 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Arg_minus_ii
% 7.94/5.76 thf(fact_9302_csqrt__ii,axiom,
% 7.94/5.76 ( ( csqrt @ imaginary_unit )
% 7.94/5.76 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % csqrt_ii
% 7.94/5.76 thf(fact_9303_csqrt__eq__0,axiom,
% 7.94/5.76 ! [Z: complex] :
% 7.94/5.76 ( ( ( csqrt @ Z )
% 7.94/5.76 = zero_zero_complex )
% 7.94/5.76 = ( Z = zero_zero_complex ) ) ).
% 7.94/5.76
% 7.94/5.76 % csqrt_eq_0
% 7.94/5.76 thf(fact_9304_csqrt__0,axiom,
% 7.94/5.76 ( ( csqrt @ zero_zero_complex )
% 7.94/5.76 = zero_zero_complex ) ).
% 7.94/5.76
% 7.94/5.76 % csqrt_0
% 7.94/5.76 thf(fact_9305_csqrt__1,axiom,
% 7.94/5.76 ( ( csqrt @ one_one_complex )
% 7.94/5.76 = one_one_complex ) ).
% 7.94/5.76
% 7.94/5.76 % csqrt_1
% 7.94/5.76 thf(fact_9306_csqrt__eq__1,axiom,
% 7.94/5.76 ! [Z: complex] :
% 7.94/5.76 ( ( ( csqrt @ Z )
% 7.94/5.76 = one_one_complex )
% 7.94/5.76 = ( Z = one_one_complex ) ) ).
% 7.94/5.76
% 7.94/5.76 % csqrt_eq_1
% 7.94/5.76 thf(fact_9307_power2__csqrt,axiom,
% 7.94/5.76 ! [Z: complex] :
% 7.94/5.76 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 7.94/5.76 = Z ) ).
% 7.94/5.76
% 7.94/5.76 % power2_csqrt
% 7.94/5.76 thf(fact_9308_Arg__ii,axiom,
% 7.94/5.76 ( ( arg @ imaginary_unit )
% 7.94/5.76 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Arg_ii
% 7.94/5.76 thf(fact_9309_Arg__zero,axiom,
% 7.94/5.76 ( ( arg @ zero_zero_complex )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % Arg_zero
% 7.94/5.76 thf(fact_9310_of__real__sqrt,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 7.94/5.76 = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % of_real_sqrt
% 7.94/5.76 thf(fact_9311_Arg__bounded,axiom,
% 7.94/5.76 ! [Z: complex] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 7.94/5.76 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 7.94/5.76
% 7.94/5.76 % Arg_bounded
% 7.94/5.76 thf(fact_9312_cis__minus__pi__half,axiom,
% 7.94/5.76 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 7.94/5.76 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 7.94/5.76
% 7.94/5.76 % cis_minus_pi_half
% 7.94/5.76 thf(fact_9313_divmod__BitM__2__eq,axiom,
% 7.94/5.76 ! [M: num] :
% 7.94/5.76 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 7.94/5.76 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 7.94/5.76
% 7.94/5.76 % divmod_BitM_2_eq
% 7.94/5.76 thf(fact_9314_norm__cis,axiom,
% 7.94/5.76 ! [A: real] :
% 7.94/5.76 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 7.94/5.76 = one_one_real ) ).
% 7.94/5.76
% 7.94/5.76 % norm_cis
% 7.94/5.76 thf(fact_9315_cis__zero,axiom,
% 7.94/5.76 ( ( cis @ zero_zero_real )
% 7.94/5.76 = one_one_complex ) ).
% 7.94/5.76
% 7.94/5.76 % cis_zero
% 7.94/5.76 thf(fact_9316_pred__numeral__simps_I2_J,axiom,
% 7.94/5.76 ! [K: num] :
% 7.94/5.76 ( ( pred_numeral @ ( bit0 @ K ) )
% 7.94/5.76 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % pred_numeral_simps(2)
% 7.94/5.76 thf(fact_9317_cis__pi,axiom,
% 7.94/5.76 ( ( cis @ pi )
% 7.94/5.76 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 7.94/5.76
% 7.94/5.76 % cis_pi
% 7.94/5.76 thf(fact_9318_cis__pi__half,axiom,
% 7.94/5.76 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 = imaginary_unit ) ).
% 7.94/5.76
% 7.94/5.76 % cis_pi_half
% 7.94/5.76 thf(fact_9319_cis__2pi,axiom,
% 7.94/5.76 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 7.94/5.76 = one_one_complex ) ).
% 7.94/5.76
% 7.94/5.76 % cis_2pi
% 7.94/5.76 thf(fact_9320_cis__neq__zero,axiom,
% 7.94/5.76 ! [A: real] :
% 7.94/5.76 ( ( cis @ A )
% 7.94/5.76 != zero_zero_complex ) ).
% 7.94/5.76
% 7.94/5.76 % cis_neq_zero
% 7.94/5.76 thf(fact_9321_semiring__norm_I26_J,axiom,
% 7.94/5.76 ( ( bitM @ one )
% 7.94/5.76 = one ) ).
% 7.94/5.76
% 7.94/5.76 % semiring_norm(26)
% 7.94/5.76 thf(fact_9322_semiring__norm_I27_J,axiom,
% 7.94/5.76 ! [N: num] :
% 7.94/5.76 ( ( bitM @ ( bit0 @ N ) )
% 7.94/5.76 = ( bit1 @ ( bitM @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % semiring_norm(27)
% 7.94/5.76 thf(fact_9323_semiring__norm_I28_J,axiom,
% 7.94/5.76 ! [N: num] :
% 7.94/5.76 ( ( bitM @ ( bit1 @ N ) )
% 7.94/5.76 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % semiring_norm(28)
% 7.94/5.76 thf(fact_9324_inc__BitM__eq,axiom,
% 7.94/5.76 ! [N: num] :
% 7.94/5.76 ( ( inc @ ( bitM @ N ) )
% 7.94/5.76 = ( bit0 @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % inc_BitM_eq
% 7.94/5.76 thf(fact_9325_BitM__inc__eq,axiom,
% 7.94/5.76 ! [N: num] :
% 7.94/5.76 ( ( bitM @ ( inc @ N ) )
% 7.94/5.76 = ( bit1 @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % BitM_inc_eq
% 7.94/5.76 thf(fact_9326_cis__Arg,axiom,
% 7.94/5.76 ! [Z: complex] :
% 7.94/5.76 ( ( Z != zero_zero_complex )
% 7.94/5.76 => ( ( cis @ ( arg @ Z ) )
% 7.94/5.76 = ( sgn_sgn_complex @ Z ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cis_Arg
% 7.94/5.76 thf(fact_9327_eval__nat__numeral_I2_J,axiom,
% 7.94/5.76 ! [N: num] :
% 7.94/5.76 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 7.94/5.76 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % eval_nat_numeral(2)
% 7.94/5.76 thf(fact_9328_one__plus__BitM,axiom,
% 7.94/5.76 ! [N: num] :
% 7.94/5.76 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 7.94/5.76 = ( bit0 @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % one_plus_BitM
% 7.94/5.76 thf(fact_9329_BitM__plus__one,axiom,
% 7.94/5.76 ! [N: num] :
% 7.94/5.76 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 7.94/5.76 = ( bit0 @ N ) ) ).
% 7.94/5.76
% 7.94/5.76 % BitM_plus_one
% 7.94/5.76 thf(fact_9330_DeMoivre,axiom,
% 7.94/5.76 ! [A: real,N: nat] :
% 7.94/5.76 ( ( power_power_complex @ ( cis @ A ) @ N )
% 7.94/5.76 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % DeMoivre
% 7.94/5.76 thf(fact_9331_cis__Arg__unique,axiom,
% 7.94/5.76 ! [Z: complex,X: real] :
% 7.94/5.76 ( ( ( sgn_sgn_complex @ Z )
% 7.94/5.76 = ( cis @ X ) )
% 7.94/5.76 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 7.94/5.76 => ( ( ord_less_eq_real @ X @ pi )
% 7.94/5.76 => ( ( arg @ Z )
% 7.94/5.76 = X ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % cis_Arg_unique
% 7.94/5.76 thf(fact_9332_Arg__correct,axiom,
% 7.94/5.76 ! [Z: complex] :
% 7.94/5.76 ( ( Z != zero_zero_complex )
% 7.94/5.76 => ( ( ( sgn_sgn_complex @ Z )
% 7.94/5.76 = ( cis @ ( arg @ Z ) ) )
% 7.94/5.76 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 7.94/5.76 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Arg_correct
% 7.94/5.76 thf(fact_9333_bij__betw__roots__unity,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( bij_betw_nat_complex
% 7.94/5.76 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 7.94/5.76 @ ( set_ord_lessThan_nat @ N )
% 7.94/5.76 @ ( collect_complex
% 7.94/5.76 @ ^ [Z6: complex] :
% 7.94/5.76 ( ( power_power_complex @ Z6 @ N )
% 7.94/5.76 = one_one_complex ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % bij_betw_roots_unity
% 7.94/5.76 thf(fact_9334_divmod__step__nat__def,axiom,
% 7.94/5.76 ( unique5026877609467782581ep_nat
% 7.94/5.76 = ( ^ [L2: num] :
% 7.94/5.76 ( produc2626176000494625587at_nat
% 7.94/5.76 @ ^ [Q6: 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 ) ) @ Q6 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ R5 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divmod_step_nat_def
% 7.94/5.76 thf(fact_9335_divmod__step__int__def,axiom,
% 7.94/5.76 ( unique5024387138958732305ep_int
% 7.94/5.76 = ( ^ [L2: num] :
% 7.94/5.76 ( produc4245557441103728435nt_int
% 7.94/5.76 @ ^ [Q6: 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 ) ) @ Q6 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ R5 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divmod_step_int_def
% 7.94/5.76 thf(fact_9336_divmod__step__integer__def,axiom,
% 7.94/5.76 ( unique4921790084139445826nteger
% 7.94/5.76 = ( ^ [L2: num] :
% 7.94/5.76 ( produc6916734918728496179nteger
% 7.94/5.76 @ ^ [Q6: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ R5 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divmod_step_integer_def
% 7.94/5.76 thf(fact_9337_divmod__nat__if,axiom,
% 7.94/5.76 ( divmod_nat
% 7.94/5.76 = ( ^ [M4: nat,N3: nat] :
% 7.94/5.76 ( if_Pro6206227464963214023at_nat
% 7.94/5.76 @ ( ( N3 = zero_zero_nat )
% 7.94/5.76 | ( ord_less_nat @ M4 @ N3 ) )
% 7.94/5.76 @ ( product_Pair_nat_nat @ zero_zero_nat @ M4 )
% 7.94/5.76 @ ( produc2626176000494625587at_nat
% 7.94/5.76 @ ^ [Q6: nat] : ( product_Pair_nat_nat @ ( suc @ Q6 ) )
% 7.94/5.76 @ ( divmod_nat @ ( minus_minus_nat @ M4 @ N3 ) @ N3 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divmod_nat_if
% 7.94/5.76 thf(fact_9338_Arg__def,axiom,
% 7.94/5.76 ( arg
% 7.94/5.76 = ( ^ [Z6: complex] :
% 7.94/5.76 ( if_real @ ( Z6 = zero_zero_complex ) @ zero_zero_real
% 7.94/5.76 @ ( fChoice_real
% 7.94/5.76 @ ^ [A3: real] :
% 7.94/5.76 ( ( ( sgn_sgn_complex @ Z6 )
% 7.94/5.76 = ( cis @ A3 ) )
% 7.94/5.76 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 7.94/5.76 & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % Arg_def
% 7.94/5.76 thf(fact_9339_arctan__def,axiom,
% 7.94/5.76 ( arctan
% 7.94/5.76 = ( ^ [Y6: real] :
% 7.94/5.76 ( the_real
% 7.94/5.76 @ ^ [X2: real] :
% 7.94/5.76 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 7.94/5.76 & ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( tan_real @ X2 )
% 7.94/5.76 = Y6 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arctan_def
% 7.94/5.76 thf(fact_9340_ln__neg__is__const,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 7.94/5.76 => ( ( ln_ln_real @ X )
% 7.94/5.76 = ( the_real
% 7.94/5.76 @ ^ [X2: real] : $false ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % ln_neg_is_const
% 7.94/5.76 thf(fact_9341_arccos__def,axiom,
% 7.94/5.76 ( arccos
% 7.94/5.76 = ( ^ [Y6: real] :
% 7.94/5.76 ( the_real
% 7.94/5.76 @ ^ [X2: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 7.94/5.76 & ( ord_less_eq_real @ X2 @ pi )
% 7.94/5.76 & ( ( cos_real @ X2 )
% 7.94/5.76 = Y6 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arccos_def
% 7.94/5.76 thf(fact_9342_divmod__nat__def,axiom,
% 7.94/5.76 ( divmod_nat
% 7.94/5.76 = ( ^ [M4: nat,N3: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M4 @ N3 ) @ ( modulo_modulo_nat @ M4 @ N3 ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % divmod_nat_def
% 7.94/5.76 thf(fact_9343_pi__half,axiom,
% 7.94/5.76 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 = ( the_real
% 7.94/5.76 @ ^ [X2: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 7.94/5.76 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 & ( ( cos_real @ X2 )
% 7.94/5.76 = zero_zero_real ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % pi_half
% 7.94/5.76 thf(fact_9344_pi__def,axiom,
% 7.94/5.76 ( pi
% 7.94/5.76 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 7.94/5.76 @ ( the_real
% 7.94/5.76 @ ^ [X2: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 7.94/5.76 & ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 7.94/5.76 & ( ( cos_real @ X2 )
% 7.94/5.76 = zero_zero_real ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % pi_def
% 7.94/5.76 thf(fact_9345_arcsin__def,axiom,
% 7.94/5.76 ( arcsin
% 7.94/5.76 = ( ^ [Y6: real] :
% 7.94/5.76 ( the_real
% 7.94/5.76 @ ^ [X2: real] :
% 7.94/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 7.94/5.76 & ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 7.94/5.76 & ( ( sin_real @ X2 )
% 7.94/5.76 = Y6 ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % arcsin_def
% 7.94/5.76 thf(fact_9346_bij__betw__nth__root__unity,axiom,
% 7.94/5.76 ! [C: complex,N: nat] :
% 7.94/5.76 ( ( C != zero_zero_complex )
% 7.94/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 7.94/5.76 @ ( collect_complex
% 7.94/5.76 @ ^ [Z6: complex] :
% 7.94/5.76 ( ( power_power_complex @ Z6 @ N )
% 7.94/5.76 = one_one_complex ) )
% 7.94/5.76 @ ( collect_complex
% 7.94/5.76 @ ^ [Z6: complex] :
% 7.94/5.76 ( ( power_power_complex @ Z6 @ N )
% 7.94/5.76 = C ) ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % bij_betw_nth_root_unity
% 7.94/5.76 thf(fact_9347_real__root__zero,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( root @ N @ zero_zero_real )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_zero
% 7.94/5.76 thf(fact_9348_real__root__Suc__0,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 7.94/5.76 = X ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_Suc_0
% 7.94/5.76 thf(fact_9349_real__root__eq__iff,axiom,
% 7.94/5.76 ! [N: nat,X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ( root @ N @ X )
% 7.94/5.76 = ( root @ N @ Y ) )
% 7.94/5.76 = ( X = Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_eq_iff
% 7.94/5.76 thf(fact_9350_root__0,axiom,
% 7.94/5.76 ! [X: real] :
% 7.94/5.76 ( ( root @ zero_zero_nat @ X )
% 7.94/5.76 = zero_zero_real ) ).
% 7.94/5.76
% 7.94/5.76 % root_0
% 7.94/5.76 thf(fact_9351_real__root__eq__0__iff,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ( root @ N @ X )
% 7.94/5.76 = zero_zero_real )
% 7.94/5.76 = ( X = zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_eq_0_iff
% 7.94/5.76 thf(fact_9352_real__root__less__iff,axiom,
% 7.94/5.76 ! [N: nat,X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 7.94/5.76 = ( ord_less_real @ X @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_less_iff
% 7.94/5.76 thf(fact_9353_real__root__le__iff,axiom,
% 7.94/5.76 ! [N: nat,X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_le_iff
% 7.94/5.76 thf(fact_9354_real__root__one,axiom,
% 7.94/5.76 ! [N: nat] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( root @ N @ one_one_real )
% 7.94/5.76 = one_one_real ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_one
% 7.94/5.76 thf(fact_9355_real__root__eq__1__iff,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ( root @ N @ X )
% 7.94/5.76 = one_one_real )
% 7.94/5.76 = ( X = one_one_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_eq_1_iff
% 7.94/5.76 thf(fact_9356_real__root__gt__0__iff,axiom,
% 7.94/5.76 ! [N: nat,Y: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 7.94/5.76 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_gt_0_iff
% 7.94/5.76 thf(fact_9357_real__root__lt__0__iff,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 7.94/5.76 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_lt_0_iff
% 7.94/5.76 thf(fact_9358_real__root__ge__0__iff,axiom,
% 7.94/5.76 ! [N: nat,Y: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_ge_0_iff
% 7.94/5.76 thf(fact_9359_real__root__le__0__iff,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 7.94/5.76 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_le_0_iff
% 7.94/5.76 thf(fact_9360_real__root__gt__1__iff,axiom,
% 7.94/5.76 ! [N: nat,Y: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 7.94/5.76 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_gt_1_iff
% 7.94/5.76 thf(fact_9361_real__root__lt__1__iff,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 7.94/5.76 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_lt_1_iff
% 7.94/5.76 thf(fact_9362_real__root__ge__1__iff,axiom,
% 7.94/5.76 ! [N: nat,Y: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 7.94/5.76 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_ge_1_iff
% 7.94/5.76 thf(fact_9363_real__root__le__1__iff,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 7.94/5.76 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_le_1_iff
% 7.94/5.76 thf(fact_9364_real__root__pow__pos2,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 7.94/5.76 = X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_pow_pos2
% 7.94/5.76 thf(fact_9365_real__root__commute,axiom,
% 7.94/5.76 ! [M: nat,N: nat,X: real] :
% 7.94/5.76 ( ( root @ M @ ( root @ N @ X ) )
% 7.94/5.76 = ( root @ N @ ( root @ M @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_commute
% 7.94/5.76 thf(fact_9366_real__root__mult__exp,axiom,
% 7.94/5.76 ! [M: nat,N: nat,X: real] :
% 7.94/5.76 ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 7.94/5.76 = ( root @ M @ ( root @ N @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_mult_exp
% 7.94/5.76 thf(fact_9367_real__root__mult,axiom,
% 7.94/5.76 ! [N: nat,X: real,Y: real] :
% 7.94/5.76 ( ( root @ N @ ( times_times_real @ X @ Y ) )
% 7.94/5.76 = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_mult
% 7.94/5.76 thf(fact_9368_real__root__minus,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 7.94/5.76 = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_minus
% 7.94/5.76 thf(fact_9369_real__root__inverse,axiom,
% 7.94/5.76 ! [N: nat,X: real] :
% 7.94/5.76 ( ( root @ N @ ( inverse_inverse_real @ X ) )
% 7.94/5.76 = ( inverse_inverse_real @ ( root @ N @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_inverse
% 7.94/5.76 thf(fact_9370_real__root__divide,axiom,
% 7.94/5.76 ! [N: nat,X: real,Y: real] :
% 7.94/5.76 ( ( root @ N @ ( divide_divide_real @ X @ Y ) )
% 7.94/5.76 = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_divide
% 7.94/5.76 thf(fact_9371_real__root__pos__pos__le,axiom,
% 7.94/5.76 ! [X: real,N: nat] :
% 7.94/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_pos_pos_le
% 7.94/5.76 thf(fact_9372_real__root__less__mono,axiom,
% 7.94/5.76 ! [N: nat,X: real,Y: real] :
% 7.94/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.76 => ( ( ord_less_real @ X @ Y )
% 7.94/5.76 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 7.94/5.76
% 7.94/5.76 % real_root_less_mono
% 7.94/5.77 thf(fact_9373_real__root__le__mono,axiom,
% 7.94/5.77 ! [N: nat,X: real,Y: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_eq_real @ X @ Y )
% 7.94/5.77 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_le_mono
% 7.94/5.77 thf(fact_9374_real__root__power,axiom,
% 7.94/5.77 ! [N: nat,X: real,K: nat] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 7.94/5.77 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_power
% 7.94/5.77 thf(fact_9375_real__root__abs,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 7.94/5.77 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_abs
% 7.94/5.77 thf(fact_9376_sgn__root,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 7.94/5.77 = ( sgn_sgn_real @ X ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % sgn_root
% 7.94/5.77 thf(fact_9377_real__root__gt__zero,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.77 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_gt_zero
% 7.94/5.77 thf(fact_9378_real__root__strict__decreasing,axiom,
% 7.94/5.77 ! [N: nat,N4: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_nat @ N @ N4 )
% 7.94/5.77 => ( ( ord_less_real @ one_one_real @ X )
% 7.94/5.77 => ( ord_less_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_strict_decreasing
% 7.94/5.77 thf(fact_9379_sqrt__def,axiom,
% 7.94/5.77 ( sqrt
% 7.94/5.77 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % sqrt_def
% 7.94/5.77 thf(fact_9380_root__abs__power,axiom,
% 7.94/5.77 ! [N: nat,Y: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 7.94/5.77 = ( abs_abs_real @ Y ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % root_abs_power
% 7.94/5.77 thf(fact_9381_real__root__pos__pos,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_pos_pos
% 7.94/5.77 thf(fact_9382_real__root__strict__increasing,axiom,
% 7.94/5.77 ! [N: nat,N4: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_nat @ N @ N4 )
% 7.94/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.77 => ( ( ord_less_real @ X @ one_one_real )
% 7.94/5.77 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_strict_increasing
% 7.94/5.77 thf(fact_9383_real__root__decreasing,axiom,
% 7.94/5.77 ! [N: nat,N4: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_eq_nat @ N @ N4 )
% 7.94/5.77 => ( ( ord_less_eq_real @ one_one_real @ X )
% 7.94/5.77 => ( ord_less_eq_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_decreasing
% 7.94/5.77 thf(fact_9384_odd__real__root__pow,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.94/5.77 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 7.94/5.77 = X ) ) ).
% 7.94/5.77
% 7.94/5.77 % odd_real_root_pow
% 7.94/5.77 thf(fact_9385_odd__real__root__unique,axiom,
% 7.94/5.77 ! [N: nat,Y: real,X: real] :
% 7.94/5.77 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.94/5.77 => ( ( ( power_power_real @ Y @ N )
% 7.94/5.77 = X )
% 7.94/5.77 => ( ( root @ N @ X )
% 7.94/5.77 = Y ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % odd_real_root_unique
% 7.94/5.77 thf(fact_9386_odd__real__root__power__cancel,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 7.94/5.77 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 7.94/5.77 = X ) ) ).
% 7.94/5.77
% 7.94/5.77 % odd_real_root_power_cancel
% 7.94/5.77 thf(fact_9387_real__root__pow__pos,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.77 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 7.94/5.77 = X ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_pow_pos
% 7.94/5.77 thf(fact_9388_real__root__power__cancel,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.77 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 7.94/5.77 = X ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_power_cancel
% 7.94/5.77 thf(fact_9389_real__root__pos__unique,axiom,
% 7.94/5.77 ! [N: nat,Y: real,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 7.94/5.77 => ( ( ( power_power_real @ Y @ N )
% 7.94/5.77 = X )
% 7.94/5.77 => ( ( root @ N @ X )
% 7.94/5.77 = Y ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_pos_unique
% 7.94/5.77 thf(fact_9390_real__root__increasing,axiom,
% 7.94/5.77 ! [N: nat,N4: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_eq_nat @ N @ N4 )
% 7.94/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 7.94/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 7.94/5.77 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % real_root_increasing
% 7.94/5.77 thf(fact_9391_root__sgn__power,axiom,
% 7.94/5.77 ! [N: nat,Y: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 7.94/5.77 = Y ) ) ).
% 7.94/5.77
% 7.94/5.77 % root_sgn_power
% 7.94/5.77 thf(fact_9392_sgn__power__root,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 7.94/5.77 = X ) ) ).
% 7.94/5.77
% 7.94/5.77 % sgn_power_root
% 7.94/5.77 thf(fact_9393_log__root,axiom,
% 7.94/5.77 ! [N: nat,A: real,B: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_real @ zero_zero_real @ A )
% 7.94/5.77 => ( ( log @ B @ ( root @ N @ A ) )
% 7.94/5.77 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % log_root
% 7.94/5.77 thf(fact_9394_log__base__root,axiom,
% 7.94/5.77 ! [N: nat,B: real,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_real @ zero_zero_real @ B )
% 7.94/5.77 => ( ( log @ ( root @ N @ B ) @ X )
% 7.94/5.77 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % log_base_root
% 7.94/5.77 thf(fact_9395_ln__root,axiom,
% 7.94/5.77 ! [N: nat,B: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_real @ zero_zero_real @ B )
% 7.94/5.77 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 7.94/5.77 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % ln_root
% 7.94/5.77 thf(fact_9396_split__root,axiom,
% 7.94/5.77 ! [P: real > $o,N: nat,X: real] :
% 7.94/5.77 ( ( P @ ( root @ N @ X ) )
% 7.94/5.77 = ( ( ( N = zero_zero_nat )
% 7.94/5.77 => ( P @ zero_zero_real ) )
% 7.94/5.77 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ! [Y6: real] :
% 7.94/5.77 ( ( ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N ) )
% 7.94/5.77 = X )
% 7.94/5.77 => ( P @ Y6 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % split_root
% 7.94/5.77 thf(fact_9397_root__powr__inverse,axiom,
% 7.94/5.77 ! [N: nat,X: real] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 7.94/5.77 => ( ( root @ N @ X )
% 7.94/5.77 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % root_powr_inverse
% 7.94/5.77 thf(fact_9398_signed__take__bit__eq__take__bit__minus,axiom,
% 7.94/5.77 ( bit_ri631733984087533419it_int
% 7.94/5.77 = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % signed_take_bit_eq_take_bit_minus
% 7.94/5.77 thf(fact_9399_not__nonnegative__int__iff,axiom,
% 7.94/5.77 ! [K: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 7.94/5.77 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 7.94/5.77
% 7.94/5.77 % not_nonnegative_int_iff
% 7.94/5.77 thf(fact_9400_not__negative__int__iff,axiom,
% 7.94/5.77 ! [K: int] :
% 7.94/5.77 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 7.94/5.77 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 7.94/5.77
% 7.94/5.77 % not_negative_int_iff
% 7.94/5.77 thf(fact_9401_signed__take__bit__nonnegative__iff,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 7.94/5.77 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % signed_take_bit_nonnegative_iff
% 7.94/5.77 thf(fact_9402_signed__take__bit__negative__iff,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 7.94/5.77 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 7.94/5.77
% 7.94/5.77 % signed_take_bit_negative_iff
% 7.94/5.77 thf(fact_9403_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 7.94/5.77 ! [W: num,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 7.94/5.77 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_minus_numeral_Bit0_Suc_iff
% 7.94/5.77 thf(fact_9404_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 7.94/5.77 ! [W: num,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 7.94/5.77 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_minus_numeral_Bit1_Suc_iff
% 7.94/5.77 thf(fact_9405_bit__minus__numeral__int_I1_J,axiom,
% 7.94/5.77 ! [W: num,N: num] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 7.94/5.77 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_minus_numeral_int(1)
% 7.94/5.77 thf(fact_9406_bit__minus__numeral__int_I2_J,axiom,
% 7.94/5.77 ! [W: num,N: num] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 7.94/5.77 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_minus_numeral_int(2)
% 7.94/5.77 thf(fact_9407_bin__nth__minus__Bit0,axiom,
% 7.94/5.77 ! [N: nat,W: num] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ N )
% 7.94/5.77 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bin_nth_minus_Bit0
% 7.94/5.77 thf(fact_9408_bin__nth__minus__Bit1,axiom,
% 7.94/5.77 ! [N: nat,W: num] :
% 7.94/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 7.94/5.77 => ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ N )
% 7.94/5.77 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bin_nth_minus_Bit1
% 7.94/5.77 thf(fact_9409_bit__not__int__iff,axiom,
% 7.94/5.77 ! [K: int,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 7.94/5.77 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_not_int_iff
% 7.94/5.77 thf(fact_9410_bit__minus__int__iff,axiom,
% 7.94/5.77 ! [K: int,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 7.94/5.77 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_minus_int_iff
% 7.94/5.77 thf(fact_9411_bit__and__int__iff,axiom,
% 7.94/5.77 ! [K: int,L: int,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N )
% 7.94/5.77 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 7.94/5.77 & ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_and_int_iff
% 7.94/5.77 thf(fact_9412_not__int__def,axiom,
% 7.94/5.77 ( bit_ri7919022796975470100ot_int
% 7.94/5.77 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % not_int_def
% 7.94/5.77 thf(fact_9413_and__not__numerals_I1_J,axiom,
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 7.94/5.77 = zero_zero_int ) ).
% 7.94/5.77
% 7.94/5.77 % and_not_numerals(1)
% 7.94/5.77 thf(fact_9414_bit__not__int__iff_H,axiom,
% 7.94/5.77 ! [K: int,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 7.94/5.77 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_not_int_iff'
% 7.94/5.77 thf(fact_9415_not__int__div__2,axiom,
% 7.94/5.77 ! [K: int] :
% 7.94/5.77 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.94/5.77 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % not_int_div_2
% 7.94/5.77 thf(fact_9416_even__not__iff__int,axiom,
% 7.94/5.77 ! [K: int] :
% 7.94/5.77 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 7.94/5.77 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % even_not_iff_int
% 7.94/5.77 thf(fact_9417_and__not__numerals_I4_J,axiom,
% 7.94/5.77 ! [M: num] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 7.94/5.77 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % and_not_numerals(4)
% 7.94/5.77 thf(fact_9418_and__not__numerals_I2_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 7.94/5.77 = one_one_int ) ).
% 7.94/5.77
% 7.94/5.77 % and_not_numerals(2)
% 7.94/5.77 thf(fact_9419_bit__imp__take__bit__positive,axiom,
% 7.94/5.77 ! [N: nat,M: nat,K: int] :
% 7.94/5.77 ( ( ord_less_nat @ N @ M )
% 7.94/5.77 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 7.94/5.77 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_imp_take_bit_positive
% 7.94/5.77 thf(fact_9420_int__bit__bound,axiom,
% 7.94/5.77 ! [K: int] :
% 7.94/5.77 ~ ! [N2: nat] :
% 7.94/5.77 ( ! [M3: nat] :
% 7.94/5.77 ( ( ord_less_eq_nat @ N2 @ M3 )
% 7.94/5.77 => ( ( bit_se1146084159140164899it_int @ K @ M3 )
% 7.94/5.77 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 7.94/5.77 => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 7.94/5.77 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 7.94/5.77 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % int_bit_bound
% 7.94/5.77 thf(fact_9421_and__not__numerals_I5_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 7.94/5.77 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % and_not_numerals(5)
% 7.94/5.77 thf(fact_9422_and__not__numerals_I7_J,axiom,
% 7.94/5.77 ! [M: num] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 7.94/5.77 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % and_not_numerals(7)
% 7.94/5.77 thf(fact_9423_and__not__numerals_I3_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 7.94/5.77 = zero_zero_int ) ).
% 7.94/5.77
% 7.94/5.77 % and_not_numerals(3)
% 7.94/5.77 thf(fact_9424_and__not__numerals_I6_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 7.94/5.77 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % and_not_numerals(6)
% 7.94/5.77 thf(fact_9425_and__not__numerals_I9_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 7.94/5.77 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % and_not_numerals(9)
% 7.94/5.77 thf(fact_9426_bit__int__def,axiom,
% 7.94/5.77 ( bit_se1146084159140164899it_int
% 7.94/5.77 = ( ^ [K3: int,N3: nat] :
% 7.94/5.77 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_int_def
% 7.94/5.77 thf(fact_9427_and__not__numerals_I8_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 7.94/5.77 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % and_not_numerals(8)
% 7.94/5.77 thf(fact_9428_not__int__rec,axiom,
% 7.94/5.77 ( bit_ri7919022796975470100ot_int
% 7.94/5.77 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % not_int_rec
% 7.94/5.77 thf(fact_9429_Bit__Operations_Oset__bit__eq,axiom,
% 7.94/5.77 ( bit_se7879613467334960850it_int
% 7.94/5.77 = ( ^ [N3: nat,K3: int] :
% 7.94/5.77 ( plus_plus_int @ K3
% 7.94/5.77 @ ( times_times_int
% 7.94/5.77 @ ( zero_n2684676970156552555ol_int
% 7.94/5.77 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N3 ) )
% 7.94/5.77 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % Bit_Operations.set_bit_eq
% 7.94/5.77 thf(fact_9430_unset__bit__eq,axiom,
% 7.94/5.77 ( bit_se4203085406695923979it_int
% 7.94/5.77 = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % unset_bit_eq
% 7.94/5.77 thf(fact_9431_take__bit__Suc__from__most,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 7.94/5.77 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % take_bit_Suc_from_most
% 7.94/5.77 thf(fact_9432_int__not__code_I1_J,axiom,
% 7.94/5.77 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 7.94/5.77 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.94/5.77
% 7.94/5.77 % int_not_code(1)
% 7.94/5.77 thf(fact_9433_bitNOT__integer__code,axiom,
% 7.94/5.77 ( bit_ri7632146776885996613nteger
% 7.94/5.77 = ( ^ [I2: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ I2 ) @ one_one_Code_integer ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bitNOT_integer_code
% 7.94/5.77 thf(fact_9434_xor__int__unfold,axiom,
% 7.94/5.77 ( bit_se6526347334894502574or_int
% 7.94/5.77 = ( ^ [K3: int,L2: int] :
% 7.94/5.77 ( if_int
% 7.94/5.77 @ ( K3
% 7.94/5.77 = ( uminus_uminus_int @ one_one_int ) )
% 7.94/5.77 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 7.94/5.77 @ ( if_int
% 7.94/5.77 @ ( L2
% 7.94/5.77 = ( uminus_uminus_int @ one_one_int ) )
% 7.94/5.77 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 7.94/5.77 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_int_unfold
% 7.94/5.77 thf(fact_9435_or__nonnegative__int__iff,axiom,
% 7.94/5.77 ! [K: int,L: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 7.94/5.77 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.94/5.77 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_nonnegative_int_iff
% 7.94/5.77 thf(fact_9436_or__negative__int__iff,axiom,
% 7.94/5.77 ! [K: int,L: int] :
% 7.94/5.77 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 7.94/5.77 = ( ( ord_less_int @ K @ zero_zero_int )
% 7.94/5.77 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_negative_int_iff
% 7.94/5.77 thf(fact_9437_xor__nonnegative__int__iff,axiom,
% 7.94/5.77 ! [K: int,L: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 7.94/5.77 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.94/5.77 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_nonnegative_int_iff
% 7.94/5.77 thf(fact_9438_xor__negative__int__iff,axiom,
% 7.94/5.77 ! [K: int,L: int] :
% 7.94/5.77 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 7.94/5.77 = ( ( ord_less_int @ K @ zero_zero_int )
% 7.94/5.77 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_negative_int_iff
% 7.94/5.77 thf(fact_9439_or__minus__numerals_I2_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_minus_numerals(2)
% 7.94/5.77 thf(fact_9440_or__minus__numerals_I6_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_minus_numerals(6)
% 7.94/5.77 thf(fact_9441_or__nat__numerals_I4_J,axiom,
% 7.94/5.77 ! [X: num] :
% 7.94/5.77 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_nat_numerals(4)
% 7.94/5.77 thf(fact_9442_or__nat__numerals_I2_J,axiom,
% 7.94/5.77 ! [Y: num] :
% 7.94/5.77 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_nat_numerals(2)
% 7.94/5.77 thf(fact_9443_or__nat__numerals_I3_J,axiom,
% 7.94/5.77 ! [X: num] :
% 7.94/5.77 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_nat_numerals(3)
% 7.94/5.77 thf(fact_9444_or__nat__numerals_I1_J,axiom,
% 7.94/5.77 ! [Y: num] :
% 7.94/5.77 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_nat_numerals(1)
% 7.94/5.77 thf(fact_9445_or__minus__minus__numerals,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.94/5.77 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_minus_minus_numerals
% 7.94/5.77 thf(fact_9446_and__minus__minus__numerals,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 7.94/5.77 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % and_minus_minus_numerals
% 7.94/5.77 thf(fact_9447_xor__int__def,axiom,
% 7.94/5.77 ( bit_se6526347334894502574or_int
% 7.94/5.77 = ( ^ [K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L2 ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_int_def
% 7.94/5.77 thf(fact_9448_int__or__code_I2_J,axiom,
% 7.94/5.77 ! [I: int] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ I @ zero_zero_int )
% 7.94/5.77 = I ) ).
% 7.94/5.77
% 7.94/5.77 % int_or_code(2)
% 7.94/5.77 thf(fact_9449_int__or__code_I1_J,axiom,
% 7.94/5.77 ! [J: int] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ zero_zero_int @ J )
% 7.94/5.77 = J ) ).
% 7.94/5.77
% 7.94/5.77 % int_or_code(1)
% 7.94/5.77 thf(fact_9450_bit__xor__int__iff,axiom,
% 7.94/5.77 ! [K: int,L: int,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N )
% 7.94/5.77 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 7.94/5.77 != ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_xor_int_iff
% 7.94/5.77 thf(fact_9451_bit__or__int__iff,axiom,
% 7.94/5.77 ! [K: int,L: int,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N )
% 7.94/5.77 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 7.94/5.77 | ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_or_int_iff
% 7.94/5.77 thf(fact_9452_or__nat__def,axiom,
% 7.94/5.77 ( bit_se1412395901928357646or_nat
% 7.94/5.77 = ( ^ [M4: nat,N3: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_nat_def
% 7.94/5.77 thf(fact_9453_bit__Suc__0__iff,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.94/5.77 = ( N = zero_zero_nat ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_Suc_0_iff
% 7.94/5.77 thf(fact_9454_not__bit__Suc__0__Suc,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 7.94/5.77
% 7.94/5.77 % not_bit_Suc_0_Suc
% 7.94/5.77 thf(fact_9455_int__xor__code_I1_J,axiom,
% 7.94/5.77 ! [J: int] :
% 7.94/5.77 ( ( bit_se6526347334894502574or_int @ zero_zero_int @ J )
% 7.94/5.77 = J ) ).
% 7.94/5.77
% 7.94/5.77 % int_xor_code(1)
% 7.94/5.77 thf(fact_9456_int__xor__code_I2_J,axiom,
% 7.94/5.77 ! [I: int] :
% 7.94/5.77 ( ( bit_se6526347334894502574or_int @ I @ zero_zero_int )
% 7.94/5.77 = I ) ).
% 7.94/5.77
% 7.94/5.77 % int_xor_code(2)
% 7.94/5.77 thf(fact_9457_XOR__lower,axiom,
% 7.94/5.77 ! [X: int,Y: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.94/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.94/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % XOR_lower
% 7.94/5.77 thf(fact_9458_OR__lower,axiom,
% 7.94/5.77 ! [X: int,Y: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.94/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 7.94/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % OR_lower
% 7.94/5.77 thf(fact_9459_or__greater__eq,axiom,
% 7.94/5.77 ! [L: int,K: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 7.94/5.77 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_greater_eq
% 7.94/5.77 thf(fact_9460_plus__and__or,axiom,
% 7.94/5.77 ! [X: int,Y: int] :
% 7.94/5.77 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 7.94/5.77 = ( plus_plus_int @ X @ Y ) ) ).
% 7.94/5.77
% 7.94/5.77 % plus_and_or
% 7.94/5.77 thf(fact_9461_or__int__def,axiom,
% 7.94/5.77 ( bit_se1409905431419307370or_int
% 7.94/5.77 = ( ^ [K3: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_int_def
% 7.94/5.77 thf(fact_9462_not__bit__Suc__0__numeral,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 7.94/5.77
% 7.94/5.77 % not_bit_Suc_0_numeral
% 7.94/5.77 thf(fact_9463_or__not__numerals_I1_J,axiom,
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 7.94/5.77 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_numerals(1)
% 7.94/5.77 thf(fact_9464_or__not__numerals_I4_J,axiom,
% 7.94/5.77 ! [M: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 7.94/5.77 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_numerals(4)
% 7.94/5.77 thf(fact_9465_or__not__numerals_I2_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 7.94/5.77 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_numerals(2)
% 7.94/5.77 thf(fact_9466_bit__nat__iff,axiom,
% 7.94/5.77 ! [K: int,N: nat] :
% 7.94/5.77 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 7.94/5.77 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 7.94/5.77 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_nat_iff
% 7.94/5.77 thf(fact_9467_or__not__numerals_I3_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 7.94/5.77 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_numerals(3)
% 7.94/5.77 thf(fact_9468_or__not__numerals_I7_J,axiom,
% 7.94/5.77 ! [M: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 7.94/5.77 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_numerals(7)
% 7.94/5.77 thf(fact_9469_bit__nat__def,axiom,
% 7.94/5.77 ( bit_se1148574629649215175it_nat
% 7.94/5.77 = ( ^ [M4: nat,N3: nat] :
% 7.94/5.77 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_nat_def
% 7.94/5.77 thf(fact_9470_or__not__numerals_I6_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 7.94/5.77 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_numerals(6)
% 7.94/5.77 thf(fact_9471_XOR__upper,axiom,
% 7.94/5.77 ! [X: int,N: nat,Y: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.94/5.77 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.94/5.77 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.94/5.77 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % XOR_upper
% 7.94/5.77 thf(fact_9472_OR__upper,axiom,
% 7.94/5.77 ! [X: int,N: nat,Y: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 7.94/5.77 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.94/5.77 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 7.94/5.77 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % OR_upper
% 7.94/5.77 thf(fact_9473_or__not__numerals_I5_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 7.94/5.77 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_numerals(5)
% 7.94/5.77 thf(fact_9474_test__bit__int__code_I1_J,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ~ ( bit_se1146084159140164899it_int @ zero_zero_int @ N ) ).
% 7.94/5.77
% 7.94/5.77 % test_bit_int_code(1)
% 7.94/5.77 thf(fact_9475_int__and__code_I2_J,axiom,
% 7.94/5.77 ! [I: int] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ I @ zero_zero_int )
% 7.94/5.77 = zero_zero_int ) ).
% 7.94/5.77
% 7.94/5.77 % int_and_code(2)
% 7.94/5.77 thf(fact_9476_int__and__code_I1_J,axiom,
% 7.94/5.77 ! [J: int] :
% 7.94/5.77 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ J )
% 7.94/5.77 = zero_zero_int ) ).
% 7.94/5.77
% 7.94/5.77 % int_and_code(1)
% 7.94/5.77 thf(fact_9477_Suc__0__or__eq,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.94/5.77 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % Suc_0_or_eq
% 7.94/5.77 thf(fact_9478_or__Suc__0__eq,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 7.94/5.77 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_Suc_0_eq
% 7.94/5.77 thf(fact_9479_or__nat__rec,axiom,
% 7.94/5.77 ( bit_se1412395901928357646or_nat
% 7.94/5.77 = ( ^ [M4: nat,N3: nat] :
% 7.94/5.77 ( plus_plus_nat
% 7.94/5.77 @ ( zero_n2687167440665602831ol_nat
% 7.94/5.77 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 )
% 7.94/5.77 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 7.94/5.77 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_nat_rec
% 7.94/5.77 thf(fact_9480_or__not__numerals_I9_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 7.94/5.77 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_numerals(9)
% 7.94/5.77 thf(fact_9481_or__not__numerals_I8_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 7.94/5.77 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_numerals(8)
% 7.94/5.77 thf(fact_9482_xor__int__rec,axiom,
% 7.94/5.77 ( bit_se6526347334894502574or_int
% 7.94/5.77 = ( ^ [K3: int,L2: int] :
% 7.94/5.77 ( plus_plus_int
% 7.94/5.77 @ ( zero_n2684676970156552555ol_int
% 7.94/5.77 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 7.94/5.77 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 7.94/5.77 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_int_rec
% 7.94/5.77 thf(fact_9483_or__int__rec,axiom,
% 7.94/5.77 ( bit_se1409905431419307370or_int
% 7.94/5.77 = ( ^ [K3: int,L2: int] :
% 7.94/5.77 ( plus_plus_int
% 7.94/5.77 @ ( zero_n2684676970156552555ol_int
% 7.94/5.77 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 7.94/5.77 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 7.94/5.77 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_int_rec
% 7.94/5.77 thf(fact_9484_or__nat__unfold,axiom,
% 7.94/5.77 ( bit_se1412395901928357646or_nat
% 7.94/5.77 = ( ^ [M4: nat,N3: nat] : ( if_nat @ ( M4 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M4 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M4 @ ( 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 @ M4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_nat_unfold
% 7.94/5.77 thf(fact_9485_or__int__unfold,axiom,
% 7.94/5.77 ( bit_se1409905431419307370or_int
% 7.94/5.77 = ( ^ [K3: int,L2: int] :
% 7.94/5.77 ( if_int
% 7.94/5.77 @ ( ( K3
% 7.94/5.77 = ( uminus_uminus_int @ one_one_int ) )
% 7.94/5.77 | ( L2
% 7.94/5.77 = ( uminus_uminus_int @ one_one_int ) ) )
% 7.94/5.77 @ ( uminus_uminus_int @ one_one_int )
% 7.94/5.77 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_int_unfold
% 7.94/5.77 thf(fact_9486_Bit__integer_Oabs__eq,axiom,
% 7.94/5.77 ! [Xa3: int,X: $o] :
% 7.94/5.77 ( ( bits_Bit_integer @ ( code_integer_of_int @ Xa3 ) @ X )
% 7.94/5.77 = ( code_integer_of_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ X ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa3 ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % Bit_integer.abs_eq
% 7.94/5.77 thf(fact_9487_or__minus__numerals_I1_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_minus_numerals(1)
% 7.94/5.77 thf(fact_9488_or__minus__numerals_I5_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_minus_numerals(5)
% 7.94/5.77 thf(fact_9489_xor__nat__numerals_I1_J,axiom,
% 7.94/5.77 ! [Y: num] :
% 7.94/5.77 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_nat_numerals(1)
% 7.94/5.77 thf(fact_9490_xor__nat__numerals_I2_J,axiom,
% 7.94/5.77 ! [Y: num] :
% 7.94/5.77 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_nat_numerals(2)
% 7.94/5.77 thf(fact_9491_xor__nat__numerals_I3_J,axiom,
% 7.94/5.77 ! [X: num] :
% 7.94/5.77 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_nat_numerals(3)
% 7.94/5.77 thf(fact_9492_xor__nat__numerals_I4_J,axiom,
% 7.94/5.77 ! [X: num] :
% 7.94/5.77 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_nat_numerals(4)
% 7.94/5.77 thf(fact_9493_or__minus__numerals_I4_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_minus_numerals(4)
% 7.94/5.77 thf(fact_9494_or__minus__numerals_I8_J,axiom,
% 7.94/5.77 ! [N: num,M: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_minus_numerals(8)
% 7.94/5.77 thf(fact_9495_or__minus__numerals_I7_J,axiom,
% 7.94/5.77 ! [N: num,M: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_minus_numerals(7)
% 7.94/5.77 thf(fact_9496_or__minus__numerals_I3_J,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_minus_numerals(3)
% 7.94/5.77 thf(fact_9497_or__not__num__neg_Osimps_I1_J,axiom,
% 7.94/5.77 ( ( bit_or_not_num_neg @ one @ one )
% 7.94/5.77 = one ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.simps(1)
% 7.94/5.77 thf(fact_9498_or__not__num__neg_Osimps_I4_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 7.94/5.77 = ( bit0 @ one ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.simps(4)
% 7.94/5.77 thf(fact_9499_or__not__num__neg_Osimps_I6_J,axiom,
% 7.94/5.77 ! [N: num,M: num] :
% 7.94/5.77 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 7.94/5.77 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.simps(6)
% 7.94/5.77 thf(fact_9500_or__not__num__neg_Osimps_I3_J,axiom,
% 7.94/5.77 ! [M: num] :
% 7.94/5.77 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 7.94/5.77 = ( bit1 @ M ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.simps(3)
% 7.94/5.77 thf(fact_9501_or__not__num__neg_Osimps_I7_J,axiom,
% 7.94/5.77 ! [N: num] :
% 7.94/5.77 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 7.94/5.77 = one ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.simps(7)
% 7.94/5.77 thf(fact_9502_or__not__num__neg_Osimps_I5_J,axiom,
% 7.94/5.77 ! [N: num,M: num] :
% 7.94/5.77 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 7.94/5.77 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.simps(5)
% 7.94/5.77 thf(fact_9503_or__not__num__neg_Osimps_I9_J,axiom,
% 7.94/5.77 ! [N: num,M: num] :
% 7.94/5.77 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 7.94/5.77 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.simps(9)
% 7.94/5.77 thf(fact_9504_xor__nat__def,axiom,
% 7.94/5.77 ( bit_se6528837805403552850or_nat
% 7.94/5.77 = ( ^ [M4: nat,N3: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_nat_def
% 7.94/5.77 thf(fact_9505_or__not__num__neg_Osimps_I2_J,axiom,
% 7.94/5.77 ! [M: num] :
% 7.94/5.77 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 7.94/5.77 = ( bit1 @ M ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.simps(2)
% 7.94/5.77 thf(fact_9506_or__not__num__neg_Osimps_I8_J,axiom,
% 7.94/5.77 ! [N: num,M: num] :
% 7.94/5.77 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 7.94/5.77 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.simps(8)
% 7.94/5.77 thf(fact_9507_or__not__num__neg_Oelims,axiom,
% 7.94/5.77 ! [X: num,Xa3: num,Y: num] :
% 7.94/5.77 ( ( ( bit_or_not_num_neg @ X @ Xa3 )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( ( X = one )
% 7.94/5.77 => ( ( Xa3 = one )
% 7.94/5.77 => ( Y != one ) ) )
% 7.94/5.77 => ( ( ( X = one )
% 7.94/5.77 => ! [M2: num] :
% 7.94/5.77 ( ( Xa3
% 7.94/5.77 = ( bit0 @ M2 ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 != ( bit1 @ M2 ) ) ) )
% 7.94/5.77 => ( ( ( X = one )
% 7.94/5.77 => ! [M2: num] :
% 7.94/5.77 ( ( Xa3
% 7.94/5.77 = ( bit1 @ M2 ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 != ( bit1 @ M2 ) ) ) )
% 7.94/5.77 => ( ( ? [N2: num] :
% 7.94/5.77 ( X
% 7.94/5.77 = ( bit0 @ N2 ) )
% 7.94/5.77 => ( ( Xa3 = one )
% 7.94/5.77 => ( Y
% 7.94/5.77 != ( bit0 @ one ) ) ) )
% 7.94/5.77 => ( ! [N2: num] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( bit0 @ N2 ) )
% 7.94/5.77 => ! [M2: num] :
% 7.94/5.77 ( ( Xa3
% 7.94/5.77 = ( bit0 @ M2 ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M2 ) ) ) ) )
% 7.94/5.77 => ( ! [N2: num] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( bit0 @ N2 ) )
% 7.94/5.77 => ! [M2: num] :
% 7.94/5.77 ( ( Xa3
% 7.94/5.77 = ( bit1 @ M2 ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 != ( bit0 @ ( bit_or_not_num_neg @ N2 @ M2 ) ) ) ) )
% 7.94/5.77 => ( ( ? [N2: num] :
% 7.94/5.77 ( X
% 7.94/5.77 = ( bit1 @ N2 ) )
% 7.94/5.77 => ( ( Xa3 = one )
% 7.94/5.77 => ( Y != one ) ) )
% 7.94/5.77 => ( ! [N2: num] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( bit1 @ N2 ) )
% 7.94/5.77 => ! [M2: num] :
% 7.94/5.77 ( ( Xa3
% 7.94/5.77 = ( bit0 @ M2 ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M2 ) ) ) ) )
% 7.94/5.77 => ~ ! [N2: num] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( bit1 @ N2 ) )
% 7.94/5.77 => ! [M2: num] :
% 7.94/5.77 ( ( Xa3
% 7.94/5.77 = ( bit1 @ M2 ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % or_not_num_neg.elims
% 7.94/5.77 thf(fact_9508_numeral__or__not__num__eq,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 7.94/5.77 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % numeral_or_not_num_eq
% 7.94/5.77 thf(fact_9509_int__numeral__not__or__num__neg,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % int_numeral_not_or_num_neg
% 7.94/5.77 thf(fact_9510_int__numeral__or__not__num__neg,axiom,
% 7.94/5.77 ! [M: num,N: num] :
% 7.94/5.77 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 7.94/5.77 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % int_numeral_or_not_num_neg
% 7.94/5.77 thf(fact_9511_xor__nat__unfold,axiom,
% 7.94/5.77 ( bit_se6528837805403552850or_nat
% 7.94/5.77 = ( ^ [M4: nat,N3: nat] : ( if_nat @ ( M4 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M4 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M4 @ ( 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 @ M4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_nat_unfold
% 7.94/5.77 thf(fact_9512_xor__nat__rec,axiom,
% 7.94/5.77 ( bit_se6528837805403552850or_nat
% 7.94/5.77 = ( ^ [M4: nat,N3: nat] :
% 7.94/5.77 ( plus_plus_nat
% 7.94/5.77 @ ( zero_n2687167440665602831ol_nat
% 7.94/5.77 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 7.94/5.77 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 7.94/5.77 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_nat_rec
% 7.94/5.77 thf(fact_9513_xor__Suc__0__eq,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 7.94/5.77 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.94/5.77 @ ( zero_n2687167440665602831ol_nat
% 7.94/5.77 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % xor_Suc_0_eq
% 7.94/5.77 thf(fact_9514_Suc__0__xor__eq,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 7.94/5.77 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 7.94/5.77 @ ( zero_n2687167440665602831ol_nat
% 7.94/5.77 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % Suc_0_xor_eq
% 7.94/5.77 thf(fact_9515_int__lsb__numeral_I1_J,axiom,
% 7.94/5.77 ~ ( least_4859182151741483524sb_int @ zero_zero_int ) ).
% 7.94/5.77
% 7.94/5.77 % int_lsb_numeral(1)
% 7.94/5.77 thf(fact_9516_int__lsb__numeral_I2_J,axiom,
% 7.94/5.77 least_4859182151741483524sb_int @ one_one_int ).
% 7.94/5.77
% 7.94/5.77 % int_lsb_numeral(2)
% 7.94/5.77 thf(fact_9517_int__lsb__numeral_I6_J,axiom,
% 7.94/5.77 ! [W: num] :
% 7.94/5.77 ~ ( least_4859182151741483524sb_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % int_lsb_numeral(6)
% 7.94/5.77 thf(fact_9518_int__lsb__numeral_I3_J,axiom,
% 7.94/5.77 least_4859182151741483524sb_int @ ( numeral_numeral_int @ one ) ).
% 7.94/5.77
% 7.94/5.77 % int_lsb_numeral(3)
% 7.94/5.77 thf(fact_9519_int__lsb__numeral_I7_J,axiom,
% 7.94/5.77 ! [W: num] : ( least_4859182151741483524sb_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % int_lsb_numeral(7)
% 7.94/5.77 thf(fact_9520_int__lsb__numeral_I4_J,axiom,
% 7.94/5.77 least_4859182151741483524sb_int @ ( uminus_uminus_int @ one_one_int ) ).
% 7.94/5.77
% 7.94/5.77 % int_lsb_numeral(4)
% 7.94/5.77 thf(fact_9521_int__lsb__numeral_I8_J,axiom,
% 7.94/5.77 ! [W: num] :
% 7.94/5.77 ~ ( least_4859182151741483524sb_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % int_lsb_numeral(8)
% 7.94/5.77 thf(fact_9522_int__lsb__numeral_I5_J,axiom,
% 7.94/5.77 least_4859182151741483524sb_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) ).
% 7.94/5.77
% 7.94/5.77 % int_lsb_numeral(5)
% 7.94/5.77 thf(fact_9523_int__lsb__numeral_I9_J,axiom,
% 7.94/5.77 ! [W: num] : ( least_4859182151741483524sb_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % int_lsb_numeral(9)
% 7.94/5.77 thf(fact_9524_lsb__integer__code,axiom,
% 7.94/5.77 ( least_7544222001954398261nteger
% 7.94/5.77 = ( ^ [X2: code_integer] : ( bit_se9216721137139052372nteger @ X2 @ zero_zero_nat ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % lsb_integer_code
% 7.94/5.77 thf(fact_9525_lsb__int__def,axiom,
% 7.94/5.77 ( least_4859182151741483524sb_int
% 7.94/5.77 = ( ^ [I2: int] : ( bit_se1146084159140164899it_int @ I2 @ zero_zero_nat ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % lsb_int_def
% 7.94/5.77 thf(fact_9526_bin__last__conv__lsb,axiom,
% 7.94/5.77 ( ( ^ [A3: int] :
% 7.94/5.77 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) )
% 7.94/5.77 = least_4859182151741483524sb_int ) ).
% 7.94/5.77
% 7.94/5.77 % bin_last_conv_lsb
% 7.94/5.77 thf(fact_9527_vebt__buildup_Opelims,axiom,
% 7.94/5.77 ! [X: nat,Y: vEBT_VEBT] :
% 7.94/5.77 ( ( ( vEBT_vebt_buildup @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 7.94/5.77 => ( ( ( X = zero_zero_nat )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( vEBT_Leaf @ $false @ $false ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 7.94/5.77 => ( ( ( X
% 7.94/5.77 = ( suc @ zero_zero_nat ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( vEBT_Leaf @ $false @ $false ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 7.94/5.77 => ~ ! [Va: nat] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( suc @ ( suc @ Va ) ) )
% 7.94/5.77 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( 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 ) ) ) ) ) ) )
% 7.94/5.77 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( 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 ) ) ) ) ) ) ) ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % vebt_buildup.pelims
% 7.94/5.77 thf(fact_9528_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Opelims,axiom,
% 7.94/5.77 ! [X: nat,Y: nat] :
% 7.94/5.77 ( ( ( vEBT_V8646137997579335489_i_l_d @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_nat @ vEBT_V5144397997797733112_d_rel @ X )
% 7.94/5.77 => ( ( ( X = zero_zero_nat )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ zero_zero_nat ) ) )
% 7.94/5.77 => ( ( ( X
% 7.94/5.77 = ( suc @ zero_zero_nat ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ zero_zero_nat ) ) ) )
% 7.94/5.77 => ~ ! [Va: nat] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( suc @ ( suc @ Va ) ) )
% 7.94/5.77 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 7.94/5.77 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.pelims
% 7.94/5.77 thf(fact_9529_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Opelims,axiom,
% 7.94/5.77 ! [X: nat,Y: nat] :
% 7.94/5.77 ( ( ( vEBT_V8346862874174094_d_u_p @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_nat @ vEBT_V1247956027447740395_p_rel @ X )
% 7.94/5.77 => ( ( ( X = zero_zero_nat )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ zero_zero_nat ) ) )
% 7.94/5.77 => ( ( ( X
% 7.94/5.77 = ( suc @ zero_zero_nat ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ zero_zero_nat ) ) ) )
% 7.94/5.77 => ~ ! [Va: nat] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( suc @ ( suc @ Va ) ) )
% 7.94/5.77 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 7.94/5.77 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.pelims
% 7.94/5.77 thf(fact_9530_VEBT__internal_OT__vebt__buildupi_Opelims,axiom,
% 7.94/5.77 ! [X: nat,Y: nat] :
% 7.94/5.77 ( ( ( vEBT_V441764108873111860ildupi @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_nat @ vEBT_V2957053500504383685pi_rel @ X )
% 7.94/5.77 => ( ( ( X = zero_zero_nat )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( suc @ zero_zero_nat ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ zero_zero_nat ) ) )
% 7.94/5.77 => ( ( ( X
% 7.94/5.77 = ( suc @ zero_zero_nat ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( suc @ zero_zero_nat ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ ( suc @ zero_zero_nat ) ) ) )
% 7.94/5.77 => ~ ! [N2: nat] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( suc @ ( suc @ N2 ) ) )
% 7.94/5.77 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.94/5.77 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 7.94/5.77 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ ( suc @ ( suc @ N2 ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % VEBT_internal.T_vebt_buildupi.pelims
% 7.94/5.77 thf(fact_9531_dup__1,axiom,
% 7.94/5.77 ( ( code_dup @ one_one_Code_integer )
% 7.94/5.77 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % dup_1
% 7.94/5.77 thf(fact_9532_Code__Numeral_Odup__code_I1_J,axiom,
% 7.94/5.77 ( ( code_dup @ zero_z3403309356797280102nteger )
% 7.94/5.77 = zero_z3403309356797280102nteger ) ).
% 7.94/5.77
% 7.94/5.77 % Code_Numeral.dup_code(1)
% 7.94/5.77 thf(fact_9533_vebt__assn__raw_Osimps_I2_J,axiom,
% 7.94/5.77 ! [Mmo: option4927543243414619207at_nat,Deg: nat,Tree_list: list_VEBT_VEBT,Summary: vEBT_VEBT,Mmoi: option4927543243414619207at_nat,Degi: nat,Tree_array: array_VEBT_VEBTi,Summaryi: vEBT_VEBTi] :
% 7.94/5.77 ( ( vEBT_vebt_assn_raw @ ( vEBT_Node @ Mmo @ Deg @ Tree_list @ Summary ) @ ( vEBT_Nodei @ Mmoi @ Degi @ Tree_array @ Summaryi ) )
% 7.94/5.77 = ( times_times_assn
% 7.94/5.77 @ ( times_times_assn
% 7.94/5.77 @ ( pure_assn
% 7.94/5.77 @ ( ( Mmoi = Mmo )
% 7.94/5.77 & ( Degi = Deg ) ) )
% 7.94/5.77 @ ( vEBT_vebt_assn_raw @ Summary @ Summaryi ) )
% 7.94/5.77 @ ( ex_ass463751140784270563_VEBTi
% 7.94/5.77 @ ^ [Tree_is2: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Tree_array @ Tree_is2 ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Tree_list @ Tree_is2 ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % vebt_assn_raw.simps(2)
% 7.94/5.77 thf(fact_9534_cis__multiple__2pi,axiom,
% 7.94/5.77 ! [N: real] :
% 7.94/5.77 ( ( member_real @ N @ ring_1_Ints_real )
% 7.94/5.77 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 7.94/5.77 = one_one_complex ) ) ).
% 7.94/5.77
% 7.94/5.77 % cis_multiple_2pi
% 7.94/5.77 thf(fact_9535_sin__times__pi__eq__0,axiom,
% 7.94/5.77 ! [X: real] :
% 7.94/5.77 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 7.94/5.77 = zero_zero_real )
% 7.94/5.77 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 7.94/5.77
% 7.94/5.77 % sin_times_pi_eq_0
% 7.94/5.77 thf(fact_9536_sin__integer__2pi,axiom,
% 7.94/5.77 ! [N: real] :
% 7.94/5.77 ( ( member_real @ N @ ring_1_Ints_real )
% 7.94/5.77 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 7.94/5.77 = zero_zero_real ) ) ).
% 7.94/5.77
% 7.94/5.77 % sin_integer_2pi
% 7.94/5.77 thf(fact_9537_cos__integer__2pi,axiom,
% 7.94/5.77 ! [N: real] :
% 7.94/5.77 ( ( member_real @ N @ ring_1_Ints_real )
% 7.94/5.77 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 7.94/5.77 = one_one_real ) ) ).
% 7.94/5.77
% 7.94/5.77 % cos_integer_2pi
% 7.94/5.77 thf(fact_9538_VEBT__internal_Ospace_Opelims,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: nat] :
% 7.94/5.77 ( ( ( vEBT_VEBT_space @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ X )
% 7.94/5.77 => ( ! [A5: $o,B2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 7.94/5.77 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary2 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList2 ) @ zero_zero_nat ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % VEBT_internal.space.pelims
% 7.94/5.77 thf(fact_9539_merge__true__star,axiom,
% 7.94/5.77 ( ( times_times_assn @ top_top_assn @ top_top_assn )
% 7.94/5.77 = top_top_assn ) ).
% 7.94/5.77
% 7.94/5.77 % merge_true_star
% 7.94/5.77 thf(fact_9540_assn__basic__inequalities_I1_J,axiom,
% 7.94/5.77 top_top_assn != one_one_assn ).
% 7.94/5.77
% 7.94/5.77 % assn_basic_inequalities(1)
% 7.94/5.77 thf(fact_9541_ent__true,axiom,
% 7.94/5.77 ! [P: assn] : ( entails @ P @ top_top_assn ) ).
% 7.94/5.77
% 7.94/5.77 % ent_true
% 7.94/5.77 thf(fact_9542_merge__true__star__ctx,axiom,
% 7.94/5.77 ! [P: assn] :
% 7.94/5.77 ( ( times_times_assn @ top_top_assn @ ( times_times_assn @ top_top_assn @ P ) )
% 7.94/5.77 = ( times_times_assn @ top_top_assn @ P ) ) ).
% 7.94/5.77
% 7.94/5.77 % merge_true_star_ctx
% 7.94/5.77 thf(fact_9543_ent__true__drop_I2_J,axiom,
% 7.94/5.77 ! [P: assn,Q: assn] :
% 7.94/5.77 ( ( entails @ P @ Q )
% 7.94/5.77 => ( entails @ P @ ( times_times_assn @ Q @ top_top_assn ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % ent_true_drop(2)
% 7.94/5.77 thf(fact_9544_ent__true__drop_I1_J,axiom,
% 7.94/5.77 ! [P: assn,Q: assn,R: assn] :
% 7.94/5.77 ( ( entails @ P @ ( times_times_assn @ Q @ top_top_assn ) )
% 7.94/5.77 => ( entails @ ( times_times_assn @ P @ R ) @ ( times_times_assn @ Q @ top_top_assn ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % ent_true_drop(1)
% 7.94/5.77 thf(fact_9545_ent__refl__true,axiom,
% 7.94/5.77 ! [A2: assn] : ( entails @ A2 @ ( times_times_assn @ A2 @ top_top_assn ) ) ).
% 7.94/5.77
% 7.94/5.77 % ent_refl_true
% 7.94/5.77 thf(fact_9546_ent__star__mono__true,axiom,
% 7.94/5.77 ! [A2: assn,A7: assn,B3: assn,B10: assn] :
% 7.94/5.77 ( ( entails @ A2 @ ( times_times_assn @ A7 @ top_top_assn ) )
% 7.94/5.77 => ( ( entails @ B3 @ ( times_times_assn @ B10 @ top_top_assn ) )
% 7.94/5.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ A2 @ B3 ) @ top_top_assn ) @ ( times_times_assn @ ( times_times_assn @ A7 @ B10 ) @ top_top_assn ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % ent_star_mono_true
% 7.94/5.77 thf(fact_9547_mod__star__trueI,axiom,
% 7.94/5.77 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 7.94/5.77 ( ( rep_assn @ P @ H2 )
% 7.94/5.77 => ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H2 ) ) ).
% 7.94/5.77
% 7.94/5.77 % mod_star_trueI
% 7.94/5.77 thf(fact_9548_mod__star__trueE,axiom,
% 7.94/5.77 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 7.94/5.77 ( ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H2 )
% 7.94/5.77 => ~ ! [H5: produc3658429121746597890et_nat] :
% 7.94/5.77 ~ ( rep_assn @ P @ H5 ) ) ).
% 7.94/5.77
% 7.94/5.77 % mod_star_trueE
% 7.94/5.77 thf(fact_9549_mod__h__bot__iff_I2_J,axiom,
% 7.94/5.77 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ top_top_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 7.94/5.77
% 7.94/5.77 % mod_h_bot_iff(2)
% 7.94/5.77 thf(fact_9550_VEBT__internal_Ospace_H_Opelims,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: nat] :
% 7.94/5.77 ( ( ( vEBT_VEBT_space2 @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ X )
% 7.94/5.77 => ( ! [A5: $o,B2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 7.94/5.77 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList2 ) @ zero_zero_nat ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % VEBT_internal.space'.pelims
% 7.94/5.77 thf(fact_9551_VEBT__internal_Ocnt_Opelims,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: real] :
% 7.94/5.77 ( ( ( vEBT_VEBT_cnt @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ X )
% 7.94/5.77 => ( ! [A5: $o,B2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.77 => ( ( Y = one_one_real )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 7.94/5.77 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary2 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList2 ) @ zero_zero_real ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % VEBT_internal.cnt.pelims
% 7.94/5.77 thf(fact_9552_VEBT__internal_Ocnt_H_Opelims,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: nat] :
% 7.94/5.77 ( ( ( vEBT_VEBT_cnt2 @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ X )
% 7.94/5.77 => ( ! [A5: $o,B2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 7.94/5.77 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_cnt2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_cnt2 @ TreeList2 ) @ zero_zero_nat ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % VEBT_internal.cnt'.pelims
% 7.94/5.77 thf(fact_9553_vebt__maxt_Opelims,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: option_nat] :
% 7.94/5.77 ( ( ( vEBT_vebt_maxt @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 7.94/5.77 => ( ! [A5: $o,B2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.77 => ( ( ( B2
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( some_nat @ one_one_nat ) ) )
% 7.94/5.77 & ( ~ B2
% 7.94/5.77 => ( ( A5
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( some_nat @ zero_zero_nat ) ) )
% 7.94/5.77 & ( ~ A5
% 7.94/5.77 => ( Y = none_nat ) ) ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 7.94/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.94/5.77 => ( ( Y = none_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 7.94/5.77 => ~ ! [Mi: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( some_nat @ Ma2 ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % vebt_maxt.pelims
% 7.94/5.77 thf(fact_9554_vebt__mint_Opelims,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: option_nat] :
% 7.94/5.77 ( ( ( vEBT_vebt_mint @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 7.94/5.77 => ( ! [A5: $o,B2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.77 => ( ( ( A5
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( some_nat @ zero_zero_nat ) ) )
% 7.94/5.77 & ( ~ A5
% 7.94/5.77 => ( ( B2
% 7.94/5.77 => ( Y
% 7.94/5.77 = ( some_nat @ one_one_nat ) ) )
% 7.94/5.77 & ( ~ B2
% 7.94/5.77 => ( Y = none_nat ) ) ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 7.94/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.94/5.77 => ( ( Y = none_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 7.94/5.77 => ~ ! [Mi: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( some_nat @ Mi ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % vebt_mint.pelims
% 7.94/5.77 thf(fact_9555_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: nat] :
% 7.94/5.77 ( ( ( vEBT_T_m_i_n_t @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X )
% 7.94/5.77 => ( ! [A5: $o,B2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A5 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 7.94/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 7.94/5.77 => ~ ! [Mi: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.pelims
% 7.94/5.77 thf(fact_9556_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: nat] :
% 7.94/5.77 ( ( ( vEBT_T_m_a_x_t @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ X )
% 7.94/5.77 => ( ! [A5: $o,B2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 7.94/5.77 => ( ( Y
% 7.94/5.77 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B2 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 7.94/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 7.94/5.77 => ~ ! [Mi: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.pelims
% 7.94/5.77 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,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: nat] :
% 7.94/5.77 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ X )
% 7.94/5.77 => ( ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ $false @ $false ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 7.94/5.77 => ( ! [Uv2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 7.94/5.77 => ( ! [Uu2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 7.94/5.77 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 7.94/5.77 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc ) )
% 7.94/5.77 => ( ( Y = one_one_nat )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.pelims
% 7.94/5.77 thf(fact_9558_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT,Y: $o] :
% 7.94/5.77 ( ( ( vEBT_VEBT_minNull @ X )
% 7.94/5.77 = Y )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 7.94/5.77 => ( ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ $false @ $false ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 7.94/5.77 => ( ! [Uv2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 7.94/5.77 => ( ~ Y
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 7.94/5.77 => ( ! [Uu2: $o] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 7.94/5.77 => ( ~ Y
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 7.94/5.77 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 7.94/5.77 => ( Y
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 7.94/5.77 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc ) )
% 7.94/5.77 => ( ~ Y
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc ) ) ) ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % VEBT_internal.minNull.pelims(1)
% 7.94/5.77 thf(fact_9559_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 7.94/5.77 ! [X: vEBT_VEBT] :
% 7.94/5.77 ( ( vEBT_VEBT_minNull @ X )
% 7.94/5.77 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 7.94/5.77 => ( ( ( X
% 7.94/5.77 = ( vEBT_Leaf @ $false @ $false ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 7.94/5.77 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 7.94/5.77 ( ( X
% 7.94/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 7.94/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % VEBT_internal.minNull.pelims(2)
% 7.94/5.77 thf(fact_9560_bin__last__integer__nbe,axiom,
% 7.94/5.77 ( bits_b8758750999018896077nteger
% 7.94/5.77 = ( ^ [I2: code_integer] :
% 7.94/5.77 ( ( modulo364778990260209775nteger @ I2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 7.94/5.77 != zero_z3403309356797280102nteger ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bin_last_integer_nbe
% 7.94/5.77 thf(fact_9561_bin__rest__integer_Oabs__eq,axiom,
% 7.94/5.77 ! [X: int] :
% 7.94/5.77 ( ( bits_b2549910563261871055nteger @ ( code_integer_of_int @ X ) )
% 7.94/5.77 = ( code_integer_of_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bin_rest_integer.abs_eq
% 7.94/5.77 thf(fact_9562_bitval__bin__last__integer,axiom,
% 7.94/5.77 ! [I: code_integer] :
% 7.94/5.77 ( ( zero_n356916108424825756nteger @ ( bits_b8758750999018896077nteger @ I ) )
% 7.94/5.77 = ( bit_se3949692690581998587nteger @ I @ one_one_Code_integer ) ) ).
% 7.94/5.77
% 7.94/5.77 % bitval_bin_last_integer
% 7.94/5.77 thf(fact_9563_bin__last__integer__code,axiom,
% 7.94/5.77 ( bits_b8758750999018896077nteger
% 7.94/5.77 = ( ^ [I2: code_integer] :
% 7.94/5.77 ( ( bit_se3949692690581998587nteger @ I2 @ one_one_Code_integer )
% 7.94/5.77 != zero_z3403309356797280102nteger ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bin_last_integer_code
% 7.94/5.77 thf(fact_9564_bitAND__integer__unfold,axiom,
% 7.94/5.77 ( bit_se3949692690581998587nteger
% 7.94/5.77 = ( ^ [X2: code_integer,Y6: code_integer] :
% 7.94/5.77 ( if_Code_integer @ ( X2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger
% 7.94/5.77 @ ( if_Code_integer
% 7.94/5.77 @ ( X2
% 7.94/5.77 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.94/5.77 @ Y6
% 7.94/5.77 @ ( bits_Bit_integer @ ( bit_se3949692690581998587nteger @ ( bits_b2549910563261871055nteger @ X2 ) @ ( bits_b2549910563261871055nteger @ Y6 ) )
% 7.94/5.77 @ ( ( bits_b8758750999018896077nteger @ X2 )
% 7.94/5.77 & ( bits_b8758750999018896077nteger @ Y6 ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bitAND_integer_unfold
% 7.94/5.77 thf(fact_9565_bitOR__integer__unfold,axiom,
% 7.94/5.77 ( bit_se1080825931792720795nteger
% 7.94/5.77 = ( ^ [X2: code_integer,Y6: code_integer] :
% 7.94/5.77 ( if_Code_integer @ ( X2 = zero_z3403309356797280102nteger ) @ Y6
% 7.94/5.77 @ ( if_Code_integer
% 7.94/5.77 @ ( X2
% 7.94/5.77 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.94/5.77 @ ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 7.94/5.77 @ ( bits_Bit_integer @ ( bit_se1080825931792720795nteger @ ( bits_b2549910563261871055nteger @ X2 ) @ ( bits_b2549910563261871055nteger @ Y6 ) )
% 7.94/5.77 @ ( ( bits_b8758750999018896077nteger @ X2 )
% 7.94/5.77 | ( bits_b8758750999018896077nteger @ Y6 ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bitOR_integer_unfold
% 7.94/5.77 thf(fact_9566_bitXOR__integer__unfold,axiom,
% 7.94/5.77 ( bit_se3222712562003087583nteger
% 7.94/5.77 = ( ^ [X2: code_integer,Y6: code_integer] :
% 7.94/5.77 ( if_Code_integer @ ( X2 = zero_z3403309356797280102nteger ) @ Y6
% 7.94/5.77 @ ( if_Code_integer
% 7.94/5.77 @ ( X2
% 7.94/5.77 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 7.94/5.77 @ ( bit_ri7632146776885996613nteger @ Y6 )
% 7.94/5.77 @ ( bits_Bit_integer @ ( bit_se3222712562003087583nteger @ ( bits_b2549910563261871055nteger @ X2 ) @ ( bits_b2549910563261871055nteger @ Y6 ) )
% 7.94/5.77 @ ( ( ~ ( bits_b8758750999018896077nteger @ X2 ) )
% 7.94/5.77 = ( bits_b8758750999018896077nteger @ Y6 ) ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bitXOR_integer_unfold
% 7.94/5.77 thf(fact_9567_bin__rest__integer__code,axiom,
% 7.94/5.77 ( bits_b2549910563261871055nteger
% 7.94/5.77 = ( ^ [I2: code_integer] : ( divide6298287555418463151nteger @ I2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bin_rest_integer_code
% 7.94/5.77 thf(fact_9568_bin__last__integer_Oabs__eq,axiom,
% 7.94/5.77 ! [X: int] :
% 7.94/5.77 ( ( bits_b8758750999018896077nteger @ ( code_integer_of_int @ X ) )
% 7.94/5.77 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bin_last_integer.abs_eq
% 7.94/5.77 thf(fact_9569_upto__aux__rec,axiom,
% 7.94/5.77 ( upto_aux
% 7.94/5.77 = ( ^ [I2: int,J2: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J2 @ I2 ) @ Js @ ( upto_aux @ I2 @ ( minus_minus_int @ J2 @ one_one_int ) @ ( cons_int @ J2 @ Js ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % upto_aux_rec
% 7.94/5.77 thf(fact_9570_concat__bit__Suc,axiom,
% 7.94/5.77 ! [N: nat,K: int,L: int] :
% 7.94/5.77 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 7.94/5.77 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_Suc
% 7.94/5.77 thf(fact_9571_drop__bit__nonnegative__int__iff,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 7.94/5.77 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_nonnegative_int_iff
% 7.94/5.77 thf(fact_9572_drop__bit__negative__int__iff,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 7.94/5.77 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_negative_int_iff
% 7.94/5.77 thf(fact_9573_drop__bit__minus__one,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 7.94/5.77 = ( uminus_uminus_int @ one_one_int ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_minus_one
% 7.94/5.77 thf(fact_9574_concat__bit__0,axiom,
% 7.94/5.77 ! [K: int,L: int] :
% 7.94/5.77 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 7.94/5.77 = L ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_0
% 7.94/5.77 thf(fact_9575_concat__bit__of__zero__2,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 7.94/5.77 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_of_zero_2
% 7.94/5.77 thf(fact_9576_concat__bit__nonnegative__iff,axiom,
% 7.94/5.77 ! [N: nat,K: int,L: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 7.94/5.77 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_nonnegative_iff
% 7.94/5.77 thf(fact_9577_concat__bit__negative__iff,axiom,
% 7.94/5.77 ! [N: nat,K: int,L: int] :
% 7.94/5.77 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 7.94/5.77 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_negative_iff
% 7.94/5.77 thf(fact_9578_drop__bit__Suc__minus__bit0,axiom,
% 7.94/5.77 ! [N: nat,K: num] :
% 7.94/5.77 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 7.94/5.77 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_Suc_minus_bit0
% 7.94/5.77 thf(fact_9579_drop__bit__of__Suc__0,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 7.94/5.77 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_of_Suc_0
% 7.94/5.77 thf(fact_9580_drop__bit__numeral__minus__bit0,axiom,
% 7.94/5.77 ! [L: num,K: num] :
% 7.94/5.77 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 7.94/5.77 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_numeral_minus_bit0
% 7.94/5.77 thf(fact_9581_drop__bit__Suc__minus__bit1,axiom,
% 7.94/5.77 ! [N: nat,K: num] :
% 7.94/5.77 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 7.94/5.77 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_Suc_minus_bit1
% 7.94/5.77 thf(fact_9582_drop__bit__numeral__minus__bit1,axiom,
% 7.94/5.77 ! [L: num,K: num] :
% 7.94/5.77 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 7.94/5.77 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_numeral_minus_bit1
% 7.94/5.77 thf(fact_9583_drop__bit__nat__eq,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 7.94/5.77 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_nat_eq
% 7.94/5.77 thf(fact_9584_drop__bit__int__code_I1_J,axiom,
% 7.94/5.77 ! [I: int] :
% 7.94/5.77 ( ( bit_se8568078237143864401it_int @ zero_zero_nat @ I )
% 7.94/5.77 = I ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_int_code(1)
% 7.94/5.77 thf(fact_9585_drop__bit__int__code_I2_J,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ zero_zero_int )
% 7.94/5.77 = zero_zero_int ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_int_code(2)
% 7.94/5.77 thf(fact_9586_concat__bit__assoc,axiom,
% 7.94/5.77 ! [N: nat,K: int,M: nat,L: int,R2: int] :
% 7.94/5.77 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R2 ) )
% 7.94/5.77 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R2 ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_assoc
% 7.94/5.77 thf(fact_9587_concat__bit__take__bit__eq,axiom,
% 7.94/5.77 ! [N: nat,B: int] :
% 7.94/5.77 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 7.94/5.77 = ( bit_concat_bit @ N @ B ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_take_bit_eq
% 7.94/5.77 thf(fact_9588_concat__bit__eq__iff,axiom,
% 7.94/5.77 ! [N: nat,K: int,L: int,R2: int,S: int] :
% 7.94/5.77 ( ( ( bit_concat_bit @ N @ K @ L )
% 7.94/5.77 = ( bit_concat_bit @ N @ R2 @ S ) )
% 7.94/5.77 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 7.94/5.77 = ( bit_se2923211474154528505it_int @ N @ R2 ) )
% 7.94/5.77 & ( L = S ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_eq_iff
% 7.94/5.77 thf(fact_9589_bit__concat__bit__iff,axiom,
% 7.94/5.77 ! [M: nat,K: int,L: int,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 7.94/5.77 = ( ( ( ord_less_nat @ N @ M )
% 7.94/5.77 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 7.94/5.77 | ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.77 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_concat_bit_iff
% 7.94/5.77 thf(fact_9590_shiftr__integer__conv__div__pow2,axiom,
% 7.94/5.77 ( bit_se3928097537394005634nteger
% 7.94/5.77 = ( ^ [N3: nat,X2: code_integer] : ( divide6298287555418463151nteger @ X2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % shiftr_integer_conv_div_pow2
% 7.94/5.77 thf(fact_9591_bin__rest__code,axiom,
% 7.94/5.77 ! [I: int] :
% 7.94/5.77 ( ( divide_divide_int @ I @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 7.94/5.77 = ( bit_se8568078237143864401it_int @ one_one_nat @ I ) ) ).
% 7.94/5.77
% 7.94/5.77 % bin_rest_code
% 7.94/5.77 thf(fact_9592_drop__bit__int__def,axiom,
% 7.94/5.77 ( bit_se8568078237143864401it_int
% 7.94/5.77 = ( ^ [N3: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_int_def
% 7.94/5.77 thf(fact_9593_signed__take__bit__eq__concat__bit,axiom,
% 7.94/5.77 ( bit_ri631733984087533419it_int
% 7.94/5.77 = ( ^ [N3: nat,K3: int] : ( bit_concat_bit @ N3 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % signed_take_bit_eq_concat_bit
% 7.94/5.77 thf(fact_9594_drop__bit__nat__def,axiom,
% 7.94/5.77 ( bit_se8570568707652914677it_nat
% 7.94/5.77 = ( ^ [N3: nat,M4: nat] : ( divide_divide_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_nat_def
% 7.94/5.77 thf(fact_9595_push__bit__nonnegative__int__iff,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 7.94/5.77 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 7.94/5.77
% 7.94/5.77 % push_bit_nonnegative_int_iff
% 7.94/5.77 thf(fact_9596_push__bit__negative__int__iff,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 7.94/5.77 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 7.94/5.77
% 7.94/5.77 % push_bit_negative_int_iff
% 7.94/5.77 thf(fact_9597_concat__bit__of__zero__1,axiom,
% 7.94/5.77 ! [N: nat,L: int] :
% 7.94/5.77 ( ( bit_concat_bit @ N @ zero_zero_int @ L )
% 7.94/5.77 = ( bit_se545348938243370406it_int @ N @ L ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_of_zero_1
% 7.94/5.77 thf(fact_9598_push__bit__of__Suc__0,axiom,
% 7.94/5.77 ! [N: nat] :
% 7.94/5.77 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 7.94/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 7.94/5.77
% 7.94/5.77 % push_bit_of_Suc_0
% 7.94/5.77 thf(fact_9599_drop__bit__push__bit__int,axiom,
% 7.94/5.77 ! [M: nat,N: nat,K: int] :
% 7.94/5.77 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 7.94/5.77 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % drop_bit_push_bit_int
% 7.94/5.77 thf(fact_9600_push__bit__int__code_I1_J,axiom,
% 7.94/5.77 ! [I: int] :
% 7.94/5.77 ( ( bit_se545348938243370406it_int @ zero_zero_nat @ I )
% 7.94/5.77 = I ) ).
% 7.94/5.77
% 7.94/5.77 % push_bit_int_code(1)
% 7.94/5.77 thf(fact_9601_push__bit__nat__eq,axiom,
% 7.94/5.77 ! [N: nat,K: int] :
% 7.94/5.77 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 7.94/5.77 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % push_bit_nat_eq
% 7.94/5.77 thf(fact_9602_set__bit__nat__def,axiom,
% 7.94/5.77 ( bit_se7882103937844011126it_nat
% 7.94/5.77 = ( ^ [M4: nat,N3: nat] : ( bit_se1412395901928357646or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M4 @ one_one_nat ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % set_bit_nat_def
% 7.94/5.77 thf(fact_9603_flip__bit__nat__def,axiom,
% 7.94/5.77 ( bit_se2161824704523386999it_nat
% 7.94/5.77 = ( ^ [M4: nat,N3: nat] : ( bit_se6528837805403552850or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M4 @ one_one_nat ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % flip_bit_nat_def
% 7.94/5.77 thf(fact_9604_Bit__integer__code_I1_J,axiom,
% 7.94/5.77 ! [I: code_integer] :
% 7.94/5.77 ( ( bits_Bit_integer @ I @ $false )
% 7.94/5.77 = ( bit_se7788150548672797655nteger @ one_one_nat @ I ) ) ).
% 7.94/5.77
% 7.94/5.77 % Bit_integer_code(1)
% 7.94/5.77 thf(fact_9605_bit__push__bit__iff__int,axiom,
% 7.94/5.77 ! [M: nat,K: int,N: nat] :
% 7.94/5.77 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 7.94/5.77 = ( ( ord_less_eq_nat @ M @ N )
% 7.94/5.77 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % bit_push_bit_iff_int
% 7.94/5.77 thf(fact_9606_concat__bit__eq,axiom,
% 7.94/5.77 ( bit_concat_bit
% 7.94/5.77 = ( ^ [N3: nat,K3: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N3 @ K3 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_eq
% 7.94/5.77 thf(fact_9607_concat__bit__def,axiom,
% 7.94/5.77 ( bit_concat_bit
% 7.94/5.77 = ( ^ [N3: nat,K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N3 @ K3 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 7.94/5.77
% 7.94/5.77 % concat_bit_def
% 7.94/5.77 thf(fact_9608_Bit__Operations_Oset__bit__int__def,axiom,
% 7.94/5.77 ( bit_se7879613467334960850it_int
% 8.01/5.77 = ( ^ [N3: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Bit_Operations.set_bit_int_def
% 8.01/5.77 thf(fact_9609_bit__push__bit__iff__nat,axiom,
% 8.01/5.77 ! [M: nat,Q3: nat,N: nat] :
% 8.01/5.77 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N )
% 8.01/5.77 = ( ( ord_less_eq_nat @ M @ N )
% 8.01/5.77 & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % bit_push_bit_iff_nat
% 8.01/5.77 thf(fact_9610_flip__bit__int__def,axiom,
% 8.01/5.77 ( bit_se2159334234014336723it_int
% 8.01/5.77 = ( ^ [N3: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % flip_bit_int_def
% 8.01/5.77 thf(fact_9611_shiftl__integer__conv__mult__pow2,axiom,
% 8.01/5.77 ( bit_se7788150548672797655nteger
% 8.01/5.77 = ( ^ [N3: nat,X2: code_integer] : ( times_3573771949741848930nteger @ X2 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % shiftl_integer_conv_mult_pow2
% 8.01/5.77 thf(fact_9612_unset__bit__int__def,axiom,
% 8.01/5.77 ( bit_se4203085406695923979it_int
% 8.01/5.77 = ( ^ [N3: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % unset_bit_int_def
% 8.01/5.77 thf(fact_9613_push__bit__int__def,axiom,
% 8.01/5.77 ( bit_se545348938243370406it_int
% 8.01/5.77 = ( ^ [N3: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % push_bit_int_def
% 8.01/5.77 thf(fact_9614_Bit__integer__code_I2_J,axiom,
% 8.01/5.77 ! [I: code_integer] :
% 8.01/5.77 ( ( bits_Bit_integer @ I @ $true )
% 8.01/5.77 = ( plus_p5714425477246183910nteger @ ( bit_se7788150548672797655nteger @ one_one_nat @ I ) @ one_one_Code_integer ) ) ).
% 8.01/5.77
% 8.01/5.77 % Bit_integer_code(2)
% 8.01/5.77 thf(fact_9615_push__bit__nat__def,axiom,
% 8.01/5.77 ( bit_se547839408752420682it_nat
% 8.01/5.77 = ( ^ [N3: nat,M4: nat] : ( times_times_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % push_bit_nat_def
% 8.01/5.77 thf(fact_9616_push__bit__minus__one,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 8.01/5.77 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % push_bit_minus_one
% 8.01/5.77 thf(fact_9617_set__bit__integer__conv__masks,axiom,
% 8.01/5.77 ( generi2397576812484419408nteger
% 8.01/5.77 = ( ^ [X2: code_integer,I2: nat,B4: $o] : ( if_Code_integer @ B4 @ ( bit_se1080825931792720795nteger @ X2 @ ( bit_se7788150548672797655nteger @ I2 @ one_one_Code_integer ) ) @ ( bit_se3949692690581998587nteger @ X2 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ I2 @ one_one_Code_integer ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % set_bit_integer_conv_masks
% 8.01/5.77 thf(fact_9618_Uint32__code,axiom,
% 8.01/5.77 ( uint322
% 8.01/5.77 = ( ^ [I2: code_integer] : ( if_uint32 @ ( bit_se9216721137139052372nteger @ ( bit_se3949692690581998587nteger @ I2 @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( uint32_signed @ ( minus_8373710615458151222nteger @ ( bit_se3949692690581998587nteger @ I2 @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( uint32_signed @ ( bit_se3949692690581998587nteger @ I2 @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Uint32_code
% 8.01/5.77 thf(fact_9619_Uint32__signed__def,axiom,
% 8.01/5.77 ( uint32_signed
% 8.01/5.77 = ( ^ [I2: code_integer] :
% 8.01/5.77 ( if_uint32
% 8.01/5.77 @ ( ( ord_le6747313008572928689nteger @ I2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 8.01/5.77 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ I2 ) )
% 8.01/5.77 @ ( undefi2040150642751712519uint32 @ uint322 @ I2 )
% 8.01/5.77 @ ( uint322 @ I2 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Uint32_signed_def
% 8.01/5.77 thf(fact_9620_Generic__set__bit_Oset__bit__int__def,axiom,
% 8.01/5.77 ( generi8991105624351003935it_int
% 8.01/5.77 = ( ^ [I2: int,N3: nat,B4: $o] : ( if_nat_int_int @ B4 @ bit_se7879613467334960850it_int @ bit_se4203085406695923979it_int @ N3 @ I2 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Generic_set_bit.set_bit_int_def
% 8.01/5.77 thf(fact_9621_int__set__bit__True__conv__OR,axiom,
% 8.01/5.77 ! [I: int,N: nat] :
% 8.01/5.77 ( ( generi8991105624351003935it_int @ I @ N @ $true )
% 8.01/5.77 = ( bit_se1409905431419307370or_int @ I @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_set_bit_True_conv_OR
% 8.01/5.77 thf(fact_9622_int__set__bit__False__conv__NAND,axiom,
% 8.01/5.77 ! [I: int,N: nat] :
% 8.01/5.77 ( ( generi8991105624351003935it_int @ I @ N @ $false )
% 8.01/5.77 = ( bit_se725231765392027082nd_int @ I @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_set_bit_False_conv_NAND
% 8.01/5.77 thf(fact_9623_int__set__bit__conv__ops,axiom,
% 8.01/5.77 ( generi8991105624351003935it_int
% 8.01/5.77 = ( ^ [I2: int,N3: nat,B4: $o] : ( if_int @ B4 @ ( bit_se1409905431419307370or_int @ I2 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) @ ( bit_se725231765392027082nd_int @ I2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_set_bit_conv_ops
% 8.01/5.77 thf(fact_9624_assn__aci_I11_J,axiom,
% 8.01/5.77 ! [X: assn,Y: assn,A: assn,B: assn] :
% 8.01/5.77 ( ( syntax7398250324933576852n_assn @ ( times_times_assn @ X @ Y ) @ A )
% 8.01/5.77 => ( ( times_times_assn @ A @ B )
% 8.01/5.77 = ( times_times_assn @ B @ A ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % assn_aci(11)
% 8.01/5.77 thf(fact_9625_horner__sum__of__bool__2__less,axiom,
% 8.01/5.77 ! [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 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % horner_sum_of_bool_2_less
% 8.01/5.77 thf(fact_9626_Cauchy__iff2,axiom,
% 8.01/5.77 ( topolo4055970368930404560y_real
% 8.01/5.77 = ( ^ [X7: nat > real] :
% 8.01/5.77 ! [J2: nat] :
% 8.01/5.77 ? [M8: nat] :
% 8.01/5.77 ! [M4: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ M8 @ M4 )
% 8.01/5.77 => ! [N3: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ M8 @ N3 )
% 8.01/5.77 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X7 @ M4 ) @ ( X7 @ N3 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J2 ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Cauchy_iff2
% 8.01/5.77 thf(fact_9627_int__sdiv__simps_I2_J,axiom,
% 8.01/5.77 ! [A: int] :
% 8.01/5.77 ( ( signed6714573509424544716de_int @ A @ zero_zero_int )
% 8.01/5.77 = zero_zero_int ) ).
% 8.01/5.77
% 8.01/5.77 % int_sdiv_simps(2)
% 8.01/5.77 thf(fact_9628_sdiv__int__0__div,axiom,
% 8.01/5.77 ! [X: int] :
% 8.01/5.77 ( ( signed6714573509424544716de_int @ zero_zero_int @ X )
% 8.01/5.77 = zero_zero_int ) ).
% 8.01/5.77
% 8.01/5.77 % sdiv_int_0_div
% 8.01/5.77 thf(fact_9629_sdiv__int__div__0,axiom,
% 8.01/5.77 ! [X: int] :
% 8.01/5.77 ( ( signed6714573509424544716de_int @ X @ zero_zero_int )
% 8.01/5.77 = zero_zero_int ) ).
% 8.01/5.77
% 8.01/5.77 % sdiv_int_div_0
% 8.01/5.77 thf(fact_9630_int__sdiv__simps_I1_J,axiom,
% 8.01/5.77 ! [A: int] :
% 8.01/5.77 ( ( signed6714573509424544716de_int @ A @ one_one_int )
% 8.01/5.77 = A ) ).
% 8.01/5.77
% 8.01/5.77 % int_sdiv_simps(1)
% 8.01/5.77 thf(fact_9631_int__sdiv__same__is__1,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( A != zero_zero_int )
% 8.01/5.77 => ( ( ( signed6714573509424544716de_int @ A @ B )
% 8.01/5.77 = A )
% 8.01/5.77 = ( B = one_one_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_sdiv_same_is_1
% 8.01/5.77 thf(fact_9632_int__sdiv__simps_I3_J,axiom,
% 8.01/5.77 ! [A: int] :
% 8.01/5.77 ( ( signed6714573509424544716de_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 8.01/5.77 = ( uminus_uminus_int @ A ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_sdiv_simps(3)
% 8.01/5.77 thf(fact_9633_sdiv__int__numeral__numeral,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( signed6714573509424544716de_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 = ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % sdiv_int_numeral_numeral
% 8.01/5.77 thf(fact_9634_length__upt,axiom,
% 8.01/5.77 ! [I: nat,J: nat] :
% 8.01/5.77 ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 8.01/5.77 = ( minus_minus_nat @ J @ I ) ) ).
% 8.01/5.77
% 8.01/5.77 % length_upt
% 8.01/5.77 thf(fact_9635_int__sdiv__negated__is__minus1,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( A != zero_zero_int )
% 8.01/5.77 => ( ( ( signed6714573509424544716de_int @ A @ B )
% 8.01/5.77 = ( uminus_uminus_int @ A ) )
% 8.01/5.77 = ( B
% 8.01/5.77 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_sdiv_negated_is_minus1
% 8.01/5.77 thf(fact_9636_nth__upt,axiom,
% 8.01/5.77 ! [I: nat,K: nat,J: nat] :
% 8.01/5.77 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 8.01/5.77 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 8.01/5.77 = ( plus_plus_nat @ I @ K ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % nth_upt
% 8.01/5.77 thf(fact_9637_upt__conv__Cons,axiom,
% 8.01/5.77 ! [I: nat,J: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I @ J )
% 8.01/5.77 => ( ( upt @ I @ J )
% 8.01/5.77 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_conv_Cons
% 8.01/5.77 thf(fact_9638_upt__conv__Cons__Cons,axiom,
% 8.01/5.77 ! [M: nat,N: nat,Ns: list_nat,Q3: nat] :
% 8.01/5.77 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 8.01/5.77 = ( upt @ M @ Q3 ) )
% 8.01/5.77 = ( ( cons_nat @ N @ Ns )
% 8.01/5.77 = ( upt @ ( suc @ M ) @ Q3 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_conv_Cons_Cons
% 8.01/5.77 thf(fact_9639_map__Suc__upt,axiom,
% 8.01/5.77 ! [M: nat,N: nat] :
% 8.01/5.77 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 8.01/5.77 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % map_Suc_upt
% 8.01/5.77 thf(fact_9640_map__add__upt_H,axiom,
% 8.01/5.77 ! [Ofs: nat,A: nat,B: nat] :
% 8.01/5.77 ( ( map_nat_nat
% 8.01/5.77 @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ Ofs )
% 8.01/5.77 @ ( upt @ A @ B ) )
% 8.01/5.77 = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % map_add_upt'
% 8.01/5.77 thf(fact_9641_map__add__upt,axiom,
% 8.01/5.77 ! [N: nat,M: nat] :
% 8.01/5.77 ( ( map_nat_nat
% 8.01/5.77 @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ N )
% 8.01/5.77 @ ( upt @ zero_zero_nat @ M ) )
% 8.01/5.77 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % map_add_upt
% 8.01/5.77 thf(fact_9642_atLeastLessThan__upt,axiom,
% 8.01/5.77 ( set_or4665077453230672383an_nat
% 8.01/5.77 = ( ^ [I2: nat,J2: nat] : ( set_nat2 @ ( upt @ I2 @ J2 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastLessThan_upt
% 8.01/5.77 thf(fact_9643_upt__eq__Cons__conv,axiom,
% 8.01/5.77 ! [I: nat,J: nat,X: nat,Xs2: list_nat] :
% 8.01/5.77 ( ( ( upt @ I @ J )
% 8.01/5.77 = ( cons_nat @ X @ Xs2 ) )
% 8.01/5.77 = ( ( ord_less_nat @ I @ J )
% 8.01/5.77 & ( I = X )
% 8.01/5.77 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 8.01/5.77 = Xs2 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_eq_Cons_conv
% 8.01/5.77 thf(fact_9644_map__decr__upt,axiom,
% 8.01/5.77 ! [M: nat,N: nat] :
% 8.01/5.77 ( ( map_nat_nat
% 8.01/5.77 @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 8.01/5.77 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 8.01/5.77 = ( upt @ M @ N ) ) ).
% 8.01/5.77
% 8.01/5.77 % map_decr_upt
% 8.01/5.77 thf(fact_9645_atLeastAtMost__upt,axiom,
% 8.01/5.77 ( set_or1269000886237332187st_nat
% 8.01/5.77 = ( ^ [N3: nat,M4: nat] : ( set_nat2 @ ( upt @ N3 @ ( suc @ M4 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastAtMost_upt
% 8.01/5.77 thf(fact_9646_atLeast__upt,axiom,
% 8.01/5.77 ( set_ord_lessThan_nat
% 8.01/5.77 = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N3 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeast_upt
% 8.01/5.77 thf(fact_9647_sgn__sdiv__eq__sgn__mult,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ( signed6714573509424544716de_int @ A @ B )
% 8.01/5.77 != zero_zero_int )
% 8.01/5.77 => ( ( sgn_sgn_int @ ( signed6714573509424544716de_int @ A @ B ) )
% 8.01/5.77 = ( sgn_sgn_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % sgn_sdiv_eq_sgn_mult
% 8.01/5.77 thf(fact_9648_atMost__upto,axiom,
% 8.01/5.77 ( set_ord_atMost_nat
% 8.01/5.77 = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N3 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % atMost_upto
% 8.01/5.77 thf(fact_9649_map__bit__range__eq__if__take__bit__eq,axiom,
% 8.01/5.77 ! [N: nat,K: int,L: int] :
% 8.01/5.77 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 8.01/5.77 = ( bit_se2923211474154528505it_int @ N @ L ) )
% 8.01/5.77 => ( ( map_nat_o @ ( bit_se1146084159140164899it_int @ K ) @ ( upt @ zero_zero_nat @ N ) )
% 8.01/5.77 = ( map_nat_o @ ( bit_se1146084159140164899it_int @ L ) @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % map_bit_range_eq_if_take_bit_eq
% 8.01/5.77 thf(fact_9650_signed__divide__int__def,axiom,
% 8.01/5.77 ( signed6714573509424544716de_int
% 8.01/5.77 = ( ^ [K3: int,L2: int] : ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K3 ) @ ( sgn_sgn_int @ L2 ) ) @ ( divide_divide_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % signed_divide_int_def
% 8.01/5.77 thf(fact_9651_entails__solve__init_I1_J,axiom,
% 8.01/5.77 ! [P: assn,Q: assn] :
% 8.01/5.77 ( ( fI_QUERY @ P @ Q @ top_top_assn )
% 8.01/5.77 => ( entails @ P @ ( times_times_assn @ Q @ top_top_assn ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % entails_solve_init(1)
% 8.01/5.77 thf(fact_9652_VEBT_Osize_I3_J,axiom,
% 8.01/5.77 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 8.01/5.77 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 8.01/5.77 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT.size(3)
% 8.01/5.77 thf(fact_9653_frame__inference__init,axiom,
% 8.01/5.77 ! [P: assn,Q: assn,F2: assn] :
% 8.01/5.77 ( ( fI_QUERY @ P @ Q @ F2 )
% 8.01/5.77 => ( entails @ P @ ( times_times_assn @ Q @ F2 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % frame_inference_init
% 8.01/5.77 thf(fact_9654_FI__QUERY__def,axiom,
% 8.01/5.77 ( fI_QUERY
% 8.01/5.77 = ( ^ [P2: assn,Q2: assn,F5: assn] : ( entails @ P2 @ ( times_times_assn @ Q2 @ F5 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % FI_QUERY_def
% 8.01/5.77 thf(fact_9655_entails__solve__init_I2_J,axiom,
% 8.01/5.77 ! [P: assn,Q: assn] :
% 8.01/5.77 ( ( fI_QUERY @ P @ Q @ one_one_assn )
% 8.01/5.77 => ( entails @ P @ Q ) ) ).
% 8.01/5.77
% 8.01/5.77 % entails_solve_init(2)
% 8.01/5.77 thf(fact_9656_VEBT_Osize__gen_I1_J,axiom,
% 8.01/5.77 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 8.01/5.77 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 8.01/5.77 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT.size_gen(1)
% 8.01/5.77 thf(fact_9657_smod__int__range,axiom,
% 8.01/5.77 ! [B: int,A: int] :
% 8.01/5.77 ( ( B != zero_zero_int )
% 8.01/5.77 => ( member_int @ ( signed6292675348222524329lo_int @ A @ B ) @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ ( uminus_uminus_int @ ( abs_abs_int @ B ) ) @ one_one_int ) @ ( minus_minus_int @ ( abs_abs_int @ B ) @ one_one_int ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_range
% 8.01/5.77 thf(fact_9658_smod__int__0__mod,axiom,
% 8.01/5.77 ! [X: int] :
% 8.01/5.77 ( ( signed6292675348222524329lo_int @ zero_zero_int @ X )
% 8.01/5.77 = zero_zero_int ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_0_mod
% 8.01/5.77 thf(fact_9659_smod__int__mod__0,axiom,
% 8.01/5.77 ! [X: int] :
% 8.01/5.77 ( ( signed6292675348222524329lo_int @ X @ zero_zero_int )
% 8.01/5.77 = X ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_mod_0
% 8.01/5.77 thf(fact_9660_smod__int__numeral__numeral,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( signed6292675348222524329lo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 = ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_numeral_numeral
% 8.01/5.77 thf(fact_9661_smod__int__compares_I1_J,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.01/5.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.01/5.77 => ( ord_less_int @ ( signed6292675348222524329lo_int @ A @ B ) @ B ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_compares(1)
% 8.01/5.77 thf(fact_9662_smod__int__compares_I2_J,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.01/5.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.01/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_compares(2)
% 8.01/5.77 thf(fact_9663_smod__int__compares_I4_J,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.01/5.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.01/5.77 => ( ord_less_eq_int @ ( signed6292675348222524329lo_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_compares(4)
% 8.01/5.77 thf(fact_9664_smod__int__compares_I6_J,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.01/5.77 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.01/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_compares(6)
% 8.01/5.77 thf(fact_9665_smod__int__compares_I7_J,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.01/5.77 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.01/5.77 => ( ord_less_eq_int @ ( signed6292675348222524329lo_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_compares(7)
% 8.01/5.77 thf(fact_9666_smod__int__compares_I8_J,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.01/5.77 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.01/5.77 => ( ord_less_eq_int @ B @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_compares(8)
% 8.01/5.77 thf(fact_9667_smod__mod__positive,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.01/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.01/5.77 => ( ( signed6292675348222524329lo_int @ A @ B )
% 8.01/5.77 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_mod_positive
% 8.01/5.77 thf(fact_9668_smod__int__compares_I3_J,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.01/5.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.01/5.77 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_compares(3)
% 8.01/5.77 thf(fact_9669_smod__int__compares_I5_J,axiom,
% 8.01/5.77 ! [A: int,B: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.01/5.77 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.01/5.77 => ( ord_less_int @ ( signed6292675348222524329lo_int @ A @ B ) @ ( uminus_uminus_int @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_compares(5)
% 8.01/5.77 thf(fact_9670_smod__int__alt__def,axiom,
% 8.01/5.77 ( signed6292675348222524329lo_int
% 8.01/5.77 = ( ^ [A3: int,B4: int] : ( times_times_int @ ( sgn_sgn_int @ A3 ) @ ( modulo_modulo_int @ ( abs_abs_int @ A3 ) @ ( abs_abs_int @ B4 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % smod_int_alt_def
% 8.01/5.77 thf(fact_9671_VEBT_Osize__gen_I2_J,axiom,
% 8.01/5.77 ! [X21: $o,X222: $o] :
% 8.01/5.77 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 8.01/5.77 = zero_zero_nat ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT.size_gen(2)
% 8.01/5.77 thf(fact_9672_valid__eq2,axiom,
% 8.01/5.77 ! [T: vEBT_VEBT,D2: nat] :
% 8.01/5.77 ( ( vEBT_VEBT_valid @ T @ D2 )
% 8.01/5.77 => ( vEBT_invar_vebt @ T @ D2 ) ) ).
% 8.01/5.77
% 8.01/5.77 % valid_eq2
% 8.01/5.77 thf(fact_9673_valid__eq,axiom,
% 8.01/5.77 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 8.01/5.77
% 8.01/5.77 % valid_eq
% 8.01/5.77 thf(fact_9674_valid__eq1,axiom,
% 8.01/5.77 ! [T: vEBT_VEBT,D2: nat] :
% 8.01/5.77 ( ( vEBT_invar_vebt @ T @ D2 )
% 8.01/5.77 => ( vEBT_VEBT_valid @ T @ D2 ) ) ).
% 8.01/5.77
% 8.01/5.77 % valid_eq1
% 8.01/5.77 thf(fact_9675_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 8.01/5.77 ! [Uu: $o,Uv: $o,D2: nat] :
% 8.01/5.77 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D2 )
% 8.01/5.77 = ( D2 = one_one_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.valid'.simps(1)
% 8.01/5.77 thf(fact_9676_uint32_Osize__eq__length,axiom,
% 8.01/5.77 ( ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 = ( type_l796852477590012082l_num1 @ type_N8448461349408098053l_num1 ) ) ).
% 8.01/5.77
% 8.01/5.77 % uint32.size_eq_length
% 8.01/5.77 thf(fact_9677_len__num0,axiom,
% 8.01/5.77 ( type_l4264026598287037464l_num0
% 8.01/5.77 = ( ^ [Uu4: itself_Numeral_num0] : zero_zero_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % len_num0
% 8.01/5.77 thf(fact_9678_len__num1,axiom,
% 8.01/5.77 ( type_l4264026598287037465l_num1
% 8.01/5.77 = ( ^ [Uu4: itself_Numeral_num1] : one_one_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % len_num1
% 8.01/5.77 thf(fact_9679_len__of__finite__1__def,axiom,
% 8.01/5.77 ( type_l31302759751748491nite_1
% 8.01/5.77 = ( ^ [X2: itself_finite_1] : one_one_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % len_of_finite_1_def
% 8.01/5.77 thf(fact_9680_len__of__finite__3__def,axiom,
% 8.01/5.77 ( type_l31302759751748493nite_3
% 8.01/5.77 = ( ^ [X2: itself_finite_3] : ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % len_of_finite_3_def
% 8.01/5.77 thf(fact_9681_len__of__finite__2__def,axiom,
% 8.01/5.77 ( type_l31302759751748492nite_2
% 8.01/5.77 = ( ^ [X2: itself_finite_2] : ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % len_of_finite_2_def
% 8.01/5.77 thf(fact_9682_bij__betw__Suc,axiom,
% 8.01/5.77 ! [M7: set_nat,N4: set_nat] :
% 8.01/5.77 ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 8.01/5.77 = ( ( image_nat_nat @ suc @ M7 )
% 8.01/5.77 = N4 ) ) ).
% 8.01/5.77
% 8.01/5.77 % bij_betw_Suc
% 8.01/5.77 thf(fact_9683_image__Suc__atLeastLessThan,axiom,
% 8.01/5.77 ! [I: nat,J: nat] :
% 8.01/5.77 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 8.01/5.77 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % image_Suc_atLeastLessThan
% 8.01/5.77 thf(fact_9684_image__Suc__atLeastAtMost,axiom,
% 8.01/5.77 ! [I: nat,J: nat] :
% 8.01/5.77 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 8.01/5.77 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % image_Suc_atLeastAtMost
% 8.01/5.77 thf(fact_9685_zero__notin__Suc__image,axiom,
% 8.01/5.77 ! [A2: set_nat] :
% 8.01/5.77 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 8.01/5.77
% 8.01/5.77 % zero_notin_Suc_image
% 8.01/5.77 thf(fact_9686_image__Suc__lessThan,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 8.01/5.77
% 8.01/5.77 % image_Suc_lessThan
% 8.01/5.77 thf(fact_9687_image__Suc__atMost,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 8.01/5.77 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % image_Suc_atMost
% 8.01/5.77 thf(fact_9688_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.01/5.77 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeast0_lessThan_Suc_eq_insert_0
% 8.01/5.77 thf(fact_9689_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.01/5.77 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeast0_atMost_Suc_eq_insert_0
% 8.01/5.77 thf(fact_9690_lessThan__Suc__eq__insert__0,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 8.01/5.77 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lessThan_Suc_eq_insert_0
% 8.01/5.77 thf(fact_9691_atMost__Suc__eq__insert__0,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 8.01/5.77 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % atMost_Suc_eq_insert_0
% 8.01/5.77 thf(fact_9692_image__add__int__atLeastLessThan,axiom,
% 8.01/5.77 ! [L: int,U: int] :
% 8.01/5.77 ( ( image_int_int
% 8.01/5.77 @ ^ [X2: int] : ( plus_plus_int @ X2 @ L )
% 8.01/5.77 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 8.01/5.77 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 8.01/5.77
% 8.01/5.77 % image_add_int_atLeastLessThan
% 8.01/5.77 thf(fact_9693_image__add__integer__atLeastLessThan,axiom,
% 8.01/5.77 ! [L: code_integer,U: code_integer] :
% 8.01/5.77 ( ( image_4470545334726330049nteger
% 8.01/5.77 @ ^ [X2: code_integer] : ( plus_p5714425477246183910nteger @ X2 @ L )
% 8.01/5.77 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 8.01/5.77 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 8.01/5.77
% 8.01/5.77 % image_add_integer_atLeastLessThan
% 8.01/5.77 thf(fact_9694_image__atLeastZeroLessThan__int,axiom,
% 8.01/5.77 ! [U: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.01/5.77 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 8.01/5.77 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % image_atLeastZeroLessThan_int
% 8.01/5.77 thf(fact_9695_image__minus__const__atLeastLessThan__nat,axiom,
% 8.01/5.77 ! [C: nat,Y: nat,X: nat] :
% 8.01/5.77 ( ( ( ord_less_nat @ C @ Y )
% 8.01/5.77 => ( ( image_nat_nat
% 8.01/5.77 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 8.01/5.77 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 8.01/5.77 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 8.01/5.77 & ( ~ ( ord_less_nat @ C @ Y )
% 8.01/5.77 => ( ( ( ord_less_nat @ X @ Y )
% 8.01/5.77 => ( ( image_nat_nat
% 8.01/5.77 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 8.01/5.77 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 8.01/5.77 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 8.01/5.77 & ( ~ ( ord_less_nat @ X @ Y )
% 8.01/5.77 => ( ( image_nat_nat
% 8.01/5.77 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 8.01/5.77 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 8.01/5.77 = bot_bot_set_nat ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % image_minus_const_atLeastLessThan_nat
% 8.01/5.77 thf(fact_9696_setceilmax,axiom,
% 8.01/5.77 ! [S: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 8.01/5.77 ( ( vEBT_invar_vebt @ S @ M )
% 8.01/5.77 => ( ! [X3: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 8.01/5.77 => ( vEBT_invar_vebt @ X3 @ N ) )
% 8.01/5.77 => ( ( M
% 8.01/5.77 = ( suc @ N ) )
% 8.01/5.77 => ( ! [X3: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 8.01/5.77 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X3 ) )
% 8.01/5.77 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 8.01/5.77 => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S ) )
% 8.01/5.77 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 8.01/5.77 => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 8.01/5.77 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % setceilmax
% 8.01/5.77 thf(fact_9697_max__idx__list,axiom,
% 8.01/5.77 ! [I: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 8.01/5.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 8.01/5.77 => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % max_idx_list
% 8.01/5.77 thf(fact_9698_height__compose__list,axiom,
% 8.01/5.77 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.01/5.77 => ( 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 ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % height_compose_list
% 8.01/5.77 thf(fact_9699_max__ins__scaled,axiom,
% 8.01/5.77 ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % max_ins_scaled
% 8.01/5.77 thf(fact_9700_height__i__max,axiom,
% 8.01/5.77 ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 8.01/5.77 => ( 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 ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % height_i_max
% 8.01/5.77 thf(fact_9701_Max__divisors__self__nat,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( N != zero_zero_nat )
% 8.01/5.77 => ( ( lattic8265883725875713057ax_nat
% 8.01/5.77 @ ( collect_nat
% 8.01/5.77 @ ^ [D: nat] : ( dvd_dvd_nat @ D @ N ) ) )
% 8.01/5.77 = N ) ) ).
% 8.01/5.77
% 8.01/5.77 % Max_divisors_self_nat
% 8.01/5.77 thf(fact_9702_divide__nat__def,axiom,
% 8.01/5.77 ( divide_divide_nat
% 8.01/5.77 = ( ^ [M4: nat,N3: nat] :
% 8.01/5.77 ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 8.01/5.77 @ ( lattic8265883725875713057ax_nat
% 8.01/5.77 @ ( collect_nat
% 8.01/5.77 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N3 ) @ M4 ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % divide_nat_def
% 8.01/5.77 thf(fact_9703_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 8.01/5.77 ! [Uu: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.01/5.77 ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu @ Deg @ TreeList @ Summary ) )
% 8.01/5.77 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.height.simps(2)
% 8.01/5.77 thf(fact_9704_VEBT__internal_Oheight_Oelims,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Y: nat] :
% 8.01/5.77 ( ( ( vEBT_VEBT_height @ X )
% 8.01/5.77 = Y )
% 8.01/5.77 => ( ( ? [A5: $o,B2: $o] :
% 8.01/5.77 ( X
% 8.01/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 8.01/5.77 => ( Y != zero_zero_nat ) )
% 8.01/5.77 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 8.01/5.77 => ( Y
% 8.01/5.77 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.height.elims
% 8.01/5.77 thf(fact_9705_VEBT__internal_Oheight_Opelims,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Y: nat] :
% 8.01/5.77 ( ( ( vEBT_VEBT_height @ X )
% 8.01/5.77 = Y )
% 8.01/5.77 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X )
% 8.01/5.77 => ( ! [A5: $o,B2: $o] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 8.01/5.77 => ( ( Y = zero_zero_nat )
% 8.01/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A5 @ B2 ) ) ) )
% 8.01/5.77 => ~ ! [Uu2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 8.01/5.77 => ( ( Y
% 8.01/5.77 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) )
% 8.01/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.height.pelims
% 8.01/5.77 thf(fact_9706_Max__divisors__self__int,axiom,
% 8.01/5.77 ! [N: int] :
% 8.01/5.77 ( ( N != zero_zero_int )
% 8.01/5.77 => ( ( lattic8263393255366662781ax_int
% 8.01/5.77 @ ( collect_int
% 8.01/5.77 @ ^ [D: int] : ( dvd_dvd_int @ D @ N ) ) )
% 8.01/5.77 = ( abs_abs_int @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Max_divisors_self_int
% 8.01/5.77 thf(fact_9707_min__Suc__Suc,axiom,
% 8.01/5.77 ! [M: nat,N: nat] :
% 8.01/5.77 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 8.01/5.77 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_Suc_Suc
% 8.01/5.77 thf(fact_9708_min__0R,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( ord_min_nat @ N @ zero_zero_nat )
% 8.01/5.77 = zero_zero_nat ) ).
% 8.01/5.77
% 8.01/5.77 % min_0R
% 8.01/5.77 thf(fact_9709_min__0L,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( ord_min_nat @ zero_zero_nat @ N )
% 8.01/5.77 = zero_zero_nat ) ).
% 8.01/5.77
% 8.01/5.77 % min_0L
% 8.01/5.77 thf(fact_9710_min__minus_H,axiom,
% 8.01/5.77 ! [M: nat,K: nat] :
% 8.01/5.77 ( ( ord_min_nat @ ( minus_minus_nat @ M @ K ) @ M )
% 8.01/5.77 = ( minus_minus_nat @ M @ K ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_minus'
% 8.01/5.77 thf(fact_9711_min__minus,axiom,
% 8.01/5.77 ! [M: nat,K: nat] :
% 8.01/5.77 ( ( ord_min_nat @ M @ ( minus_minus_nat @ M @ K ) )
% 8.01/5.77 = ( minus_minus_nat @ M @ K ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_minus
% 8.01/5.77 thf(fact_9712_min__Suc__gt_I1_J,axiom,
% 8.01/5.77 ! [A: nat,B: nat] :
% 8.01/5.77 ( ( ord_less_nat @ A @ B )
% 8.01/5.77 => ( ( ord_min_nat @ ( suc @ A ) @ B )
% 8.01/5.77 = ( suc @ A ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_Suc_gt(1)
% 8.01/5.77 thf(fact_9713_min__Suc__gt_I2_J,axiom,
% 8.01/5.77 ! [A: nat,B: nat] :
% 8.01/5.77 ( ( ord_less_nat @ A @ B )
% 8.01/5.77 => ( ( ord_min_nat @ B @ ( suc @ A ) )
% 8.01/5.77 = ( suc @ A ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_Suc_gt(2)
% 8.01/5.77 thf(fact_9714_min__pm,axiom,
% 8.01/5.77 ! [A: nat,B: nat] :
% 8.01/5.77 ( ( plus_plus_nat @ ( ord_min_nat @ A @ B ) @ ( minus_minus_nat @ A @ B ) )
% 8.01/5.77 = A ) ).
% 8.01/5.77
% 8.01/5.77 % min_pm
% 8.01/5.77 thf(fact_9715_min__pm1,axiom,
% 8.01/5.77 ! [A: nat,B: nat] :
% 8.01/5.77 ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ ( ord_min_nat @ A @ B ) )
% 8.01/5.77 = A ) ).
% 8.01/5.77
% 8.01/5.77 % min_pm1
% 8.01/5.77 thf(fact_9716_rev__min__pm,axiom,
% 8.01/5.77 ! [B: nat,A: nat] :
% 8.01/5.77 ( ( plus_plus_nat @ ( ord_min_nat @ B @ A ) @ ( minus_minus_nat @ A @ B ) )
% 8.01/5.77 = A ) ).
% 8.01/5.77
% 8.01/5.77 % rev_min_pm
% 8.01/5.77 thf(fact_9717_rev__min__pm1,axiom,
% 8.01/5.77 ! [A: nat,B: nat] :
% 8.01/5.77 ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ ( ord_min_nat @ B @ A ) )
% 8.01/5.77 = A ) ).
% 8.01/5.77
% 8.01/5.77 % rev_min_pm1
% 8.01/5.77 thf(fact_9718_min__numeral__Suc,axiom,
% 8.01/5.77 ! [K: num,N: nat] :
% 8.01/5.77 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 8.01/5.77 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_numeral_Suc
% 8.01/5.77 thf(fact_9719_min__Suc__numeral,axiom,
% 8.01/5.77 ! [N: nat,K: num] :
% 8.01/5.77 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 8.01/5.77 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_Suc_numeral
% 8.01/5.77 thf(fact_9720_concat__bit__assoc__sym,axiom,
% 8.01/5.77 ! [M: nat,N: nat,K: int,L: int,R2: int] :
% 8.01/5.77 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L ) @ R2 )
% 8.01/5.77 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L @ R2 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % concat_bit_assoc_sym
% 8.01/5.77 thf(fact_9721_nat__mult__min__right,axiom,
% 8.01/5.77 ! [M: nat,N: nat,Q3: nat] :
% 8.01/5.77 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q3 ) )
% 8.01/5.77 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % nat_mult_min_right
% 8.01/5.77 thf(fact_9722_nat__mult__min__left,axiom,
% 8.01/5.77 ! [M: nat,N: nat,Q3: nat] :
% 8.01/5.77 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q3 )
% 8.01/5.77 = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % nat_mult_min_left
% 8.01/5.77 thf(fact_9723_min__diff,axiom,
% 8.01/5.77 ! [M: nat,I: nat,N: nat] :
% 8.01/5.77 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 8.01/5.77 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_diff
% 8.01/5.77 thf(fact_9724_take__bit__concat__bit__eq,axiom,
% 8.01/5.77 ! [M: nat,N: nat,K: int,L: int] :
% 8.01/5.77 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L ) )
% 8.01/5.77 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_concat_bit_eq
% 8.01/5.77 thf(fact_9725_mod__mod__power,axiom,
% 8.01/5.77 ! [K: nat,M: nat,N: nat] :
% 8.01/5.77 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ K @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.01/5.77 = ( modulo_modulo_nat @ K @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( ord_min_nat @ M @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % mod_mod_power
% 8.01/5.77 thf(fact_9726_min__enat__simps_I2_J,axiom,
% 8.01/5.77 ! [Q3: extended_enat] :
% 8.01/5.77 ( ( ord_mi8085742599997312461d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 8.01/5.77 = zero_z5237406670263579293d_enat ) ).
% 8.01/5.77
% 8.01/5.77 % min_enat_simps(2)
% 8.01/5.77 thf(fact_9727_min__enat__simps_I3_J,axiom,
% 8.01/5.77 ! [Q3: extended_enat] :
% 8.01/5.77 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 8.01/5.77 = zero_z5237406670263579293d_enat ) ).
% 8.01/5.77
% 8.01/5.77 % min_enat_simps(3)
% 8.01/5.77 thf(fact_9728_range__mult,axiom,
% 8.01/5.77 ! [A: real] :
% 8.01/5.77 ( ( ( A = zero_zero_real )
% 8.01/5.77 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 8.01/5.77 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 8.01/5.77 & ( ( A != zero_zero_real )
% 8.01/5.77 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 8.01/5.77 = top_top_set_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % range_mult
% 8.01/5.77 thf(fact_9729_range__mod,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( image_nat_nat
% 8.01/5.77 @ ^ [M4: nat] : ( modulo_modulo_nat @ M4 @ N )
% 8.01/5.77 @ top_top_set_nat )
% 8.01/5.77 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % range_mod
% 8.01/5.77 thf(fact_9730_UNIV__nat__eq,axiom,
% 8.01/5.77 ( top_top_set_nat
% 8.01/5.77 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % UNIV_nat_eq
% 8.01/5.77 thf(fact_9731_int__set__bits__K__False,axiom,
% 8.01/5.77 ( ( bit_bi6516823479961619367ts_int
% 8.01/5.77 @ ^ [Uu3: nat] : $false )
% 8.01/5.77 = zero_zero_int ) ).
% 8.01/5.77
% 8.01/5.77 % int_set_bits_K_False
% 8.01/5.77 thf(fact_9732_int__set__bits__K__True,axiom,
% 8.01/5.77 ( ( bit_bi6516823479961619367ts_int
% 8.01/5.77 @ ^ [Uu3: nat] : $true )
% 8.01/5.77 = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_set_bits_K_True
% 8.01/5.77 thf(fact_9733_root__def,axiom,
% 8.01/5.77 ( root
% 8.01/5.77 = ( ^ [N3: nat,X2: real] :
% 8.01/5.77 ( if_real @ ( N3 = zero_zero_nat ) @ zero_zero_real
% 8.01/5.77 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 8.01/5.77 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N3 ) )
% 8.01/5.77 @ X2 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % root_def
% 8.01/5.77 thf(fact_9734_bin__last__set__bits,axiom,
% 8.01/5.77 ! [F: nat > $o] :
% 8.01/5.77 ( ( bit_wf_set_bits_int @ F )
% 8.01/5.77 => ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_bi6516823479961619367ts_int @ F ) ) )
% 8.01/5.77 = ( F @ zero_zero_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % bin_last_set_bits
% 8.01/5.77 thf(fact_9735_wf__set__bits__int__Suc,axiom,
% 8.01/5.77 ! [F: nat > $o] :
% 8.01/5.77 ( ( bit_wf_set_bits_int
% 8.01/5.77 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) ) )
% 8.01/5.77 = ( bit_wf_set_bits_int @ F ) ) ).
% 8.01/5.77
% 8.01/5.77 % wf_set_bits_int_Suc
% 8.01/5.77 thf(fact_9736_int__set__bits__unfold__BIT,axiom,
% 8.01/5.77 ! [F: nat > $o] :
% 8.01/5.77 ( ( bit_wf_set_bits_int @ F )
% 8.01/5.77 => ( ( bit_bi6516823479961619367ts_int @ F )
% 8.01/5.77 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( F @ zero_zero_nat ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_bi6516823479961619367ts_int @ ( comp_nat_o_nat @ F @ suc ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_set_bits_unfold_BIT
% 8.01/5.77 thf(fact_9737_bin__rest__set__bits,axiom,
% 8.01/5.77 ! [F: nat > $o] :
% 8.01/5.77 ( ( bit_wf_set_bits_int @ F )
% 8.01/5.77 => ( ( divide_divide_int @ ( bit_bi6516823479961619367ts_int @ F ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.01/5.77 = ( bit_bi6516823479961619367ts_int @ ( comp_nat_o_nat @ F @ suc ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % bin_rest_set_bits
% 8.01/5.77 thf(fact_9738_shiftl__Suc__0,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( bit_Sh3965577149348748681tl_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.01/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.01/5.77
% 8.01/5.77 % shiftl_Suc_0
% 8.01/5.77 thf(fact_9739_card_Ocomp__fun__commute__on,axiom,
% 8.01/5.77 ( ( comp_nat_nat_nat @ suc @ suc )
% 8.01/5.77 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 8.01/5.77
% 8.01/5.77 % card.comp_fun_commute_on
% 8.01/5.77 thf(fact_9740_Code__Target__Int_Onegative__def,axiom,
% 8.01/5.77 ( code_Target_negative
% 8.01/5.77 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % Code_Target_Int.negative_def
% 8.01/5.77 thf(fact_9741_shiftr__Suc__0,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( bit_Sh2154871086232339855tr_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.01/5.77 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % shiftr_Suc_0
% 8.01/5.77 thf(fact_9742_DERIV__real__root__generic,axiom,
% 8.01/5.77 ! [N: nat,X: real,D4: real] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( X != zero_zero_real )
% 8.01/5.77 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.01/5.77 => ( D4
% 8.01/5.77 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 8.01/5.77 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.01/5.77 => ( ( ord_less_real @ X @ zero_zero_real )
% 8.01/5.77 => ( D4
% 8.01/5.77 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 8.01/5.77 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.01/5.77 => ( D4
% 8.01/5.77 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_real_root_generic
% 8.01/5.77 thf(fact_9743_DERIV__even__real__root,axiom,
% 8.01/5.77 ! [N: nat,X: real] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.01/5.77 => ( ( ord_less_real @ X @ zero_zero_real )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_even_real_root
% 8.01/5.77 thf(fact_9744_inj__on__diff__nat,axiom,
% 8.01/5.77 ! [N4: set_nat,K: nat] :
% 8.01/5.77 ( ! [N2: nat] :
% 8.01/5.77 ( ( member_nat @ N2 @ N4 )
% 8.01/5.77 => ( ord_less_eq_nat @ K @ N2 ) )
% 8.01/5.77 => ( inj_on_nat_nat
% 8.01/5.77 @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ K )
% 8.01/5.77 @ N4 ) ) ).
% 8.01/5.77
% 8.01/5.77 % inj_on_diff_nat
% 8.01/5.77 thf(fact_9745_inj__on__set__encode,axiom,
% 8.01/5.77 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 8.01/5.77
% 8.01/5.77 % inj_on_set_encode
% 8.01/5.77 thf(fact_9746_inj__Suc,axiom,
% 8.01/5.77 ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 8.01/5.77
% 8.01/5.77 % inj_Suc
% 8.01/5.77 thf(fact_9747_DERIV__const__ratio__const,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real,K: real] :
% 8.01/5.77 ( ( A != B )
% 8.01/5.77 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 8.01/5.77 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_const_ratio_const
% 8.01/5.77 thf(fact_9748_MVT2,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real,F6: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_eq_real @ X3 @ B )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 8.01/5.77 => ? [Z3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ Z3 )
% 8.01/5.77 & ( ord_less_real @ Z3 @ B )
% 8.01/5.77 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 8.01/5.77 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F6 @ Z3 ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % MVT2
% 8.01/5.77 thf(fact_9749_DERIV__pos__inc__right,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ L )
% 8.01/5.77 => ? [D3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.01/5.77 & ! [H6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H6 )
% 8.01/5.77 => ( ( ord_less_real @ H6 @ D3 )
% 8.01/5.77 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H6 ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_pos_inc_right
% 8.01/5.77 thf(fact_9750_DERIV__neg__dec__right,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ L @ zero_zero_real )
% 8.01/5.77 => ? [D3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.01/5.77 & ! [H6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H6 )
% 8.01/5.77 => ( ( ord_less_real @ H6 @ D3 )
% 8.01/5.77 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_neg_dec_right
% 8.01/5.77 thf(fact_9751_DERIV__const__ratio__const2,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real,K: real] :
% 8.01/5.77 ( ( A != B )
% 8.01/5.77 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 8.01/5.77 = K ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_const_ratio_const2
% 8.01/5.77 thf(fact_9752_DERIV__ln,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_ln
% 8.01/5.77 thf(fact_9753_deriv__nonneg__imp__mono,axiom,
% 8.01/5.77 ! [A: real,B: real,G: real > real,G2: real > real] :
% 8.01/5.77 ( ! [X3: real] :
% 8.01/5.77 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 8.01/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 8.01/5.77 => ( ( ord_less_eq_real @ A @ B )
% 8.01/5.77 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % deriv_nonneg_imp_mono
% 8.01/5.77 thf(fact_9754_DERIV__neg__imp__decreasing,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_eq_real @ X3 @ B )
% 8.01/5.77 => ? [Y4: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 8.01/5.77 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_neg_imp_decreasing
% 8.01/5.77 thf(fact_9755_DERIV__pos__imp__increasing,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_eq_real @ X3 @ B )
% 8.01/5.77 => ? [Y4: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 8.01/5.77 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_pos_imp_increasing
% 8.01/5.77 thf(fact_9756_DERIV__nonpos__imp__nonincreasing,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ B )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_eq_real @ X3 @ B )
% 8.01/5.77 => ? [Y4: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 8.01/5.77 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_nonpos_imp_nonincreasing
% 8.01/5.77 thf(fact_9757_DERIV__nonneg__imp__nondecreasing,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ B )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_eq_real @ X3 @ B )
% 8.01/5.77 => ? [Y4: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 8.01/5.77 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_nonneg_imp_nondecreasing
% 8.01/5.77 thf(fact_9758_DERIV__local__const,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real,D2: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 8.01/5.77 => ( ! [Y3: real] :
% 8.01/5.77 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 8.01/5.77 => ( ( F @ X )
% 8.01/5.77 = ( F @ Y3 ) ) )
% 8.01/5.77 => ( L = zero_zero_real ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_local_const
% 8.01/5.77 thf(fact_9759_DERIV__pos__inc__left,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ L )
% 8.01/5.77 => ? [D3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.01/5.77 & ! [H6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H6 )
% 8.01/5.77 => ( ( ord_less_real @ H6 @ D3 )
% 8.01/5.77 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_pos_inc_left
% 8.01/5.77 thf(fact_9760_DERIV__neg__dec__left,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ L @ zero_zero_real )
% 8.01/5.77 => ? [D3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.01/5.77 & ! [H6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H6 )
% 8.01/5.77 => ( ( ord_less_real @ H6 @ D3 )
% 8.01/5.77 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H6 ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_neg_dec_left
% 8.01/5.77 thf(fact_9761_DERIV__isconst__all,axiom,
% 8.01/5.77 ! [F: real > real,X: real,Y: real] :
% 8.01/5.77 ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 => ( ( F @ X )
% 8.01/5.77 = ( F @ Y ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_isconst_all
% 8.01/5.77 thf(fact_9762_has__real__derivative__neg__dec__right,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real,S3: set_real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 8.01/5.77 => ( ( ord_less_real @ L @ zero_zero_real )
% 8.01/5.77 => ? [D3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.01/5.77 & ! [H6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H6 )
% 8.01/5.77 => ( ( member_real @ ( plus_plus_real @ X @ H6 ) @ S3 )
% 8.01/5.77 => ( ( ord_less_real @ H6 @ D3 )
% 8.01/5.77 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % has_real_derivative_neg_dec_right
% 8.01/5.77 thf(fact_9763_has__real__derivative__pos__inc__right,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real,S3: set_real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ L )
% 8.01/5.77 => ? [D3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.01/5.77 & ! [H6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H6 )
% 8.01/5.77 => ( ( member_real @ ( plus_plus_real @ X @ H6 ) @ S3 )
% 8.01/5.77 => ( ( ord_less_real @ H6 @ D3 )
% 8.01/5.77 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H6 ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % has_real_derivative_pos_inc_right
% 8.01/5.77 thf(fact_9764_has__real__derivative__pos__inc__left,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real,S3: set_real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ L )
% 8.01/5.77 => ? [D3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.01/5.77 & ! [H6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H6 )
% 8.01/5.77 => ( ( member_real @ ( minus_minus_real @ X @ H6 ) @ S3 )
% 8.01/5.77 => ( ( ord_less_real @ H6 @ D3 )
% 8.01/5.77 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % has_real_derivative_pos_inc_left
% 8.01/5.77 thf(fact_9765_has__real__derivative__neg__dec__left,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real,S3: set_real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 8.01/5.77 => ( ( ord_less_real @ L @ zero_zero_real )
% 8.01/5.77 => ? [D3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ D3 )
% 8.01/5.77 & ! [H6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H6 )
% 8.01/5.77 => ( ( member_real @ ( minus_minus_real @ X @ H6 ) @ S3 )
% 8.01/5.77 => ( ( ord_less_real @ H6 @ D3 )
% 8.01/5.77 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H6 ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % has_real_derivative_neg_dec_left
% 8.01/5.77 thf(fact_9766_DERIV__const__average,axiom,
% 8.01/5.77 ! [A: real,B: real,V: real > real,K: real] :
% 8.01/5.77 ( ( A != B )
% 8.01/5.77 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.01/5.77 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_const_average
% 8.01/5.77 thf(fact_9767_DERIV__local__min,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real,D2: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 8.01/5.77 => ( ! [Y3: real] :
% 8.01/5.77 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 8.01/5.77 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 8.01/5.77 => ( L = zero_zero_real ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_local_min
% 8.01/5.77 thf(fact_9768_DERIV__local__max,axiom,
% 8.01/5.77 ! [F: real > real,L: real,X: real,D2: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 8.01/5.77 => ( ! [Y3: real] :
% 8.01/5.77 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 8.01/5.77 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 8.01/5.77 => ( L = zero_zero_real ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_local_max
% 8.01/5.77 thf(fact_9769_DERIV__ln__divide,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_ln_divide
% 8.01/5.77 thf(fact_9770_DERIV__pow,axiom,
% 8.01/5.77 ! [N: nat,X: real,S: set_real] :
% 8.01/5.77 ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [X2: real] : ( power_power_real @ X2 @ N )
% 8.01/5.77 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_pow
% 8.01/5.77 thf(fact_9771_DERIV__fun__pow,axiom,
% 8.01/5.77 ! [G: real > real,M: real,X: real,N: nat] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [X2: real] : ( power_power_real @ ( G @ X2 ) @ N )
% 8.01/5.77 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_fun_pow
% 8.01/5.77 thf(fact_9772_has__real__derivative__powr,axiom,
% 8.01/5.77 ! [Z: real,R2: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ Z )
% 8.01/5.77 => ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [Z6: real] : ( powr_real @ Z6 @ R2 )
% 8.01/5.77 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % has_real_derivative_powr
% 8.01/5.77 thf(fact_9773_summable__reindex,axiom,
% 8.01/5.77 ! [F: nat > real,G: nat > nat] :
% 8.01/5.77 ( ( summable_real @ F )
% 8.01/5.77 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 8.01/5.77 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 8.01/5.77 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_reindex
% 8.01/5.77 thf(fact_9774_DERIV__fun__powr,axiom,
% 8.01/5.77 ! [G: real > real,M: real,X: real,R2: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ R2 )
% 8.01/5.77 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_fun_powr
% 8.01/5.77 thf(fact_9775_DERIV__log,axiom,
% 8.01/5.77 ! [X: real,B: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 8.01/5.77 => ( 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 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_log
% 8.01/5.77 thf(fact_9776_DERIV__powr,axiom,
% 8.01/5.77 ! [G: real > real,M: real,X: real,F: real > real,R2: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 8.01/5.77 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [X2: real] : ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) )
% 8.01/5.77 @ ( 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 ) ) ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_powr
% 8.01/5.77 thf(fact_9777_DERIV__real__sqrt,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_real_sqrt
% 8.01/5.77 thf(fact_9778_DERIV__arctan,axiom,
% 8.01/5.77 ! [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 ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_arctan
% 8.01/5.77 thf(fact_9779_arsinh__real__has__field__derivative,axiom,
% 8.01/5.77 ! [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 ) ) ).
% 8.01/5.77
% 8.01/5.77 % arsinh_real_has_field_derivative
% 8.01/5.77 thf(fact_9780_DERIV__real__sqrt__generic,axiom,
% 8.01/5.77 ! [X: real,D4: real] :
% 8.01/5.77 ( ( X != zero_zero_real )
% 8.01/5.77 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 8.01/5.77 => ( D4
% 8.01/5.77 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 8.01/5.77 => ( D4
% 8.01/5.77 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_real_sqrt_generic
% 8.01/5.77 thf(fact_9781_arcosh__real__has__field__derivative,axiom,
% 8.01/5.77 ! [X: real,A2: set_real] :
% 8.01/5.77 ( ( ord_less_real @ one_one_real @ X )
% 8.01/5.77 => ( 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 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % arcosh_real_has_field_derivative
% 8.01/5.77 thf(fact_9782_artanh__real__has__field__derivative,axiom,
% 8.01/5.77 ! [X: real,A2: set_real] :
% 8.01/5.77 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.01/5.77 => ( 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 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % artanh_real_has_field_derivative
% 8.01/5.77 thf(fact_9783_suminf__reindex__mono,axiom,
% 8.01/5.77 ! [F: nat > real,G: nat > nat] :
% 8.01/5.77 ( ( summable_real @ F )
% 8.01/5.77 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 8.01/5.77 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 8.01/5.77 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % suminf_reindex_mono
% 8.01/5.77 thf(fact_9784_DERIV__real__root,axiom,
% 8.01/5.77 ! [N: nat,X: real] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_real_root
% 8.01/5.77 thf(fact_9785_DERIV__arccos,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.01/5.77 => ( ( ord_less_real @ X @ one_one_real )
% 8.01/5.77 => ( 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 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_arccos
% 8.01/5.77 thf(fact_9786_DERIV__arcsin,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.01/5.77 => ( ( ord_less_real @ X @ one_one_real )
% 8.01/5.77 => ( 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 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_arcsin
% 8.01/5.77 thf(fact_9787_suminf__reindex,axiom,
% 8.01/5.77 ! [F: nat > real,G: nat > nat] :
% 8.01/5.77 ( ( summable_real @ F )
% 8.01/5.77 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 8.01/5.77 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 8.01/5.77 => ( ! [X3: nat] :
% 8.01/5.77 ( ~ ( member_nat @ X3 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 8.01/5.77 => ( ( F @ X3 )
% 8.01/5.77 = zero_zero_real ) )
% 8.01/5.77 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 8.01/5.77 = ( suminf_real @ F ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % suminf_reindex
% 8.01/5.77 thf(fact_9788_Maclaurin__all__le,axiom,
% 8.01/5.77 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 8.01/5.77 ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 => ( ! [M2: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.01/5.77 & ( ( F @ X )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ X @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Maclaurin_all_le
% 8.01/5.77 thf(fact_9789_Maclaurin__all__le__objl,axiom,
% 8.01/5.77 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 8.01/5.77 ( ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 & ! [M2: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.01/5.77 & ( ( F @ X )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ X @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Maclaurin_all_le_objl
% 8.01/5.77 thf(fact_9790_DERIV__odd__real__root,axiom,
% 8.01/5.77 ! [N: nat,X: real] :
% 8.01/5.77 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.01/5.77 => ( ( X != zero_zero_real )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_odd_real_root
% 8.01/5.77 thf(fact_9791_Maclaurin,axiom,
% 8.01/5.77 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H2 )
% 8.01/5.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 => ( ! [M2: nat,T6: real] :
% 8.01/5.77 ( ( ( ord_less_nat @ M2 @ N )
% 8.01/5.77 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.01/5.77 & ( ord_less_eq_real @ T6 @ H2 ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.01/5.77 & ( ord_less_real @ T6 @ H2 )
% 8.01/5.77 & ( ( F @ H2 )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ H2 @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Maclaurin
% 8.01/5.77 thf(fact_9792_Maclaurin2,axiom,
% 8.01/5.77 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ H2 )
% 8.01/5.77 => ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 => ( ! [M2: nat,T6: real] :
% 8.01/5.77 ( ( ( ord_less_nat @ M2 @ N )
% 8.01/5.77 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.01/5.77 & ( ord_less_eq_real @ T6 @ H2 ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.01/5.77 & ( ord_less_eq_real @ T6 @ H2 )
% 8.01/5.77 & ( ( F @ H2 )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ H2 @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Maclaurin2
% 8.01/5.77 thf(fact_9793_Maclaurin__minus,axiom,
% 8.01/5.77 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ H2 @ zero_zero_real )
% 8.01/5.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 => ( ! [M2: nat,T6: real] :
% 8.01/5.77 ( ( ( ord_less_nat @ M2 @ N )
% 8.01/5.77 & ( ord_less_eq_real @ H2 @ T6 )
% 8.01/5.77 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ord_less_real @ H2 @ T6 )
% 8.01/5.77 & ( ord_less_real @ T6 @ zero_zero_real )
% 8.01/5.77 & ( ( F @ H2 )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ H2 @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Maclaurin_minus
% 8.01/5.77 thf(fact_9794_Maclaurin__all__lt,axiom,
% 8.01/5.77 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 8.01/5.77 ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( X != zero_zero_real )
% 8.01/5.77 => ( ! [M2: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 8.01/5.77 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.01/5.77 & ( ( F @ X )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ X @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Maclaurin_all_lt
% 8.01/5.77 thf(fact_9795_Maclaurin__bi__le,axiom,
% 8.01/5.77 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 8.01/5.77 ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 => ( ! [M2: nat,T6: real] :
% 8.01/5.77 ( ( ( ord_less_nat @ M2 @ N )
% 8.01/5.77 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.01/5.77 & ( ( F @ X )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ X @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Maclaurin_bi_le
% 8.01/5.77 thf(fact_9796_Taylor__down,axiom,
% 8.01/5.77 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 => ( ! [M2: nat,T6: real] :
% 8.01/5.77 ( ( ( ord_less_nat @ M2 @ N )
% 8.01/5.77 & ( ord_less_eq_real @ A @ T6 )
% 8.01/5.77 & ( ord_less_eq_real @ T6 @ B ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.01/5.77 => ( ( ord_less_real @ A @ C )
% 8.01/5.77 => ( ( ord_less_eq_real @ C @ B )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ T6 )
% 8.01/5.77 & ( ord_less_real @ T6 @ C )
% 8.01/5.77 & ( ( F @ A )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ C ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Taylor_down
% 8.01/5.77 thf(fact_9797_Taylor__up,axiom,
% 8.01/5.77 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 => ( ! [M2: nat,T6: real] :
% 8.01/5.77 ( ( ( ord_less_nat @ M2 @ N )
% 8.01/5.77 & ( ord_less_eq_real @ A @ T6 )
% 8.01/5.77 & ( ord_less_eq_real @ T6 @ B ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.01/5.77 => ( ( ord_less_eq_real @ A @ C )
% 8.01/5.77 => ( ( ord_less_real @ C @ B )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ord_less_real @ C @ T6 )
% 8.01/5.77 & ( ord_less_real @ T6 @ B )
% 8.01/5.77 & ( ( F @ B )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ C ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Taylor_up
% 8.01/5.77 thf(fact_9798_Taylor,axiom,
% 8.01/5.77 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( ( Diff @ zero_zero_nat )
% 8.01/5.77 = F )
% 8.01/5.77 => ( ! [M2: nat,T6: real] :
% 8.01/5.77 ( ( ( ord_less_nat @ M2 @ N )
% 8.01/5.77 & ( ord_less_eq_real @ A @ T6 )
% 8.01/5.77 & ( ord_less_eq_real @ T6 @ B ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.01/5.77 => ( ( ord_less_eq_real @ A @ C )
% 8.01/5.77 => ( ( ord_less_eq_real @ C @ B )
% 8.01/5.77 => ( ( ord_less_eq_real @ A @ X )
% 8.01/5.77 => ( ( ord_less_eq_real @ X @ B )
% 8.01/5.77 => ( ( X != C )
% 8.01/5.77 => ? [T6: real] :
% 8.01/5.77 ( ( ( ord_less_real @ X @ C )
% 8.01/5.77 => ( ( ord_less_real @ X @ T6 )
% 8.01/5.77 & ( ord_less_real @ T6 @ C ) ) )
% 8.01/5.77 & ( ~ ( ord_less_real @ X @ C )
% 8.01/5.77 => ( ( ord_less_real @ C @ T6 )
% 8.01/5.77 & ( ord_less_real @ T6 @ X ) ) )
% 8.01/5.77 & ( ( F @ X )
% 8.01/5.77 = ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [M4: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M4 @ C ) @ ( semiri2265585572941072030t_real @ M4 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M4 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 8.01/5.77 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Taylor
% 8.01/5.77 thf(fact_9799_inj__sgn__power,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( inj_on_real_real
% 8.01/5.77 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N ) )
% 8.01/5.77 @ top_top_set_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % inj_sgn_power
% 8.01/5.77 thf(fact_9800_Maclaurin__lemma2,axiom,
% 8.01/5.77 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B3: real] :
% 8.01/5.77 ( ! [M2: nat,T6: real] :
% 8.01/5.77 ( ( ( ord_less_nat @ M2 @ N )
% 8.01/5.77 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.01/5.77 & ( ord_less_eq_real @ T6 @ H2 ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ ( Diff @ M2 ) @ ( Diff @ ( suc @ M2 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.01/5.77 => ( ( N
% 8.01/5.77 = ( suc @ K ) )
% 8.01/5.77 => ! [M3: nat,T7: real] :
% 8.01/5.77 ( ( ( ord_less_nat @ M3 @ N )
% 8.01/5.77 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 8.01/5.77 & ( ord_less_eq_real @ T7 @ H2 ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [U2: real] :
% 8.01/5.77 ( minus_minus_real @ ( Diff @ M3 @ U2 )
% 8.01/5.77 @ ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M3 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M3 ) ) )
% 8.01/5.77 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M3 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M3 ) ) ) ) ) )
% 8.01/5.77 @ ( minus_minus_real @ ( Diff @ ( suc @ M3 ) @ T7 )
% 8.01/5.77 @ ( plus_plus_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M3 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T7 @ P5 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) )
% 8.01/5.77 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) ) ) ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Maclaurin_lemma2
% 8.01/5.77 thf(fact_9801_DERIV__arctan__series,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.01/5.77 => ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [X10: real] :
% 8.01/5.77 ( suminf_real
% 8.01/5.77 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X10 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_arctan_series
% 8.01/5.77 thf(fact_9802_DERIV__power__series_H,axiom,
% 8.01/5.77 ! [R: real,F: nat > real,X0: real] :
% 8.01/5.77 ( ! [X3: real] :
% 8.01/5.77 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 8.01/5.77 => ( summable_real
% 8.01/5.77 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X3 @ N3 ) ) ) )
% 8.01/5.77 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ R )
% 8.01/5.77 => ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( suminf_real
% 8.01/5.77 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X2 @ ( suc @ N3 ) ) ) )
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X0 @ N3 ) ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_power_series'
% 8.01/5.77 thf(fact_9803_tanh__real__bounds,axiom,
% 8.01/5.77 ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % tanh_real_bounds
% 8.01/5.77 thf(fact_9804_DERIV__isconst3,axiom,
% 8.01/5.77 ! [A: real,B: real,X: real,Y: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.01/5.77 => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 8.01/5.77 => ( ( F @ X )
% 8.01/5.77 = ( F @ Y ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_isconst3
% 8.01/5.77 thf(fact_9805_DERIV__series_H,axiom,
% 8.01/5.77 ! [F: real > nat > real,F6: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 8.01/5.77 ( ! [N2: nat] :
% 8.01/5.77 ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [X2: real] : ( F @ X2 @ N2 )
% 8.01/5.77 @ ( F6 @ X0 @ N2 )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.01/5.77 => ( summable_real @ ( F @ X3 ) ) )
% 8.01/5.77 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.01/5.77 => ( ( summable_real @ ( F6 @ X0 ) )
% 8.01/5.77 => ( ( summable_real @ L5 )
% 8.01/5.77 => ( ! [N2: nat,X3: real,Y3: real] :
% 8.01/5.77 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.01/5.77 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.01/5.77 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N2 ) @ ( F @ Y3 @ N2 ) ) ) @ ( times_times_real @ ( L5 @ N2 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 8.01/5.77 => ( has_fi5821293074295781190e_real
% 8.01/5.77 @ ^ [X2: real] : ( suminf_real @ ( F @ X2 ) )
% 8.01/5.77 @ ( suminf_real @ ( F6 @ X0 ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_series'
% 8.01/5.77 thf(fact_9806_atLeastSucLessThan__greaterThanLessThan,axiom,
% 8.01/5.77 ! [L: nat,U: nat] :
% 8.01/5.77 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 8.01/5.77 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastSucLessThan_greaterThanLessThan
% 8.01/5.77 thf(fact_9807_LIM__fun__less__zero,axiom,
% 8.01/5.77 ! [F: real > real,L: real,C: real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ L @ zero_zero_real )
% 8.01/5.77 => ? [R3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ R3 )
% 8.01/5.77 & ! [X5: real] :
% 8.01/5.77 ( ( ( X5 != C )
% 8.01/5.77 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 8.01/5.77 => ( ord_less_real @ ( F @ X5 ) @ zero_zero_real ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIM_fun_less_zero
% 8.01/5.77 thf(fact_9808_LIM__fun__not__zero,axiom,
% 8.01/5.77 ! [F: real > real,L: real,C: real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 8.01/5.77 => ( ( L != zero_zero_real )
% 8.01/5.77 => ? [R3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ R3 )
% 8.01/5.77 & ! [X5: real] :
% 8.01/5.77 ( ( ( X5 != C )
% 8.01/5.77 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 8.01/5.77 => ( ( F @ X5 )
% 8.01/5.77 != zero_zero_real ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIM_fun_not_zero
% 8.01/5.77 thf(fact_9809_LIM__fun__gt__zero,axiom,
% 8.01/5.77 ! [F: real > real,L: real,C: real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ L )
% 8.01/5.77 => ? [R3: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ R3 )
% 8.01/5.77 & ! [X5: real] :
% 8.01/5.77 ( ( ( X5 != C )
% 8.01/5.77 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 8.01/5.77 => ( ord_less_real @ zero_zero_real @ ( F @ X5 ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIM_fun_gt_zero
% 8.01/5.77 thf(fact_9810_isCont__real__sqrt,axiom,
% 8.01/5.77 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 8.01/5.77
% 8.01/5.77 % isCont_real_sqrt
% 8.01/5.77 thf(fact_9811_isCont__real__root,axiom,
% 8.01/5.77 ! [X: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N ) ) ).
% 8.01/5.77
% 8.01/5.77 % isCont_real_root
% 8.01/5.77 thf(fact_9812_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 8.01/5.77 ! [L: int,U: int] :
% 8.01/5.77 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 8.01/5.77 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 8.01/5.77 thf(fact_9813_greaterThanLessThan__upt,axiom,
% 8.01/5.77 ( set_or5834768355832116004an_nat
% 8.01/5.77 = ( ^ [N3: nat,M4: nat] : ( set_nat2 @ ( upt @ ( suc @ N3 ) @ M4 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % greaterThanLessThan_upt
% 8.01/5.77 thf(fact_9814_isCont__inverse__function2,axiom,
% 8.01/5.77 ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ X )
% 8.01/5.77 => ( ( ord_less_real @ X @ B )
% 8.01/5.77 => ( ! [Z3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ Z3 )
% 8.01/5.77 => ( ( ord_less_eq_real @ Z3 @ B )
% 8.01/5.77 => ( ( G @ ( F @ Z3 ) )
% 8.01/5.77 = Z3 ) ) )
% 8.01/5.77 => ( ! [Z3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ Z3 )
% 8.01/5.77 => ( ( ord_less_eq_real @ Z3 @ B )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % isCont_inverse_function2
% 8.01/5.77 thf(fact_9815_isCont__ln,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( X != zero_zero_real )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ln_ln_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % isCont_ln
% 8.01/5.77 thf(fact_9816_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 8.01/5.77 ! [L: code_integer,U: code_integer] :
% 8.01/5.77 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 8.01/5.77 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 8.01/5.77 thf(fact_9817_isCont__arcosh,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ one_one_real @ X )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % isCont_arcosh
% 8.01/5.77 thf(fact_9818_LIM__cos__div__sin,axiom,
% 8.01/5.77 ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( cos_real @ X2 ) @ ( sin_real @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIM_cos_div_sin
% 8.01/5.77 thf(fact_9819_DERIV__inverse__function,axiom,
% 8.01/5.77 ! [F: real > real,D4: real,G: real > real,X: real,A: real,B: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X ) @ top_top_set_real ) )
% 8.01/5.77 => ( ( D4 != zero_zero_real )
% 8.01/5.77 => ( ( ord_less_real @ A @ X )
% 8.01/5.77 => ( ( ord_less_real @ X @ B )
% 8.01/5.77 => ( ! [Y3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ Y3 )
% 8.01/5.77 => ( ( ord_less_real @ Y3 @ B )
% 8.01/5.77 => ( ( F @ ( G @ Y3 ) )
% 8.01/5.77 = Y3 ) ) )
% 8.01/5.77 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ G )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_inverse_function
% 8.01/5.77 thf(fact_9820_isCont__arccos,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.01/5.77 => ( ( ord_less_real @ X @ one_one_real )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % isCont_arccos
% 8.01/5.77 thf(fact_9821_isCont__arcsin,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.01/5.77 => ( ( ord_less_real @ X @ one_one_real )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % isCont_arcsin
% 8.01/5.77 thf(fact_9822_LIM__less__bound,axiom,
% 8.01/5.77 ! [B: real,X: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ B @ X )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 8.01/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 8.01/5.77 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 8.01/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIM_less_bound
% 8.01/5.77 thf(fact_9823_isCont__artanh,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.01/5.77 => ( ( ord_less_real @ X @ one_one_real )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % isCont_artanh
% 8.01/5.77 thf(fact_9824_isCont__inverse__function,axiom,
% 8.01/5.77 ! [D2: real,X: real,G: real > real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ D2 )
% 8.01/5.77 => ( ! [Z3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D2 )
% 8.01/5.77 => ( ( G @ ( F @ Z3 ) )
% 8.01/5.77 = Z3 ) )
% 8.01/5.77 => ( ! [Z3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z3 @ X ) ) @ D2 )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % isCont_inverse_function
% 8.01/5.77 thf(fact_9825_GMVT_H,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F6: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ! [Z3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ Z3 )
% 8.01/5.77 => ( ( ord_less_eq_real @ Z3 @ B )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 8.01/5.77 => ( ! [Z3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ A @ Z3 )
% 8.01/5.77 => ( ( ord_less_eq_real @ Z3 @ B )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 8.01/5.77 => ( ! [Z3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ Z3 )
% 8.01/5.77 => ( ( ord_less_real @ Z3 @ B )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 8.01/5.77 => ( ! [Z3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ Z3 )
% 8.01/5.77 => ( ( ord_less_real @ Z3 @ B )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 8.01/5.77 => ? [C3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ C3 )
% 8.01/5.77 & ( ord_less_real @ C3 @ B )
% 8.01/5.77 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 8.01/5.77 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F6 @ C3 ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % GMVT'
% 8.01/5.77 thf(fact_9826_summable__Leibniz_I2_J,axiom,
% 8.01/5.77 ! [A: nat > real] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ( topolo6980174941875973593q_real @ A )
% 8.01/5.77 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 8.01/5.77 => ! [N9: nat] :
% 8.01/5.77 ( member_real
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 8.01/5.77 @ ( set_or1222579329274155063t_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_Leibniz(2)
% 8.01/5.77 thf(fact_9827_summable__Leibniz_I3_J,axiom,
% 8.01/5.77 ! [A: nat > real] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ( topolo6980174941875973593q_real @ A )
% 8.01/5.77 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 8.01/5.77 => ! [N9: nat] :
% 8.01/5.77 ( member_real
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 8.01/5.77 @ ( set_or1222579329274155063t_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_Leibniz(3)
% 8.01/5.77 thf(fact_9828_mult__nat__right__at__top,axiom,
% 8.01/5.77 ! [C: nat] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.01/5.77 => ( filterlim_nat_nat
% 8.01/5.77 @ ^ [X2: nat] : ( times_times_nat @ X2 @ C )
% 8.01/5.77 @ at_top_nat
% 8.01/5.77 @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % mult_nat_right_at_top
% 8.01/5.77 thf(fact_9829_mult__nat__left__at__top,axiom,
% 8.01/5.77 ! [C: nat] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ C )
% 8.01/5.77 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % mult_nat_left_at_top
% 8.01/5.77 thf(fact_9830_LIMSEQ__root,axiom,
% 8.01/5.77 ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( root @ N3 @ ( semiri5074537144036343181t_real @ N3 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.01/5.77 @ at_top_nat ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_root
% 8.01/5.77 thf(fact_9831_nested__sequence__unique,axiom,
% 8.01/5.77 ! [F: nat > real,G: nat > real] :
% 8.01/5.77 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N2 ) ) @ ( G @ N2 ) )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 8.01/5.77 => ( ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_nat )
% 8.01/5.77 => ? [L4: real] :
% 8.01/5.77 ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L4 )
% 8.01/5.77 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 8.01/5.77 & ! [N9: nat] : ( ord_less_eq_real @ L4 @ ( G @ N9 ) )
% 8.01/5.77 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % nested_sequence_unique
% 8.01/5.77 thf(fact_9832_LIMSEQ__inverse__zero,axiom,
% 8.01/5.77 ! [X9: nat > real] :
% 8.01/5.77 ( ! [R3: real] :
% 8.01/5.77 ? [N10: nat] :
% 8.01/5.77 ! [N2: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N10 @ N2 )
% 8.01/5.77 => ( ord_less_real @ R3 @ ( X9 @ N2 ) ) )
% 8.01/5.77 => ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( inverse_inverse_real @ ( X9 @ N3 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_inverse_zero
% 8.01/5.77 thf(fact_9833_lim__inverse__n_H,axiom,
% 8.01/5.77 ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N3 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_nat ) ).
% 8.01/5.77
% 8.01/5.77 % lim_inverse_n'
% 8.01/5.77 thf(fact_9834_LIMSEQ__inverse__real__of__nat,axiom,
% 8.01/5.77 ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_nat ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_inverse_real_of_nat
% 8.01/5.77 thf(fact_9835_LIMSEQ__root__const,axiom,
% 8.01/5.77 ! [C: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ C )
% 8.01/5.77 => ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( root @ N3 @ C )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.01/5.77 @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_root_const
% 8.01/5.77 thf(fact_9836_LIMSEQ__inverse__real__of__nat__add,axiom,
% 8.01/5.77 ! [R2: real] :
% 8.01/5.77 ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ R2 )
% 8.01/5.77 @ at_top_nat ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_inverse_real_of_nat_add
% 8.01/5.77 thf(fact_9837_increasing__LIMSEQ,axiom,
% 8.01/5.77 ! [F: nat > real,L: real] :
% 8.01/5.77 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ L )
% 8.01/5.77 => ( ! [E2: real] :
% 8.01/5.77 ( ( ord_less_real @ zero_zero_real @ E2 )
% 8.01/5.77 => ? [N9: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N9 ) @ E2 ) ) )
% 8.01/5.77 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % increasing_LIMSEQ
% 8.01/5.77 thf(fact_9838_LIMSEQ__realpow__zero,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.01/5.77 => ( ( ord_less_real @ X @ one_one_real )
% 8.01/5.77 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_realpow_zero
% 8.01/5.77 thf(fact_9839_LIMSEQ__divide__realpow__zero,axiom,
% 8.01/5.77 ! [X: real,A: real] :
% 8.01/5.77 ( ( ord_less_real @ one_one_real @ X )
% 8.01/5.77 => ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N3 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_divide_realpow_zero
% 8.01/5.77 thf(fact_9840_LIMSEQ__abs__realpow__zero2,axiom,
% 8.01/5.77 ! [C: real] :
% 8.01/5.77 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 8.01/5.77 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_abs_realpow_zero2
% 8.01/5.77 thf(fact_9841_LIMSEQ__abs__realpow__zero,axiom,
% 8.01/5.77 ! [C: real] :
% 8.01/5.77 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 8.01/5.77 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_abs_realpow_zero
% 8.01/5.77 thf(fact_9842_LIMSEQ__inverse__realpow__zero,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_real @ one_one_real @ X )
% 8.01/5.77 => ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N3 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_inverse_realpow_zero
% 8.01/5.77 thf(fact_9843_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 8.01/5.77 ! [R2: real] :
% 8.01/5.77 ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ R2 )
% 8.01/5.77 @ at_top_nat ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_inverse_real_of_nat_add_minus
% 8.01/5.77 thf(fact_9844_tendsto__exp__limit__sequentially,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ) @ N3 )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 8.01/5.77 @ at_top_nat ) ).
% 8.01/5.77
% 8.01/5.77 % tendsto_exp_limit_sequentially
% 8.01/5.77 thf(fact_9845_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 8.01/5.77 ! [R2: real] :
% 8.01/5.77 ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ R2 )
% 8.01/5.77 @ at_top_nat ) ).
% 8.01/5.77
% 8.01/5.77 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 8.01/5.77 thf(fact_9846_summable__Leibniz_I1_J,axiom,
% 8.01/5.77 ! [A: nat > real] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ( topolo6980174941875973593q_real @ A )
% 8.01/5.77 => ( summable_real
% 8.01/5.77 @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_Leibniz(1)
% 8.01/5.77 thf(fact_9847_summable,axiom,
% 8.01/5.77 ! [A: nat > real] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 8.01/5.77 => ( summable_real
% 8.01/5.77 @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable
% 8.01/5.77 thf(fact_9848_cos__diff__limit__1,axiom,
% 8.01/5.77 ! [Theta: nat > real,Theta2: real] :
% 8.01/5.77 ( ( filterlim_nat_real
% 8.01/5.77 @ ^ [J2: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J2 ) @ Theta2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.01/5.77 @ at_top_nat )
% 8.01/5.77 => ~ ! [K2: nat > int] :
% 8.01/5.77 ~ ( filterlim_nat_real
% 8.01/5.77 @ ^ [J2: nat] : ( minus_minus_real @ ( Theta @ J2 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ Theta2 )
% 8.01/5.77 @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % cos_diff_limit_1
% 8.01/5.77 thf(fact_9849_cos__limit__1,axiom,
% 8.01/5.77 ! [Theta: nat > real] :
% 8.01/5.77 ( ( filterlim_nat_real
% 8.01/5.77 @ ^ [J2: nat] : ( cos_real @ ( Theta @ J2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.01/5.77 @ at_top_nat )
% 8.01/5.77 => ? [K2: nat > int] :
% 8.01/5.77 ( filterlim_nat_real
% 8.01/5.77 @ ^ [J2: nat] : ( minus_minus_real @ ( Theta @ J2 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % cos_limit_1
% 8.01/5.77 thf(fact_9850_summable__Leibniz_I4_J,axiom,
% 8.01/5.77 ! [A: nat > real] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ( topolo6980174941875973593q_real @ A )
% 8.01/5.77 => ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 8.01/5.77 @ at_top_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_Leibniz(4)
% 8.01/5.77 thf(fact_9851_zeroseq__arctan__series,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.01/5.77 => ( filterlim_nat_real
% 8.01/5.77 @ ^ [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 ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % zeroseq_arctan_series
% 8.01/5.77 thf(fact_9852_summable__Leibniz_H_I2_J,axiom,
% 8.01/5.77 ! [A: nat > real,N: nat] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 8.01/5.77 => ( ord_less_eq_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_Leibniz'(2)
% 8.01/5.77 thf(fact_9853_summable__Leibniz_H_I3_J,axiom,
% 8.01/5.77 ! [A: nat > real] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 8.01/5.77 => ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 8.01/5.77 @ at_top_nat ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_Leibniz'(3)
% 8.01/5.77 thf(fact_9854_sums__alternating__upper__lower,axiom,
% 8.01/5.77 ! [A: nat > real] :
% 8.01/5.77 ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 8.01/5.77 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ? [L4: real] :
% 8.01/5.77 ( ! [N9: nat] :
% 8.01/5.77 ( ord_less_eq_real
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 8.01/5.77 @ L4 )
% 8.01/5.77 & ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ L4 )
% 8.01/5.77 @ at_top_nat )
% 8.01/5.77 & ! [N9: nat] :
% 8.01/5.77 ( ord_less_eq_real @ L4
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 8.01/5.77 & ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ L4 )
% 8.01/5.77 @ at_top_nat ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % sums_alternating_upper_lower
% 8.01/5.77 thf(fact_9855_summable__Leibniz_I5_J,axiom,
% 8.01/5.77 ! [A: nat > real] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ( topolo6980174941875973593q_real @ A )
% 8.01/5.77 => ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 8.01/5.77 @ at_top_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_Leibniz(5)
% 8.01/5.77 thf(fact_9856_summable__Leibniz_H_I5_J,axiom,
% 8.01/5.77 ! [A: nat > real] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 8.01/5.77 => ( filterlim_nat_real
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 8.01/5.77 @ at_top_nat ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_Leibniz'(5)
% 8.01/5.77 thf(fact_9857_summable__Leibniz_H_I4_J,axiom,
% 8.01/5.77 ! [A: nat > real,N: nat] :
% 8.01/5.77 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 8.01/5.77 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 8.01/5.77 => ( ord_less_eq_real
% 8.01/5.77 @ ( suminf_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 8.01/5.77 @ ( groups6591440286371151544t_real
% 8.01/5.77 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 8.01/5.77 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % summable_Leibniz'(4)
% 8.01/5.77 thf(fact_9858_real__bounded__linear,axiom,
% 8.01/5.77 ( real_V5970128139526366754l_real
% 8.01/5.77 = ( ^ [F3: real > real] :
% 8.01/5.77 ? [C4: real] :
% 8.01/5.77 ( F3
% 8.01/5.77 = ( ^ [X2: real] : ( times_times_real @ X2 @ C4 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % real_bounded_linear
% 8.01/5.77 thf(fact_9859_filterlim__Suc,axiom,
% 8.01/5.77 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 8.01/5.77
% 8.01/5.77 % filterlim_Suc
% 8.01/5.77 thf(fact_9860_tendsto__exp__limit__at__right,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( filterlim_real_real
% 8.01/5.77 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y6 ) ) @ ( divide_divide_real @ one_one_real @ Y6 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % tendsto_exp_limit_at_right
% 8.01/5.77 thf(fact_9861_tendsto__arctan__at__bot,axiom,
% 8.01/5.77 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 8.01/5.77
% 8.01/5.77 % tendsto_arctan_at_bot
% 8.01/5.77 thf(fact_9862_ln__at__0,axiom,
% 8.01/5.77 filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % ln_at_0
% 8.01/5.77 thf(fact_9863_artanh__real__at__right__1,axiom,
% 8.01/5.77 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 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % artanh_real_at_right_1
% 8.01/5.77 thf(fact_9864_filterlim__tan__at__right,axiom,
% 8.01/5.77 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 ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % filterlim_tan_at_right
% 8.01/5.77 thf(fact_9865_exp__at__bot,axiom,
% 8.01/5.77 filterlim_real_real @ exp_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_bot_real ).
% 8.01/5.77
% 8.01/5.77 % exp_at_bot
% 8.01/5.77 thf(fact_9866_filterlim__inverse__at__bot__neg,axiom,
% 8.01/5.77 filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % filterlim_inverse_at_bot_neg
% 8.01/5.77 thf(fact_9867_log__inj,axiom,
% 8.01/5.77 ! [B: real] :
% 8.01/5.77 ( ( ord_less_real @ one_one_real @ B )
% 8.01/5.77 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % log_inj
% 8.01/5.77 thf(fact_9868_tanh__real__at__bot,axiom,
% 8.01/5.77 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 8.01/5.77
% 8.01/5.77 % tanh_real_at_bot
% 8.01/5.77 thf(fact_9869_tendsto__arcosh__at__left__1,axiom,
% 8.01/5.77 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % tendsto_arcosh_at_left_1
% 8.01/5.77 thf(fact_9870_DERIV__pos__imp__increasing__at__bot,axiom,
% 8.01/5.77 ! [B: real,F: real > real,Flim: real] :
% 8.01/5.77 ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ X3 @ B )
% 8.01/5.77 => ? [Y4: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 8.01/5.77 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 8.01/5.77 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_pos_imp_increasing_at_bot
% 8.01/5.77 thf(fact_9871_filterlim__pow__at__bot__odd,axiom,
% 8.01/5.77 ! [N: nat,F: real > real,F2: filter_real] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 8.01/5.77 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 8.01/5.77 @ at_bot_real
% 8.01/5.77 @ F2 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % filterlim_pow_at_bot_odd
% 8.01/5.77 thf(fact_9872_filterlim__pow__at__bot__even,axiom,
% 8.01/5.77 ! [N: nat,F: real > real,F2: filter_real] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 8.01/5.77 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( power_power_real @ ( F @ X2 ) @ N )
% 8.01/5.77 @ at_top_real
% 8.01/5.77 @ F2 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % filterlim_pow_at_bot_even
% 8.01/5.77 thf(fact_9873_sqrt__at__top,axiom,
% 8.01/5.77 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 8.01/5.77
% 8.01/5.77 % sqrt_at_top
% 8.01/5.77 thf(fact_9874_greaterThan__0,axiom,
% 8.01/5.77 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 8.01/5.77 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % greaterThan_0
% 8.01/5.77 thf(fact_9875_greaterThan__Suc,axiom,
% 8.01/5.77 ! [K: nat] :
% 8.01/5.77 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 8.01/5.77 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % greaterThan_Suc
% 8.01/5.77 thf(fact_9876_tanh__real__at__top,axiom,
% 8.01/5.77 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 8.01/5.77
% 8.01/5.77 % tanh_real_at_top
% 8.01/5.77 thf(fact_9877_artanh__real__at__left__1,axiom,
% 8.01/5.77 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % artanh_real_at_left_1
% 8.01/5.77 thf(fact_9878_ln__x__over__x__tendsto__0,axiom,
% 8.01/5.77 ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_real ) ).
% 8.01/5.77
% 8.01/5.77 % ln_x_over_x_tendsto_0
% 8.01/5.77 thf(fact_9879_filterlim__inverse__at__top__right,axiom,
% 8.01/5.77 filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % filterlim_inverse_at_top_right
% 8.01/5.77 thf(fact_9880_filterlim__inverse__at__right__top,axiom,
% 8.01/5.77 filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 8.01/5.77
% 8.01/5.77 % filterlim_inverse_at_right_top
% 8.01/5.77 thf(fact_9881_tendsto__power__div__exp__0,axiom,
% 8.01/5.77 ! [K: nat] :
% 8.01/5.77 ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( power_power_real @ X2 @ K ) @ ( exp_real @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.01/5.77 @ at_top_real ) ).
% 8.01/5.77
% 8.01/5.77 % tendsto_power_div_exp_0
% 8.01/5.77 thf(fact_9882_tendsto__exp__limit__at__top,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( filterlim_real_real
% 8.01/5.77 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y6 ) ) @ Y6 )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 8.01/5.77 @ at_top_real ) ).
% 8.01/5.77
% 8.01/5.77 % tendsto_exp_limit_at_top
% 8.01/5.77 thf(fact_9883_filterlim__tan__at__left,axiom,
% 8.01/5.77 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 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % filterlim_tan_at_left
% 8.01/5.77 thf(fact_9884_tendsto__arctan__at__top,axiom,
% 8.01/5.77 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 8.01/5.77
% 8.01/5.77 % tendsto_arctan_at_top
% 8.01/5.77 thf(fact_9885_DERIV__neg__imp__decreasing__at__top,axiom,
% 8.01/5.77 ! [B: real,F: real > real,Flim: real] :
% 8.01/5.77 ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ B @ X3 )
% 8.01/5.77 => ? [Y4: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 8.01/5.77 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_neg_imp_decreasing_at_top
% 8.01/5.77 thf(fact_9886_lhopital__left__at__top,axiom,
% 8.01/5.77 ! [G: real > real,X: real,G2: real > real,F: real > real,F6: real > real,Y: real] :
% 8.01/5.77 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G2 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ Y )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ Y )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_left_at_top
% 8.01/5.77 thf(fact_9887_eventually__sequentially__Suc,axiom,
% 8.01/5.77 ! [P: nat > $o] :
% 8.01/5.77 ( ( eventually_nat
% 8.01/5.77 @ ^ [I2: nat] : ( P @ ( suc @ I2 ) )
% 8.01/5.77 @ at_top_nat )
% 8.01/5.77 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % eventually_sequentially_Suc
% 8.01/5.77 thf(fact_9888_eventually__sequentially__seg,axiom,
% 8.01/5.77 ! [P: nat > $o,K: nat] :
% 8.01/5.77 ( ( eventually_nat
% 8.01/5.77 @ ^ [N3: nat] : ( P @ ( plus_plus_nat @ N3 @ K ) )
% 8.01/5.77 @ at_top_nat )
% 8.01/5.77 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % eventually_sequentially_seg
% 8.01/5.77 thf(fact_9889_sequentially__offset,axiom,
% 8.01/5.77 ! [P: nat > $o,K: nat] :
% 8.01/5.77 ( ( eventually_nat @ P @ at_top_nat )
% 8.01/5.77 => ( eventually_nat
% 8.01/5.77 @ ^ [I2: nat] : ( P @ ( plus_plus_nat @ I2 @ K ) )
% 8.01/5.77 @ at_top_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % sequentially_offset
% 8.01/5.77 thf(fact_9890_eventually__at__right__to__0,axiom,
% 8.01/5.77 ! [P: real > $o,A: real] :
% 8.01/5.77 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 = ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( P @ ( plus_plus_real @ X2 @ A ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % eventually_at_right_to_0
% 8.01/5.77 thf(fact_9891_eventually__at__right__real,axiom,
% 8.01/5.77 ! [A: real,B: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % eventually_at_right_real
% 8.01/5.77 thf(fact_9892_eventually__at__left__real,axiom,
% 8.01/5.77 ! [B: real,A: real] :
% 8.01/5.77 ( ( ord_less_real @ B @ A )
% 8.01/5.77 => ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( member_real @ X2 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % eventually_at_left_real
% 8.01/5.77 thf(fact_9893_eventually__at__top__to__right,axiom,
% 8.01/5.77 ! [P: real > $o] :
% 8.01/5.77 ( ( eventually_real @ P @ at_top_real )
% 8.01/5.77 = ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( P @ ( inverse_inverse_real @ X2 ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % eventually_at_top_to_right
% 8.01/5.77 thf(fact_9894_eventually__at__right__to__top,axiom,
% 8.01/5.77 ! [P: real > $o] :
% 8.01/5.77 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 = ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( P @ ( inverse_inverse_real @ X2 ) )
% 8.01/5.77 @ at_top_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % eventually_at_right_to_top
% 8.01/5.77 thf(fact_9895_lhopital__at__top__at__top,axiom,
% 8.01/5.77 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ at_top_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ at_top_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_at_top_at_top
% 8.01/5.77 thf(fact_9896_lhopital,axiom,
% 8.01/5.77 ! [F: real > real,X: real,G: real > real,G2: real > real,F6: real > real,F2: filter_real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G2 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ F2
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ F2
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital
% 8.01/5.77 thf(fact_9897_lhopital__right__at__top__at__top,axiom,
% 8.01/5.77 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ at_top_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ at_top_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_right_at_top_at_top
% 8.01/5.77 thf(fact_9898_lhopital__at__top__at__bot,axiom,
% 8.01/5.77 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ at_bot_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ at_bot_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_at_top_at_bot
% 8.01/5.77 thf(fact_9899_lhopital__left__at__top__at__top,axiom,
% 8.01/5.77 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ at_top_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ at_top_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_left_at_top_at_top
% 8.01/5.77 thf(fact_9900_lhopital__at__top,axiom,
% 8.01/5.77 ! [G: real > real,X: real,G2: real > real,F: real > real,F6: real > real,Y: real] :
% 8.01/5.77 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G2 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ Y )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ Y )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_at_top
% 8.01/5.77 thf(fact_9901_lhospital__at__top__at__top,axiom,
% 8.01/5.77 ! [G: real > real,G2: real > real,F: real > real,F6: real > real,X: real] :
% 8.01/5.77 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G2 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ at_top_real )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ at_top_real )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ at_top_real )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ X )
% 8.01/5.77 @ at_top_real )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ X )
% 8.01/5.77 @ at_top_real ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhospital_at_top_at_top
% 8.01/5.77 thf(fact_9902_lhopital__right,axiom,
% 8.01/5.77 ! [F: real > real,X: real,G: real > real,G2: real > real,F6: real > real,F2: filter_real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G2 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ F2
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ F2
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_right
% 8.01/5.77 thf(fact_9903_lhopital__right__0,axiom,
% 8.01/5.77 ! [F0: real > real,G0: real > real,G2: real > real,F6: real > real,F2: filter_real] :
% 8.01/5.77 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G0 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G2 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ F2
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F0 @ X2 ) @ ( G0 @ X2 ) )
% 8.01/5.77 @ F2
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_right_0
% 8.01/5.77 thf(fact_9904_lhopital__left,axiom,
% 8.01/5.77 ! [F: real > real,X: real,G: real > real,G2: real > real,F6: real > real,F2: filter_real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G2 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ F2
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ F2
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_left
% 8.01/5.77 thf(fact_9905_lhopital__right__at__top__at__bot,axiom,
% 8.01/5.77 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ at_bot_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ at_bot_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_right_at_top_at_bot
% 8.01/5.77 thf(fact_9906_lhopital__left__at__top__at__bot,axiom,
% 8.01/5.77 ! [F: real > real,A: real,G: real > real,F6: real > real,G2: real > real] :
% 8.01/5.77 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ at_bot_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ at_bot_real
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_left_at_top_at_bot
% 8.01/5.77 thf(fact_9907_lhopital__right__at__top,axiom,
% 8.01/5.77 ! [G: real > real,X: real,G2: real > real,F: real > real,F6: real > real,Y: real] :
% 8.01/5.77 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G2 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ Y )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ Y )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_right_at_top
% 8.01/5.77 thf(fact_9908_lhopital__right__0__at__top,axiom,
% 8.01/5.77 ! [G: real > real,G2: real > real,F: real > real,F6: real > real,X: real] :
% 8.01/5.77 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] :
% 8.01/5.77 ( ( G2 @ X2 )
% 8.01/5.77 != zero_zero_real )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ F @ ( F6 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( eventually_real
% 8.01/5.77 @ ^ [X2: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F6 @ X2 ) @ ( G2 @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ X )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 8.01/5.77 => ( filterlim_real_real
% 8.01/5.77 @ ^ [X2: real] : ( divide_divide_real @ ( F @ X2 ) @ ( G @ X2 ) )
% 8.01/5.77 @ ( topolo2815343760600316023s_real @ X )
% 8.01/5.77 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % lhopital_right_0_at_top
% 8.01/5.77 thf(fact_9909_Bseq__realpow,axiom,
% 8.01/5.77 ! [X: real] :
% 8.01/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.01/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.01/5.77 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Bseq_realpow
% 8.01/5.77 thf(fact_9910_atLeastSucAtMost__greaterThanAtMost,axiom,
% 8.01/5.77 ! [L: nat,U: nat] :
% 8.01/5.77 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 8.01/5.77 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastSucAtMost_greaterThanAtMost
% 8.01/5.77 thf(fact_9911_greaterThanAtMost__upt,axiom,
% 8.01/5.77 ( set_or6659071591806873216st_nat
% 8.01/5.77 = ( ^ [N3: nat,M4: nat] : ( set_nat2 @ ( upt @ ( suc @ N3 ) @ ( suc @ M4 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % greaterThanAtMost_upt
% 8.01/5.77 thf(fact_9912_rat__inverse__code,axiom,
% 8.01/5.77 ! [P4: rat] :
% 8.01/5.77 ( ( quotient_of @ ( inverse_inverse_rat @ P4 ) )
% 8.01/5.77 = ( produc4245557441103728435nt_int
% 8.01/5.77 @ ^ [A3: int,B4: 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 ) @ B4 ) @ ( abs_abs_int @ A3 ) ) )
% 8.01/5.77 @ ( quotient_of @ P4 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % rat_inverse_code
% 8.01/5.77 thf(fact_9913_rat__one__code,axiom,
% 8.01/5.77 ( ( quotient_of @ one_one_rat )
% 8.01/5.77 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % rat_one_code
% 8.01/5.77 thf(fact_9914_quotient__of__number_I3_J,axiom,
% 8.01/5.77 ! [K: num] :
% 8.01/5.77 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 8.01/5.77 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % quotient_of_number(3)
% 8.01/5.77 thf(fact_9915_rat__zero__code,axiom,
% 8.01/5.77 ( ( quotient_of @ zero_zero_rat )
% 8.01/5.77 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % rat_zero_code
% 8.01/5.77 thf(fact_9916_quotient__of__number_I4_J,axiom,
% 8.01/5.77 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.01/5.77 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % quotient_of_number(4)
% 8.01/5.77 thf(fact_9917_quotient__of__number_I5_J,axiom,
% 8.01/5.77 ! [K: num] :
% 8.01/5.77 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 8.01/5.77 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % quotient_of_number(5)
% 8.01/5.77 thf(fact_9918_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 8.01/5.77 ! [L: int,U: int] :
% 8.01/5.77 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 8.01/5.77 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 8.01/5.77 thf(fact_9919_quotient__of__denom__pos,axiom,
% 8.01/5.77 ! [R2: rat,P4: int,Q3: int] :
% 8.01/5.77 ( ( ( quotient_of @ R2 )
% 8.01/5.77 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 8.01/5.77 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 8.01/5.77
% 8.01/5.77 % quotient_of_denom_pos
% 8.01/5.77 thf(fact_9920_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 8.01/5.77 ! [L: code_integer,U: code_integer] :
% 8.01/5.77 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 8.01/5.77 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 8.01/5.77 thf(fact_9921_quotient__of__int,axiom,
% 8.01/5.77 ! [A: int] :
% 8.01/5.77 ( ( quotient_of @ ( of_int @ A ) )
% 8.01/5.77 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % quotient_of_int
% 8.01/5.77 thf(fact_9922_GMVT,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real,G: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ( ord_less_eq_real @ A @ X3 )
% 8.01/5.77 & ( ord_less_eq_real @ X3 @ B ) )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F ) )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 & ( ord_less_real @ X3 @ B ) )
% 8.01/5.77 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ( ord_less_eq_real @ A @ X3 )
% 8.01/5.77 & ( ord_less_eq_real @ X3 @ B ) )
% 8.01/5.77 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G ) )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 & ( ord_less_real @ X3 @ B ) )
% 8.01/5.77 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 8.01/5.77 => ? [G_c: real,F_c: real,C3: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 8.01/5.77 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 8.01/5.77 & ( ord_less_real @ A @ C3 )
% 8.01/5.77 & ( ord_less_real @ C3 @ B )
% 8.01/5.77 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 8.01/5.77 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % GMVT
% 8.01/5.77 thf(fact_9923_obtain__pos__sum,axiom,
% 8.01/5.77 ! [R2: rat] :
% 8.01/5.77 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 8.01/5.77 => ~ ! [S2: rat] :
% 8.01/5.77 ( ( ord_less_rat @ zero_zero_rat @ S2 )
% 8.01/5.77 => ! [T6: rat] :
% 8.01/5.77 ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 8.01/5.77 => ( R2
% 8.01/5.77 != ( plus_plus_rat @ S2 @ T6 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % obtain_pos_sum
% 8.01/5.77 thf(fact_9924_abs__rat__def,axiom,
% 8.01/5.77 ( abs_abs_rat
% 8.01/5.77 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % abs_rat_def
% 8.01/5.77 thf(fact_9925_sgn__rat__def,axiom,
% 8.01/5.77 ( sgn_sgn_rat
% 8.01/5.77 = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % sgn_rat_def
% 8.01/5.77 thf(fact_9926_Frct__code__post_I5_J,axiom,
% 8.01/5.77 ! [K: num] :
% 8.01/5.77 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 8.01/5.77 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Frct_code_post(5)
% 8.01/5.77 thf(fact_9927_normalize__negative,axiom,
% 8.01/5.77 ! [Q3: int,P4: int] :
% 8.01/5.77 ( ( ord_less_int @ Q3 @ zero_zero_int )
% 8.01/5.77 => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q3 ) )
% 8.01/5.77 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P4 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % normalize_negative
% 8.01/5.77 thf(fact_9928_normalize__denom__zero,axiom,
% 8.01/5.77 ! [P4: int] :
% 8.01/5.77 ( ( normalize @ ( product_Pair_int_int @ P4 @ zero_zero_int ) )
% 8.01/5.77 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % normalize_denom_zero
% 8.01/5.77 thf(fact_9929_less__eq__rat__def,axiom,
% 8.01/5.77 ( ord_less_eq_rat
% 8.01/5.77 = ( ^ [X2: rat,Y6: rat] :
% 8.01/5.77 ( ( ord_less_rat @ X2 @ Y6 )
% 8.01/5.77 | ( X2 = Y6 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % less_eq_rat_def
% 8.01/5.77 thf(fact_9930_normalize__denom__pos,axiom,
% 8.01/5.77 ! [R2: product_prod_int_int,P4: int,Q3: int] :
% 8.01/5.77 ( ( ( normalize @ R2 )
% 8.01/5.77 = ( product_Pair_int_int @ P4 @ Q3 ) )
% 8.01/5.77 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 8.01/5.77
% 8.01/5.77 % normalize_denom_pos
% 8.01/5.77 thf(fact_9931_normalize__crossproduct,axiom,
% 8.01/5.77 ! [Q3: int,S: int,P4: int,R2: int] :
% 8.01/5.77 ( ( Q3 != zero_zero_int )
% 8.01/5.77 => ( ( S != zero_zero_int )
% 8.01/5.77 => ( ( ( normalize @ ( product_Pair_int_int @ P4 @ Q3 ) )
% 8.01/5.77 = ( normalize @ ( product_Pair_int_int @ R2 @ S ) ) )
% 8.01/5.77 => ( ( times_times_int @ P4 @ S )
% 8.01/5.77 = ( times_times_int @ R2 @ Q3 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % normalize_crossproduct
% 8.01/5.77 thf(fact_9932_Frct__code__post_I2_J,axiom,
% 8.01/5.77 ! [A: int] :
% 8.01/5.77 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 8.01/5.77 = zero_zero_rat ) ).
% 8.01/5.77
% 8.01/5.77 % Frct_code_post(2)
% 8.01/5.77 thf(fact_9933_Frct__code__post_I1_J,axiom,
% 8.01/5.77 ! [A: int] :
% 8.01/5.77 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 8.01/5.77 = zero_zero_rat ) ).
% 8.01/5.77
% 8.01/5.77 % Frct_code_post(1)
% 8.01/5.77 thf(fact_9934_Frct__code__post_I3_J,axiom,
% 8.01/5.77 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 8.01/5.77 = one_one_rat ) ).
% 8.01/5.77
% 8.01/5.77 % Frct_code_post(3)
% 8.01/5.77 thf(fact_9935_Frct__code__post_I6_J,axiom,
% 8.01/5.77 ! [K: num,L: num] :
% 8.01/5.77 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 8.01/5.77 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Frct_code_post(6)
% 8.01/5.77 thf(fact_9936_Frct__code__post_I4_J,axiom,
% 8.01/5.77 ! [K: num] :
% 8.01/5.77 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 8.01/5.77 = ( numeral_numeral_rat @ K ) ) ).
% 8.01/5.77
% 8.01/5.77 % Frct_code_post(4)
% 8.01/5.77 thf(fact_9937_MVT,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_real @ X3 @ B )
% 8.01/5.77 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 8.01/5.77 => ? [L4: real,Z3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ Z3 )
% 8.01/5.77 & ( ord_less_real @ Z3 @ B )
% 8.01/5.77 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 8.01/5.77 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 8.01/5.77 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % MVT
% 8.01/5.77 thf(fact_9938_set__bits__int__def,axiom,
% 8.01/5.77 ( bit_bi6516823479961619367ts_int
% 8.01/5.77 = ( ^ [F3: nat > $o] :
% 8.01/5.77 ( if_int
% 8.01/5.77 @ ? [N3: nat] :
% 8.01/5.77 ! [M4: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N3 @ M4 )
% 8.01/5.77 => ( ( F3 @ M4 )
% 8.01/5.77 = ( F3 @ N3 ) ) )
% 8.01/5.77 @ ( bit_ri631733984087533419it_int
% 8.01/5.77 @ ( ord_Least_nat
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ! [M4: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N3 @ M4 )
% 8.01/5.77 => ( ( F3 @ M4 )
% 8.01/5.77 = ( F3 @ N3 ) ) ) )
% 8.01/5.77 @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 8.01/5.77 @ ( map_nat_o @ F3
% 8.01/5.77 @ ( upt @ zero_zero_nat
% 8.01/5.77 @ ( suc
% 8.01/5.77 @ ( ord_Least_nat
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ! [M4: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N3 @ M4 )
% 8.01/5.77 => ( ( F3 @ M4 )
% 8.01/5.77 = ( F3 @ N3 ) ) ) ) ) ) ) ) )
% 8.01/5.77 @ zero_zero_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % set_bits_int_def
% 8.01/5.77 thf(fact_9939_Least__eq__0,axiom,
% 8.01/5.77 ! [P: nat > $o] :
% 8.01/5.77 ( ( P @ zero_zero_nat )
% 8.01/5.77 => ( ( ord_Least_nat @ P )
% 8.01/5.77 = zero_zero_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % Least_eq_0
% 8.01/5.77 thf(fact_9940_Least__Suc,axiom,
% 8.01/5.77 ! [P: nat > $o,N: nat] :
% 8.01/5.77 ( ( P @ N )
% 8.01/5.77 => ( ~ ( P @ zero_zero_nat )
% 8.01/5.77 => ( ( ord_Least_nat @ P )
% 8.01/5.77 = ( suc
% 8.01/5.77 @ ( ord_Least_nat
% 8.01/5.77 @ ^ [M4: nat] : ( P @ ( suc @ M4 ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Least_Suc
% 8.01/5.77 thf(fact_9941_Least__Suc2,axiom,
% 8.01/5.77 ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 8.01/5.77 ( ( P @ N )
% 8.01/5.77 => ( ( Q @ M )
% 8.01/5.77 => ( ~ ( P @ zero_zero_nat )
% 8.01/5.77 => ( ! [K2: nat] :
% 8.01/5.77 ( ( P @ ( suc @ K2 ) )
% 8.01/5.77 = ( Q @ K2 ) )
% 8.01/5.77 => ( ( ord_Least_nat @ P )
% 8.01/5.77 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Least_Suc2
% 8.01/5.77 thf(fact_9942_continuous__on__arcosh_H,axiom,
% 8.01/5.77 ! [A2: set_real,F: real > real] :
% 8.01/5.77 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( member_real @ X3 @ A2 )
% 8.01/5.77 => ( ord_less_eq_real @ one_one_real @ ( F @ X3 ) ) )
% 8.01/5.77 => ( topolo5044208981011980120l_real @ A2
% 8.01/5.77 @ ^ [X2: real] : ( arcosh_real @ ( F @ X2 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % continuous_on_arcosh'
% 8.01/5.77 thf(fact_9943_continuous__on__arccos_H,axiom,
% 8.01/5.77 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 8.01/5.77
% 8.01/5.77 % continuous_on_arccos'
% 8.01/5.77 thf(fact_9944_continuous__on__arcsin_H,axiom,
% 8.01/5.77 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 8.01/5.77
% 8.01/5.77 % continuous_on_arcsin'
% 8.01/5.77 thf(fact_9945_continuous__on__artanh,axiom,
% 8.01/5.77 ! [A2: set_real] :
% 8.01/5.77 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 8.01/5.77 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 8.01/5.77
% 8.01/5.77 % continuous_on_artanh
% 8.01/5.77 thf(fact_9946_continuous__on__artanh_H,axiom,
% 8.01/5.77 ! [A2: set_real,F: real > real] :
% 8.01/5.77 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( member_real @ X3 @ A2 )
% 8.01/5.77 => ( member_real @ ( F @ X3 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 8.01/5.77 => ( topolo5044208981011980120l_real @ A2
% 8.01/5.77 @ ^ [X2: real] : ( artanh_real @ ( F @ X2 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % continuous_on_artanh'
% 8.01/5.77 thf(fact_9947_Rolle__deriv,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real,F6: real > real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ( ( F @ A )
% 8.01/5.77 = ( F @ B ) )
% 8.01/5.77 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_real @ X3 @ B )
% 8.01/5.77 => ( has_de1759254742604945161l_real @ F @ ( F6 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 8.01/5.77 => ? [Z3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ Z3 )
% 8.01/5.77 & ( ord_less_real @ Z3 @ B )
% 8.01/5.77 & ( ( F6 @ Z3 )
% 8.01/5.77 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Rolle_deriv
% 8.01/5.77 thf(fact_9948_mvt,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real,F6: real > real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_real @ X3 @ B )
% 8.01/5.77 => ( has_de1759254742604945161l_real @ F @ ( F6 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 8.01/5.77 => ~ ! [Xi2: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ Xi2 )
% 8.01/5.77 => ( ( ord_less_real @ Xi2 @ B )
% 8.01/5.77 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 8.01/5.77 != ( F6 @ Xi2 @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % mvt
% 8.01/5.77 thf(fact_9949_DERIV__pos__imp__increasing__open,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_real @ X3 @ B )
% 8.01/5.77 => ? [Y4: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 8.01/5.77 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.01/5.77 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_pos_imp_increasing_open
% 8.01/5.77 thf(fact_9950_DERIV__neg__imp__decreasing__open,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_real @ X3 @ B )
% 8.01/5.77 => ? [Y4: real] :
% 8.01/5.77 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.01/5.77 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 8.01/5.77 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.01/5.77 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_neg_imp_decreasing_open
% 8.01/5.77 thf(fact_9951_DERIV__isconst__end,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_real @ X3 @ B )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 8.01/5.77 => ( ( F @ B )
% 8.01/5.77 = ( F @ A ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_isconst_end
% 8.01/5.77 thf(fact_9952_DERIV__isconst2,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real,X: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_real @ X3 @ B )
% 8.01/5.77 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 8.01/5.77 => ( ( ord_less_eq_real @ A @ X )
% 8.01/5.77 => ( ( ord_less_eq_real @ X @ B )
% 8.01/5.77 => ( ( F @ X )
% 8.01/5.77 = ( F @ A ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % DERIV_isconst2
% 8.01/5.77 thf(fact_9953_Rolle,axiom,
% 8.01/5.77 ! [A: real,B: real,F: real > real] :
% 8.01/5.77 ( ( ord_less_real @ A @ B )
% 8.01/5.77 => ( ( ( F @ A )
% 8.01/5.77 = ( F @ B ) )
% 8.01/5.77 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 8.01/5.77 => ( ! [X3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ X3 )
% 8.01/5.77 => ( ( ord_less_real @ X3 @ B )
% 8.01/5.77 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 8.01/5.77 => ? [Z3: real] :
% 8.01/5.77 ( ( ord_less_real @ A @ Z3 )
% 8.01/5.77 & ( ord_less_real @ Z3 @ B )
% 8.01/5.77 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % Rolle
% 8.01/5.77 thf(fact_9954_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Xa3: nat,Y: $o] :
% 8.01/5.77 ( ( ( vEBT_VEBT_valid @ X @ Xa3 )
% 8.01/5.77 = Y )
% 8.01/5.77 => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.01/5.77 ( X
% 8.01/5.77 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.01/5.77 => ( Y
% 8.01/5.77 = ( Xa3 != one_one_nat ) ) )
% 8.01/5.77 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 8.01/5.77 => ( Y
% 8.01/5.77 = ( ~ ( ( Deg2 = Xa3 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.01/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 & ( case_o184042715313410164at_nat
% 8.01/5.77 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 @ ( produc6081775807080527818_nat_o
% 8.01/5.77 @ ^ [Mi2: nat,Ma3: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ Mi2 @ Ma3 )
% 8.01/5.77 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 & ! [I2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 8.01/5.77 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 8.01/5.77 & ( ( Mi2 = Ma3 )
% 8.01/5.77 => ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 & ( ( Mi2 != Ma3 )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 8.01/5.77 & ! [X2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 8.01/5.77 => ( ( ord_less_nat @ Mi2 @ X2 )
% 8.01/5.77 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 8.01/5.77 @ Mima ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.valid'.elims(1)
% 8.01/5.77 thf(fact_9955_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Xa3: nat] :
% 8.01/5.77 ( ( vEBT_VEBT_valid @ X @ Xa3 )
% 8.01/5.77 => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.01/5.77 ( X
% 8.01/5.77 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.01/5.77 => ( Xa3 != one_one_nat ) )
% 8.01/5.77 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 8.01/5.77 => ~ ( ( Deg2 = Xa3 )
% 8.01/5.77 & ! [X5: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.01/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 & ( case_o184042715313410164at_nat
% 8.01/5.77 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 @ ( produc6081775807080527818_nat_o
% 8.01/5.77 @ ^ [Mi2: nat,Ma3: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ Mi2 @ Ma3 )
% 8.01/5.77 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 & ! [I2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 8.01/5.77 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 8.01/5.77 & ( ( Mi2 = Ma3 )
% 8.01/5.77 => ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 & ( ( Mi2 != Ma3 )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 8.01/5.77 & ! [X2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 8.01/5.77 => ( ( ord_less_nat @ Mi2 @ X2 )
% 8.01/5.77 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 8.01/5.77 @ Mima ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.valid'.elims(2)
% 8.01/5.77 thf(fact_9956_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 8.01/5.77 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 8.01/5.77 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 8.01/5.77 = ( ( Deg = Deg4 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.01/5.77 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.01/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 & ( case_o184042715313410164at_nat
% 8.01/5.77 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X7 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 @ ( produc6081775807080527818_nat_o
% 8.01/5.77 @ ^ [Mi2: nat,Ma3: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ Mi2 @ Ma3 )
% 8.01/5.77 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.01/5.77 & ! [I2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X7 ) )
% 8.01/5.77 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 8.01/5.77 & ( ( Mi2 = Ma3 )
% 8.01/5.77 => ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 & ( ( Mi2 != Ma3 )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 8.01/5.77 & ! [X2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X2 )
% 8.01/5.77 => ( ( ord_less_nat @ Mi2 @ X2 )
% 8.01/5.77 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 8.01/5.77 @ Mima2 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.valid'.simps(2)
% 8.01/5.77 thf(fact_9957_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Xa3: nat] :
% 8.01/5.77 ( ~ ( vEBT_VEBT_valid @ X @ Xa3 )
% 8.01/5.77 => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.01/5.77 ( X
% 8.01/5.77 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.01/5.77 => ( Xa3 = one_one_nat ) )
% 8.01/5.77 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 8.01/5.77 => ( ( Deg2 = Xa3 )
% 8.01/5.77 & ! [X3: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.01/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 & ( case_o184042715313410164at_nat
% 8.01/5.77 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 @ ( produc6081775807080527818_nat_o
% 8.01/5.77 @ ^ [Mi2: nat,Ma3: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ Mi2 @ Ma3 )
% 8.01/5.77 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 & ! [I2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 8.01/5.77 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 8.01/5.77 & ( ( Mi2 = Ma3 )
% 8.01/5.77 => ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 & ( ( Mi2 != Ma3 )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 8.01/5.77 & ! [X2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 8.01/5.77 => ( ( ord_less_nat @ Mi2 @ X2 )
% 8.01/5.77 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 8.01/5.77 @ Mima ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.valid'.elims(3)
% 8.01/5.77 thf(fact_9958_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Xa3: nat,Y: $o] :
% 8.01/5.77 ( ( ( vEBT_VEBT_valid @ X @ Xa3 )
% 8.01/5.77 = Y )
% 8.01/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 8.01/5.77 => ( ! [Uu2: $o,Uv2: $o] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.01/5.77 => ( ( Y
% 8.01/5.77 = ( Xa3 = one_one_nat ) )
% 8.01/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa3 ) ) ) )
% 8.01/5.77 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 8.01/5.77 => ( ( Y
% 8.01/5.77 = ( ( Deg2 = Xa3 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.01/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 & ( case_o184042715313410164at_nat
% 8.01/5.77 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 @ ( produc6081775807080527818_nat_o
% 8.01/5.77 @ ^ [Mi2: nat,Ma3: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ Mi2 @ Ma3 )
% 8.01/5.77 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 & ! [I2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 8.01/5.77 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 8.01/5.77 & ( ( Mi2 = Ma3 )
% 8.01/5.77 => ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 & ( ( Mi2 != Ma3 )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 8.01/5.77 & ! [X2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 8.01/5.77 => ( ( ord_less_nat @ Mi2 @ X2 )
% 8.01/5.77 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 8.01/5.77 @ Mima ) ) )
% 8.01/5.77 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa3 ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.valid'.pelims(1)
% 8.01/5.77 thf(fact_9959_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Xa3: nat] :
% 8.01/5.77 ( ( vEBT_VEBT_valid @ X @ Xa3 )
% 8.01/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 8.01/5.77 => ( ! [Uu2: $o,Uv2: $o] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.01/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa3 ) )
% 8.01/5.77 => ( Xa3 != one_one_nat ) ) )
% 8.01/5.77 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 8.01/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa3 ) )
% 8.01/5.77 => ~ ( ( Deg2 = Xa3 )
% 8.01/5.77 & ! [X5: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.01/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 & ( case_o184042715313410164at_nat
% 8.01/5.77 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 @ ( produc6081775807080527818_nat_o
% 8.01/5.77 @ ^ [Mi2: nat,Ma3: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ Mi2 @ Ma3 )
% 8.01/5.77 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 & ! [I2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 8.01/5.77 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 8.01/5.77 & ( ( Mi2 = Ma3 )
% 8.01/5.77 => ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 & ( ( Mi2 != Ma3 )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 8.01/5.77 & ! [X2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 8.01/5.77 => ( ( ord_less_nat @ Mi2 @ X2 )
% 8.01/5.77 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 8.01/5.77 @ Mima ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.valid'.pelims(2)
% 8.01/5.77 thf(fact_9960_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Xa3: nat] :
% 8.01/5.77 ( ~ ( vEBT_VEBT_valid @ X @ Xa3 )
% 8.01/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa3 ) )
% 8.01/5.77 => ( ! [Uu2: $o,Uv2: $o] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.01/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa3 ) )
% 8.01/5.77 => ( Xa3 = one_one_nat ) ) )
% 8.01/5.77 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 8.01/5.77 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa3 ) )
% 8.01/5.77 => ( ( Deg2 = Xa3 )
% 8.01/5.77 & ! [X3: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.01/5.77 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.01/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 & ( case_o184042715313410164at_nat
% 8.01/5.77 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.01/5.77 & ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 @ ( produc6081775807080527818_nat_o
% 8.01/5.77 @ ^ [Mi2: nat,Ma3: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ Mi2 @ Ma3 )
% 8.01/5.77 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 & ! [I2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.01/5.77 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X7 ) )
% 8.01/5.77 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 8.01/5.77 & ( ( Mi2 = Ma3 )
% 8.01/5.77 => ! [X2: vEBT_VEBT] :
% 8.01/5.77 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.01/5.77 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X7 ) ) )
% 8.01/5.77 & ( ( Mi2 != Ma3 )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 8.01/5.77 & ! [X2: nat] :
% 8.01/5.77 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.01/5.77 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X2 )
% 8.01/5.77 => ( ( ord_less_nat @ Mi2 @ X2 )
% 8.01/5.77 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) )
% 8.01/5.77 @ Mima ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.valid'.pelims(3)
% 8.01/5.77 thf(fact_9961_take__bit__numeral__minus__numeral__int,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 = ( case_option_int_num @ zero_zero_int
% 8.01/5.77 @ ^ [Q6: 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 @ Q6 ) ) )
% 8.01/5.77 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_numeral_minus_numeral_int
% 8.01/5.77 thf(fact_9962_take__bit__num__simps_I1_J,axiom,
% 8.01/5.77 ! [M: num] :
% 8.01/5.77 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 8.01/5.77 = none_num ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_num_simps(1)
% 8.01/5.77 thf(fact_9963_take__bit__num__simps_I2_J,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 8.01/5.77 = ( some_num @ one ) ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_num_simps(2)
% 8.01/5.77 thf(fact_9964_take__bit__num__simps_I5_J,axiom,
% 8.01/5.77 ! [R2: num] :
% 8.01/5.77 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 8.01/5.77 = ( some_num @ one ) ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_num_simps(5)
% 8.01/5.77 thf(fact_9965_take__bit__num__simps_I3_J,axiom,
% 8.01/5.77 ! [N: nat,M: num] :
% 8.01/5.77 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 8.01/5.77 = ( case_o6005452278849405969um_num @ none_num
% 8.01/5.77 @ ^ [Q6: num] : ( some_num @ ( bit0 @ Q6 ) )
% 8.01/5.77 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_num_simps(3)
% 8.01/5.77 thf(fact_9966_take__bit__num__simps_I4_J,axiom,
% 8.01/5.77 ! [N: nat,M: num] :
% 8.01/5.77 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 8.01/5.77 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_num_simps(4)
% 8.01/5.77 thf(fact_9967_take__bit__num__simps_I6_J,axiom,
% 8.01/5.77 ! [R2: num,M: num] :
% 8.01/5.77 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 8.01/5.77 = ( case_o6005452278849405969um_num @ none_num
% 8.01/5.77 @ ^ [Q6: num] : ( some_num @ ( bit0 @ Q6 ) )
% 8.01/5.77 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_num_simps(6)
% 8.01/5.77 thf(fact_9968_take__bit__num__simps_I7_J,axiom,
% 8.01/5.77 ! [R2: num,M: num] :
% 8.01/5.77 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 8.01/5.77 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_num_simps(7)
% 8.01/5.77 thf(fact_9969_and__minus__numerals_I7_J,axiom,
% 8.01/5.77 ! [N: num,M: num] :
% 8.01/5.77 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 8.01/5.77 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_minus_numerals(7)
% 8.01/5.77 thf(fact_9970_and__minus__numerals_I3_J,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.01/5.77 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_minus_numerals(3)
% 8.01/5.77 thf(fact_9971_and__minus__numerals_I8_J,axiom,
% 8.01/5.77 ! [N: num,M: num] :
% 8.01/5.77 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 8.01/5.77 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_minus_numerals(8)
% 8.01/5.77 thf(fact_9972_and__minus__numerals_I4_J,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.01/5.77 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_minus_numerals(4)
% 8.01/5.77 thf(fact_9973_and__not__num_Osimps_I1_J,axiom,
% 8.01/5.77 ( ( bit_and_not_num @ one @ one )
% 8.01/5.77 = none_num ) ).
% 8.01/5.77
% 8.01/5.77 % and_not_num.simps(1)
% 8.01/5.77 thf(fact_9974_and__not__num_Osimps_I4_J,axiom,
% 8.01/5.77 ! [M: num] :
% 8.01/5.77 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 8.01/5.77 = ( some_num @ ( bit0 @ M ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_not_num.simps(4)
% 8.01/5.77 thf(fact_9975_and__not__num_Osimps_I2_J,axiom,
% 8.01/5.77 ! [N: num] :
% 8.01/5.77 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 8.01/5.77 = ( some_num @ one ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_not_num.simps(2)
% 8.01/5.77 thf(fact_9976_and__not__num_Osimps_I3_J,axiom,
% 8.01/5.77 ! [N: num] :
% 8.01/5.77 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 8.01/5.77 = none_num ) ).
% 8.01/5.77
% 8.01/5.77 % and_not_num.simps(3)
% 8.01/5.77 thf(fact_9977_and__not__num_Osimps_I7_J,axiom,
% 8.01/5.77 ! [M: num] :
% 8.01/5.77 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 8.01/5.77 = ( some_num @ ( bit0 @ M ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_not_num.simps(7)
% 8.01/5.77 thf(fact_9978_and__not__num__eq__Some__iff,axiom,
% 8.01/5.77 ! [M: num,N: num,Q3: num] :
% 8.01/5.77 ( ( ( bit_and_not_num @ M @ N )
% 8.01/5.77 = ( some_num @ Q3 ) )
% 8.01/5.77 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 = ( numeral_numeral_int @ Q3 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_not_num_eq_Some_iff
% 8.01/5.77 thf(fact_9979_and__not__num_Osimps_I8_J,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 8.01/5.77 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 8.01/5.77 @ ^ [N11: num] : ( some_num @ ( bit1 @ N11 ) )
% 8.01/5.77 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_not_num.simps(8)
% 8.01/5.77 thf(fact_9980_and__not__num__eq__None__iff,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( ( bit_and_not_num @ M @ N )
% 8.01/5.77 = none_num )
% 8.01/5.77 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 = zero_zero_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % and_not_num_eq_None_iff
% 8.01/5.77 thf(fact_9981_int__numeral__and__not__num,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_numeral_and_not_num
% 8.01/5.77 thf(fact_9982_int__numeral__not__and__num,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % int_numeral_not_and_num
% 8.01/5.77 thf(fact_9983_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 8.01/5.77 ! [N: nat,M: num] :
% 8.01/5.77 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 8.01/5.77 = ( case_nat_option_num @ none_num
% 8.01/5.77 @ ^ [N3: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N3 @ M ) ) )
% 8.01/5.77 @ N ) ) ).
% 8.01/5.77
% 8.01/5.77 % Code_Abstract_Nat.take_bit_num_code(3)
% 8.01/5.77 thf(fact_9984_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 8.01/5.77 ! [N: nat,M: num] :
% 8.01/5.77 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 8.01/5.77 = ( case_nat_option_num @ none_num
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ( case_o6005452278849405969um_num @ none_num
% 8.01/5.77 @ ^ [Q6: num] : ( some_num @ ( bit0 @ Q6 ) )
% 8.01/5.77 @ ( bit_take_bit_num @ N3 @ M ) )
% 8.01/5.77 @ N ) ) ).
% 8.01/5.77
% 8.01/5.77 % Code_Abstract_Nat.take_bit_num_code(2)
% 8.01/5.77 thf(fact_9985_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( bit_take_bit_num @ N @ one )
% 8.01/5.77 = ( case_nat_option_num @ none_num
% 8.01/5.77 @ ^ [N3: nat] : ( some_num @ one )
% 8.01/5.77 @ N ) ) ).
% 8.01/5.77
% 8.01/5.77 % Code_Abstract_Nat.take_bit_num_code(1)
% 8.01/5.77 thf(fact_9986_take__bit__num__def,axiom,
% 8.01/5.77 ( bit_take_bit_num
% 8.01/5.77 = ( ^ [N3: nat,M4: num] :
% 8.01/5.77 ( if_option_num
% 8.01/5.77 @ ( ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M4 ) )
% 8.01/5.77 = zero_zero_nat )
% 8.01/5.77 @ none_num
% 8.01/5.77 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M4 ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % take_bit_num_def
% 8.01/5.77 thf(fact_9987_num__of__nat__numeral__eq,axiom,
% 8.01/5.77 ! [Q3: num] :
% 8.01/5.77 ( ( num_of_nat @ ( numeral_numeral_nat @ Q3 ) )
% 8.01/5.77 = Q3 ) ).
% 8.01/5.77
% 8.01/5.77 % num_of_nat_numeral_eq
% 8.01/5.77 thf(fact_9988_nat_Odisc__eq__case_I2_J,axiom,
% 8.01/5.77 ! [Nat: nat] :
% 8.01/5.77 ( ( Nat != zero_zero_nat )
% 8.01/5.77 = ( case_nat_o @ $false
% 8.01/5.77 @ ^ [Uu3: nat] : $true
% 8.01/5.77 @ Nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % nat.disc_eq_case(2)
% 8.01/5.77 thf(fact_9989_nat_Odisc__eq__case_I1_J,axiom,
% 8.01/5.77 ! [Nat: nat] :
% 8.01/5.77 ( ( Nat = zero_zero_nat )
% 8.01/5.77 = ( case_nat_o @ $true
% 8.01/5.77 @ ^ [Uu3: nat] : $false
% 8.01/5.77 @ Nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % nat.disc_eq_case(1)
% 8.01/5.77 thf(fact_9990_num__of__nat_Osimps_I1_J,axiom,
% 8.01/5.77 ( ( num_of_nat @ zero_zero_nat )
% 8.01/5.77 = one ) ).
% 8.01/5.77
% 8.01/5.77 % num_of_nat.simps(1)
% 8.01/5.77 thf(fact_9991_less__eq__nat_Osimps_I2_J,axiom,
% 8.01/5.77 ! [M: nat,N: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 8.01/5.77 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 8.01/5.77
% 8.01/5.77 % less_eq_nat.simps(2)
% 8.01/5.77 thf(fact_9992_max__Suc1,axiom,
% 8.01/5.77 ! [N: nat,M: nat] :
% 8.01/5.77 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 8.01/5.77 = ( case_nat_nat @ ( suc @ N )
% 8.01/5.77 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ N @ M5 ) )
% 8.01/5.77 @ M ) ) ).
% 8.01/5.77
% 8.01/5.77 % max_Suc1
% 8.01/5.77 thf(fact_9993_max__Suc2,axiom,
% 8.01/5.77 ! [M: nat,N: nat] :
% 8.01/5.77 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 8.01/5.77 = ( case_nat_nat @ ( suc @ N )
% 8.01/5.77 @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ M5 @ N ) )
% 8.01/5.77 @ M ) ) ).
% 8.01/5.77
% 8.01/5.77 % max_Suc2
% 8.01/5.77 thf(fact_9994_numeral__num__of__nat,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 8.01/5.77 = N ) ) ).
% 8.01/5.77
% 8.01/5.77 % numeral_num_of_nat
% 8.01/5.77 thf(fact_9995_num__of__nat__One,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 8.01/5.77 => ( ( num_of_nat @ N )
% 8.01/5.77 = one ) ) ).
% 8.01/5.77
% 8.01/5.77 % num_of_nat_One
% 8.01/5.77 thf(fact_9996_diff__Suc,axiom,
% 8.01/5.77 ! [M: nat,N: nat] :
% 8.01/5.77 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 8.01/5.77 = ( case_nat_nat @ zero_zero_nat
% 8.01/5.77 @ ^ [K3: nat] : K3
% 8.01/5.77 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % diff_Suc
% 8.01/5.77 thf(fact_9997_min__Suc1,axiom,
% 8.01/5.77 ! [N: nat,M: nat] :
% 8.01/5.77 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 8.01/5.77 = ( case_nat_nat @ zero_zero_nat
% 8.01/5.77 @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ N @ M5 ) )
% 8.01/5.77 @ M ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_Suc1
% 8.01/5.77 thf(fact_9998_min__Suc2,axiom,
% 8.01/5.77 ! [M: nat,N: nat] :
% 8.01/5.77 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 8.01/5.77 = ( case_nat_nat @ zero_zero_nat
% 8.01/5.77 @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ M5 @ N ) )
% 8.01/5.77 @ M ) ) ).
% 8.01/5.77
% 8.01/5.77 % min_Suc2
% 8.01/5.77 thf(fact_9999_num__of__nat__double,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 8.01/5.77 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % num_of_nat_double
% 8.01/5.77 thf(fact_10000_num__of__nat__plus__distrib,axiom,
% 8.01/5.77 ! [M: nat,N: nat] :
% 8.01/5.77 ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.01/5.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 8.01/5.77 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % num_of_nat_plus_distrib
% 8.01/5.77 thf(fact_10001_num__of__nat_Osimps_I2_J,axiom,
% 8.01/5.77 ! [N: nat] :
% 8.01/5.77 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( num_of_nat @ ( suc @ N ) )
% 8.01/5.77 = ( inc @ ( num_of_nat @ N ) ) ) )
% 8.01/5.77 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.77 => ( ( num_of_nat @ ( suc @ N ) )
% 8.01/5.77 = one ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % num_of_nat.simps(2)
% 8.01/5.77 thf(fact_10002_set__bits__int__unfold_H,axiom,
% 8.01/5.77 ( bit_bi6516823479961619367ts_int
% 8.01/5.77 = ( ^ [F3: nat > $o] :
% 8.01/5.77 ( if_int
% 8.01/5.77 @ ? [N3: nat] :
% 8.01/5.77 ! [N11: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N3 @ N11 )
% 8.01/5.77 => ~ ( F3 @ N11 ) )
% 8.01/5.77 @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 8.01/5.77 @ ( map_nat_o @ F3
% 8.01/5.77 @ ( upt @ zero_zero_nat
% 8.01/5.77 @ ( ord_Least_nat
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ! [N11: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N3 @ N11 )
% 8.01/5.77 => ~ ( F3 @ N11 ) ) ) ) ) )
% 8.01/5.77 @ ( if_int
% 8.01/5.77 @ ? [N3: nat] :
% 8.01/5.77 ! [N11: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N3 @ N11 )
% 8.01/5.77 => ( F3 @ N11 ) )
% 8.01/5.77 @ ( bit_ri631733984087533419it_int
% 8.01/5.77 @ ( ord_Least_nat
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ! [N11: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N3 @ N11 )
% 8.01/5.77 => ( F3 @ N11 ) ) )
% 8.01/5.77 @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 8.01/5.77 @ ( append_o
% 8.01/5.77 @ ( map_nat_o @ F3
% 8.01/5.77 @ ( upt @ zero_zero_nat
% 8.01/5.77 @ ( ord_Least_nat
% 8.01/5.77 @ ^ [N3: nat] :
% 8.01/5.77 ! [N11: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ N3 @ N11 )
% 8.01/5.77 => ( F3 @ N11 ) ) ) ) )
% 8.01/5.77 @ ( cons_o @ $true @ nil_o ) ) ) )
% 8.01/5.77 @ zero_zero_int ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % set_bits_int_unfold'
% 8.01/5.77 thf(fact_10003_star__false__left,axiom,
% 8.01/5.77 ! [P: assn] :
% 8.01/5.77 ( ( times_times_assn @ bot_bot_assn @ P )
% 8.01/5.77 = bot_bot_assn ) ).
% 8.01/5.77
% 8.01/5.77 % star_false_left
% 8.01/5.77 thf(fact_10004_star__false__right,axiom,
% 8.01/5.77 ! [P: assn] :
% 8.01/5.77 ( ( times_times_assn @ P @ bot_bot_assn )
% 8.01/5.77 = bot_bot_assn ) ).
% 8.01/5.77
% 8.01/5.77 % star_false_right
% 8.01/5.77 thf(fact_10005_pure__false,axiom,
% 8.01/5.77 ( ( pure_assn @ $false )
% 8.01/5.77 = bot_bot_assn ) ).
% 8.01/5.77
% 8.01/5.77 % pure_false
% 8.01/5.77 thf(fact_10006_pure__assn__eq__false__iff,axiom,
% 8.01/5.77 ! [P: $o] :
% 8.01/5.77 ( ( ( pure_assn @ P )
% 8.01/5.77 = bot_bot_assn )
% 8.01/5.77 = ~ P ) ).
% 8.01/5.77
% 8.01/5.77 % pure_assn_eq_false_iff
% 8.01/5.77 thf(fact_10007_assn__basic__inequalities_I3_J,axiom,
% 8.01/5.77 bot_bot_assn != one_one_assn ).
% 8.01/5.77
% 8.01/5.77 % assn_basic_inequalities(3)
% 8.01/5.77 thf(fact_10008_assn__basic__inequalities_I5_J,axiom,
% 8.01/5.77 top_top_assn != bot_bot_assn ).
% 8.01/5.77
% 8.01/5.77 % assn_basic_inequalities(5)
% 8.01/5.77 thf(fact_10009_ent__false__iff,axiom,
% 8.01/5.77 ! [P: assn] :
% 8.01/5.77 ( ( entails @ P @ bot_bot_assn )
% 8.01/5.77 = ( ! [H: produc3658429121746597890et_nat] :
% 8.01/5.77 ~ ( rep_assn @ P @ H ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % ent_false_iff
% 8.01/5.77 thf(fact_10010_bot__nat__def,axiom,
% 8.01/5.77 bot_bot_nat = zero_zero_nat ).
% 8.01/5.77
% 8.01/5.77 % bot_nat_def
% 8.01/5.77 thf(fact_10011_bot__enat__def,axiom,
% 8.01/5.77 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 8.01/5.77
% 8.01/5.77 % bot_enat_def
% 8.01/5.77 thf(fact_10012_ent__false,axiom,
% 8.01/5.77 ! [P: assn] : ( entails @ bot_bot_assn @ P ) ).
% 8.01/5.77
% 8.01/5.77 % ent_false
% 8.01/5.77 thf(fact_10013_mod__false,axiom,
% 8.01/5.77 ! [H2: produc3658429121746597890et_nat] :
% 8.01/5.77 ~ ( rep_assn @ bot_bot_assn @ H2 ) ).
% 8.01/5.77
% 8.01/5.77 % mod_false
% 8.01/5.77 thf(fact_10014_vebt__assn__raw_Osimps_I4_J,axiom,
% 8.01/5.77 ! [Vd: $o,Ve: $o,V: option4927543243414619207at_nat,Va2: nat,Vb: array_VEBT_VEBTi,Vc2: vEBT_VEBTi] :
% 8.01/5.77 ( ( vEBT_vebt_assn_raw @ ( vEBT_Leaf @ Vd @ Ve ) @ ( vEBT_Nodei @ V @ Va2 @ Vb @ Vc2 ) )
% 8.01/5.77 = bot_bot_assn ) ).
% 8.01/5.77
% 8.01/5.77 % vebt_assn_raw.simps(4)
% 8.01/5.77 thf(fact_10015_vebt__assn__raw_Oelims,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Xa3: vEBT_VEBTi,Y: assn] :
% 8.01/5.77 ( ( ( vEBT_vebt_assn_raw @ X @ Xa3 )
% 8.01/5.77 = Y )
% 8.01/5.77 => ( ! [A5: $o,B2: $o] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 8.01/5.77 => ! [Ai: $o,Bi: $o] :
% 8.01/5.77 ( ( Xa3
% 8.01/5.77 = ( vEBT_Leafi @ Ai @ Bi ) )
% 8.01/5.77 => ( Y
% 8.01/5.77 != ( pure_assn
% 8.01/5.77 @ ( ( Ai = A5 )
% 8.01/5.77 & ( Bi = B2 ) ) ) ) ) )
% 8.01/5.77 => ( ! [Mmo2: option4927543243414619207at_nat,Deg2: nat,Tree_list2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) )
% 8.01/5.77 => ! [Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 8.01/5.77 ( ( Xa3
% 8.01/5.77 = ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) )
% 8.01/5.77 => ( Y
% 8.01/5.77 != ( times_times_assn
% 8.01/5.77 @ ( times_times_assn
% 8.01/5.77 @ ( pure_assn
% 8.01/5.77 @ ( ( Mmoi2 = Mmo2 )
% 8.01/5.77 & ( Degi2 = Deg2 ) ) )
% 8.01/5.77 @ ( vEBT_vebt_assn_raw @ Summary2 @ Summaryi2 ) )
% 8.01/5.77 @ ( ex_ass463751140784270563_VEBTi
% 8.01/5.77 @ ^ [Tree_is2: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Tree_array2 @ Tree_is2 ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Tree_list2 @ Tree_is2 ) ) ) ) ) ) )
% 8.01/5.77 => ( ( ? [V3: option4927543243414619207at_nat,Va: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT] :
% 8.01/5.77 ( X
% 8.01/5.77 = ( vEBT_Node @ V3 @ Va @ Vb3 @ Vc3 ) )
% 8.01/5.77 => ( ? [Vd3: $o,Ve3: $o] :
% 8.01/5.77 ( Xa3
% 8.01/5.77 = ( vEBT_Leafi @ Vd3 @ Ve3 ) )
% 8.01/5.77 => ( Y != bot_bot_assn ) ) )
% 8.01/5.77 => ~ ( ? [Vd3: $o,Ve3: $o] :
% 8.01/5.77 ( X
% 8.01/5.77 = ( vEBT_Leaf @ Vd3 @ Ve3 ) )
% 8.01/5.77 => ( ? [V3: option4927543243414619207at_nat,Va: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 8.01/5.77 ( Xa3
% 8.01/5.77 = ( vEBT_Nodei @ V3 @ Va @ Vb3 @ Vc3 ) )
% 8.01/5.77 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % vebt_assn_raw.elims
% 8.01/5.77 thf(fact_10016_less__eq__char__simp,axiom,
% 8.01/5.77 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o,C0: $o,C1: $o,C22: $o,C32: $o,C42: $o,C52: $o,C6: $o,C7: $o] :
% 8.01/5.77 ( ( ord_less_eq_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) @ ( char2 @ C0 @ C1 @ C22 @ C32 @ C42 @ C52 @ C6 @ C7 ) )
% 8.01/5.77 = ( ord_less_eq_nat
% 8.01/5.77 @ ( foldr_o_nat
% 8.01/5.77 @ ^ [B4: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.01/5.77 @ ( cons_o @ B0 @ ( cons_o @ B1 @ ( cons_o @ B22 @ ( cons_o @ B32 @ ( cons_o @ B42 @ ( cons_o @ B52 @ ( cons_o @ B62 @ ( cons_o @ B72 @ nil_o ) ) ) ) ) ) ) )
% 8.01/5.77 @ zero_zero_nat )
% 8.01/5.77 @ ( foldr_o_nat
% 8.01/5.77 @ ^ [B4: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.01/5.77 @ ( cons_o @ C0 @ ( cons_o @ C1 @ ( cons_o @ C22 @ ( cons_o @ C32 @ ( cons_o @ C42 @ ( cons_o @ C52 @ ( cons_o @ C6 @ ( cons_o @ C7 @ nil_o ) ) ) ) ) ) ) )
% 8.01/5.77 @ zero_zero_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % less_eq_char_simp
% 8.01/5.77 thf(fact_10017_VEBTi_Oinject_I2_J,axiom,
% 8.01/5.77 ! [X21: $o,X222: $o,Y21: $o,Y222: $o] :
% 8.01/5.77 ( ( ( vEBT_Leafi @ X21 @ X222 )
% 8.01/5.77 = ( vEBT_Leafi @ Y21 @ Y222 ) )
% 8.01/5.77 = ( ( X21 = Y21 )
% 8.01/5.77 & ( X222 = Y222 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBTi.inject(2)
% 8.01/5.77 thf(fact_10018_upt__0__eq__Nil__conv,axiom,
% 8.01/5.77 ! [J: nat] :
% 8.01/5.77 ( ( ( upt @ zero_zero_nat @ J )
% 8.01/5.77 = nil_nat )
% 8.01/5.77 = ( J = zero_zero_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_0_eq_Nil_conv
% 8.01/5.77 thf(fact_10019_upt__conv__Nil,axiom,
% 8.01/5.77 ! [J: nat,I: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ J @ I )
% 8.01/5.77 => ( ( upt @ I @ J )
% 8.01/5.77 = nil_nat ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_conv_Nil
% 8.01/5.77 thf(fact_10020_upt__eq__Nil__conv,axiom,
% 8.01/5.77 ! [I: nat,J: nat] :
% 8.01/5.77 ( ( ( upt @ I @ J )
% 8.01/5.77 = nil_nat )
% 8.01/5.77 = ( ( J = zero_zero_nat )
% 8.01/5.77 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_eq_Nil_conv
% 8.01/5.77 thf(fact_10021_upt__rec__numeral,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.01/5.77 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.01/5.77 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 8.01/5.77 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.01/5.77 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 8.01/5.77 = nil_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_rec_numeral
% 8.01/5.77 thf(fact_10022_less__char__simp,axiom,
% 8.01/5.77 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o,C0: $o,C1: $o,C22: $o,C32: $o,C42: $o,C52: $o,C6: $o,C7: $o] :
% 8.01/5.77 ( ( ord_less_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) @ ( char2 @ C0 @ C1 @ C22 @ C32 @ C42 @ C52 @ C6 @ C7 ) )
% 8.01/5.77 = ( ord_less_nat
% 8.01/5.77 @ ( foldr_o_nat
% 8.01/5.77 @ ^ [B4: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.01/5.77 @ ( cons_o @ B0 @ ( cons_o @ B1 @ ( cons_o @ B22 @ ( cons_o @ B32 @ ( cons_o @ B42 @ ( cons_o @ B52 @ ( cons_o @ B62 @ ( cons_o @ B72 @ nil_o ) ) ) ) ) ) ) )
% 8.01/5.77 @ zero_zero_nat )
% 8.01/5.77 @ ( foldr_o_nat
% 8.01/5.77 @ ^ [B4: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.01/5.77 @ ( cons_o @ C0 @ ( cons_o @ C1 @ ( cons_o @ C22 @ ( cons_o @ C32 @ ( cons_o @ C42 @ ( cons_o @ C52 @ ( cons_o @ C6 @ ( cons_o @ C7 @ nil_o ) ) ) ) ) ) ) )
% 8.01/5.77 @ zero_zero_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % less_char_simp
% 8.01/5.77 thf(fact_10023_upt__0,axiom,
% 8.01/5.77 ! [I: nat] :
% 8.01/5.77 ( ( upt @ I @ zero_zero_nat )
% 8.01/5.77 = nil_nat ) ).
% 8.01/5.77
% 8.01/5.77 % upt_0
% 8.01/5.77 thf(fact_10024_list__encode_Ocases,axiom,
% 8.01/5.77 ! [X: list_nat] :
% 8.01/5.77 ( ( X != nil_nat )
% 8.01/5.77 => ~ ! [X3: nat,Xs3: list_nat] :
% 8.01/5.77 ( X
% 8.01/5.77 != ( cons_nat @ X3 @ Xs3 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % list_encode.cases
% 8.01/5.77 thf(fact_10025_vebt__assn__raw_Osimps_I3_J,axiom,
% 8.01/5.77 ! [V: option4927543243414619207at_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc2: vEBT_VEBT,Vd: $o,Ve: $o] :
% 8.01/5.77 ( ( vEBT_vebt_assn_raw @ ( vEBT_Node @ V @ Va2 @ Vb @ Vc2 ) @ ( vEBT_Leafi @ Vd @ Ve ) )
% 8.01/5.77 = bot_bot_assn ) ).
% 8.01/5.77
% 8.01/5.77 % vebt_assn_raw.simps(3)
% 8.01/5.77 thf(fact_10026_upt__Suc,axiom,
% 8.01/5.77 ! [I: nat,J: nat] :
% 8.01/5.77 ( ( ( ord_less_eq_nat @ I @ J )
% 8.01/5.77 => ( ( upt @ I @ ( suc @ J ) )
% 8.01/5.77 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 8.01/5.77 & ( ~ ( ord_less_eq_nat @ I @ J )
% 8.01/5.77 => ( ( upt @ I @ ( suc @ J ) )
% 8.01/5.77 = nil_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_Suc
% 8.01/5.77 thf(fact_10027_upt__Suc__append,axiom,
% 8.01/5.77 ! [I: nat,J: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ I @ J )
% 8.01/5.77 => ( ( upt @ I @ ( suc @ J ) )
% 8.01/5.77 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_Suc_append
% 8.01/5.77 thf(fact_10028_upt__append,axiom,
% 8.01/5.77 ! [I: nat,J: nat] :
% 8.01/5.77 ( ( ord_less_nat @ I @ J )
% 8.01/5.77 => ( ( append_nat @ ( upt @ zero_zero_nat @ I ) @ ( upt @ I @ J ) )
% 8.01/5.77 = ( upt @ zero_zero_nat @ J ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_append
% 8.01/5.77 thf(fact_10029_upt__add__eq__append,axiom,
% 8.01/5.77 ! [I: nat,J: nat,K: nat] :
% 8.01/5.77 ( ( ord_less_eq_nat @ I @ J )
% 8.01/5.77 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 8.01/5.77 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_add_eq_append
% 8.01/5.77 thf(fact_10030_VEBTi_Odistinct_I1_J,axiom,
% 8.01/5.77 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi,X21: $o,X222: $o] :
% 8.01/5.77 ( ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 )
% 8.01/5.77 != ( vEBT_Leafi @ X21 @ X222 ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBTi.distinct(1)
% 8.01/5.77 thf(fact_10031_VEBTi_Oexhaust,axiom,
% 8.01/5.77 ! [Y: vEBT_VEBTi] :
% 8.01/5.77 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: array_VEBT_VEBTi,X142: vEBT_VEBTi] :
% 8.01/5.77 ( Y
% 8.01/5.77 != ( vEBT_Nodei @ X112 @ X122 @ X132 @ X142 ) )
% 8.01/5.77 => ~ ! [X212: $o,X223: $o] :
% 8.01/5.77 ( Y
% 8.01/5.77 != ( vEBT_Leafi @ X212 @ X223 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBTi.exhaust
% 8.01/5.77 thf(fact_10032_VEBT__internal_Ovebt__buildupi_H_Osimps_I1_J,axiom,
% 8.01/5.77 ( ( vEBT_V739175172307565963ildupi @ zero_zero_nat )
% 8.01/5.77 = ( heap_T3630416162098727440_VEBTi @ ( vEBT_Leafi @ $false @ $false ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.vebt_buildupi'.simps(1)
% 8.01/5.77 thf(fact_10033_VEBTi_Osize_I4_J,axiom,
% 8.01/5.77 ! [X21: $o,X222: $o] :
% 8.01/5.77 ( ( size_size_VEBT_VEBTi @ ( vEBT_Leafi @ X21 @ X222 ) )
% 8.01/5.77 = zero_zero_nat ) ).
% 8.01/5.77
% 8.01/5.77 % VEBTi.size(4)
% 8.01/5.77 thf(fact_10034_VEBTi_Osize__gen_I2_J,axiom,
% 8.01/5.77 ! [X21: $o,X222: $o] :
% 8.01/5.77 ( ( vEBT_size_VEBTi @ ( vEBT_Leafi @ X21 @ X222 ) )
% 8.01/5.77 = zero_zero_nat ) ).
% 8.01/5.77
% 8.01/5.77 % VEBTi.size_gen(2)
% 8.01/5.77 thf(fact_10035_VEBT__internal_Ovebt__buildupi_H_Osimps_I2_J,axiom,
% 8.01/5.77 ( ( vEBT_V739175172307565963ildupi @ ( suc @ zero_zero_nat ) )
% 8.01/5.77 = ( heap_T3630416162098727440_VEBTi @ ( vEBT_Leafi @ $false @ $false ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % VEBT_internal.vebt_buildupi'.simps(2)
% 8.01/5.77 thf(fact_10036_vebt__assn__raw_Ocases,axiom,
% 8.01/5.77 ! [X: produc3625547720036274456_VEBTi] :
% 8.01/5.77 ( ! [A5: $o,B2: $o,Ai: $o,Bi: $o] :
% 8.01/5.77 ( X
% 8.01/5.77 != ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ A5 @ B2 ) @ ( vEBT_Leafi @ Ai @ Bi ) ) )
% 8.01/5.77 => ( ! [Mmo2: option4927543243414619207at_nat,Deg2: nat,Tree_list2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 8.01/5.77 ( X
% 8.01/5.77 != ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) @ ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) ) )
% 8.01/5.77 => ( ! [V3: option4927543243414619207at_nat,Va: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT,Vd3: $o,Ve3: $o] :
% 8.01/5.77 ( X
% 8.01/5.77 != ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ V3 @ Va @ Vb3 @ Vc3 ) @ ( vEBT_Leafi @ Vd3 @ Ve3 ) ) )
% 8.01/5.77 => ~ ! [Vd3: $o,Ve3: $o,V3: option4927543243414619207at_nat,Va: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 8.01/5.77 ( X
% 8.01/5.77 != ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ Vd3 @ Ve3 ) @ ( vEBT_Nodei @ V3 @ Va @ Vb3 @ Vc3 ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % vebt_assn_raw.cases
% 8.01/5.77 thf(fact_10037_vebt__assn__raw_Osimps_I1_J,axiom,
% 8.01/5.77 ! [A: $o,B: $o,Ai2: $o,Bi2: $o] :
% 8.01/5.77 ( ( vEBT_vebt_assn_raw @ ( vEBT_Leaf @ A @ B ) @ ( vEBT_Leafi @ Ai2 @ Bi2 ) )
% 8.01/5.77 = ( pure_assn
% 8.01/5.77 @ ( ( Ai2 = A )
% 8.01/5.77 & ( Bi2 = B ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % vebt_assn_raw.simps(1)
% 8.01/5.77 thf(fact_10038_upt__rec,axiom,
% 8.01/5.77 ( upt
% 8.01/5.77 = ( ^ [I2: nat,J2: nat] : ( if_list_nat @ ( ord_less_nat @ I2 @ J2 ) @ ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J2 ) ) @ nil_nat ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_rec
% 8.01/5.77 thf(fact_10039_upt__eq__lel__conv,axiom,
% 8.01/5.77 ! [L: nat,H2: nat,Is1: list_nat,I: nat,Is2: list_nat] :
% 8.01/5.77 ( ( ( upt @ L @ H2 )
% 8.01/5.77 = ( append_nat @ Is1 @ ( cons_nat @ I @ Is2 ) ) )
% 8.01/5.77 = ( ( Is1
% 8.01/5.77 = ( upt @ L @ I ) )
% 8.01/5.77 & ( Is2
% 8.01/5.77 = ( upt @ ( suc @ I ) @ H2 ) )
% 8.01/5.77 & ( ord_less_eq_nat @ L @ I )
% 8.01/5.77 & ( ord_less_nat @ I @ H2 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upt_eq_lel_conv
% 8.01/5.77 thf(fact_10040_integer__of__char__code,axiom,
% 8.01/5.77 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 8.01/5.77 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 8.01/5.77 = ( 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 ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % integer_of_char_code
% 8.01/5.77 thf(fact_10041_less__char__def,axiom,
% 8.01/5.77 ( ord_less_char
% 8.01/5.77 = ( ^ [C12: char,C23: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C12 ) @ ( comm_s629917340098488124ar_nat @ C23 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % less_char_def
% 8.01/5.77 thf(fact_10042_nat__of__char__less__256,axiom,
% 8.01/5.77 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % nat_of_char_less_256
% 8.01/5.77 thf(fact_10043_range__nat__of__char,axiom,
% 8.01/5.77 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 8.01/5.77 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % range_nat_of_char
% 8.01/5.77 thf(fact_10044_char_Osize_I2_J,axiom,
% 8.01/5.77 ! [X15: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 8.01/5.77 ( ( size_size_char @ ( char2 @ X15 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 8.01/5.77 = zero_zero_nat ) ).
% 8.01/5.77
% 8.01/5.77 % char.size(2)
% 8.01/5.77 thf(fact_10045_char_Osize__gen,axiom,
% 8.01/5.77 ! [X15: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 8.01/5.77 ( ( size_char @ ( char2 @ X15 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 8.01/5.77 = zero_zero_nat ) ).
% 8.01/5.77
% 8.01/5.77 % char.size_gen
% 8.01/5.77 thf(fact_10046_inj__on__char__of__nat,axiom,
% 8.01/5.77 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % inj_on_char_of_nat
% 8.01/5.77 thf(fact_10047_UNIV__char__of__nat,axiom,
% 8.01/5.77 ( top_top_set_char
% 8.01/5.77 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % UNIV_char_of_nat
% 8.01/5.77 thf(fact_10048_vebt__assn__raw_Opelims,axiom,
% 8.01/5.77 ! [X: vEBT_VEBT,Xa3: vEBT_VEBTi,Y: assn] :
% 8.01/5.77 ( ( ( vEBT_vebt_assn_raw @ X @ Xa3 )
% 8.01/5.77 = Y )
% 8.01/5.77 => ( ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ X @ Xa3 ) )
% 8.01/5.77 => ( ! [A5: $o,B2: $o] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Leaf @ A5 @ B2 ) )
% 8.01/5.77 => ! [Ai: $o,Bi: $o] :
% 8.01/5.77 ( ( Xa3
% 8.01/5.77 = ( vEBT_Leafi @ Ai @ Bi ) )
% 8.01/5.77 => ( ( Y
% 8.01/5.77 = ( pure_assn
% 8.01/5.77 @ ( ( Ai = A5 )
% 8.01/5.77 & ( Bi = B2 ) ) ) )
% 8.01/5.77 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ A5 @ B2 ) @ ( vEBT_Leafi @ Ai @ Bi ) ) ) ) ) )
% 8.01/5.77 => ( ! [Mmo2: option4927543243414619207at_nat,Deg2: nat,Tree_list2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) )
% 8.01/5.77 => ! [Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 8.01/5.77 ( ( Xa3
% 8.01/5.77 = ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) )
% 8.01/5.77 => ( ( Y
% 8.01/5.77 = ( times_times_assn
% 8.01/5.77 @ ( times_times_assn
% 8.01/5.77 @ ( pure_assn
% 8.01/5.77 @ ( ( Mmoi2 = Mmo2 )
% 8.01/5.77 & ( Degi2 = Deg2 ) ) )
% 8.01/5.77 @ ( vEBT_vebt_assn_raw @ Summary2 @ Summaryi2 ) )
% 8.01/5.77 @ ( ex_ass463751140784270563_VEBTi
% 8.01/5.77 @ ^ [Tree_is2: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Tree_array2 @ Tree_is2 ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Tree_list2 @ Tree_is2 ) ) ) ) )
% 8.01/5.77 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) @ ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) ) ) ) ) )
% 8.01/5.77 => ( ! [V3: option4927543243414619207at_nat,Va: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Node @ V3 @ Va @ Vb3 @ Vc3 ) )
% 8.01/5.77 => ! [Vd3: $o,Ve3: $o] :
% 8.01/5.77 ( ( Xa3
% 8.01/5.77 = ( vEBT_Leafi @ Vd3 @ Ve3 ) )
% 8.01/5.77 => ( ( Y = bot_bot_assn )
% 8.01/5.77 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ V3 @ Va @ Vb3 @ Vc3 ) @ ( vEBT_Leafi @ Vd3 @ Ve3 ) ) ) ) ) )
% 8.01/5.77 => ~ ! [Vd3: $o,Ve3: $o] :
% 8.01/5.77 ( ( X
% 8.01/5.77 = ( vEBT_Leaf @ Vd3 @ Ve3 ) )
% 8.01/5.77 => ! [V3: option4927543243414619207at_nat,Va: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 8.01/5.77 ( ( Xa3
% 8.01/5.77 = ( vEBT_Nodei @ V3 @ Va @ Vb3 @ Vc3 ) )
% 8.01/5.77 => ( ( Y = bot_bot_assn )
% 8.01/5.77 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ Vd3 @ Ve3 ) @ ( vEBT_Nodei @ V3 @ Va @ Vb3 @ Vc3 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % vebt_assn_raw.pelims
% 8.01/5.77 thf(fact_10049_String_Ochar__of__ascii__of,axiom,
% 8.01/5.77 ! [C: char] :
% 8.01/5.77 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 8.01/5.77 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % String.char_of_ascii_of
% 8.01/5.77 thf(fact_10050_upto_Opelims,axiom,
% 8.01/5.77 ! [X: int,Xa3: int,Y: list_int] :
% 8.01/5.77 ( ( ( upto @ X @ Xa3 )
% 8.01/5.77 = Y )
% 8.01/5.77 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa3 ) )
% 8.01/5.77 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa3 )
% 8.01/5.77 => ( Y
% 8.01/5.77 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa3 ) ) ) )
% 8.01/5.77 & ( ~ ( ord_less_eq_int @ X @ Xa3 )
% 8.01/5.77 => ( Y = nil_int ) ) )
% 8.01/5.77 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa3 ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto.pelims
% 8.01/5.77 thf(fact_10051_upto__Nil,axiom,
% 8.01/5.77 ! [I: int,J: int] :
% 8.01/5.77 ( ( ( upto @ I @ J )
% 8.01/5.77 = nil_int )
% 8.01/5.77 = ( ord_less_int @ J @ I ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_Nil
% 8.01/5.77 thf(fact_10052_upto__Nil2,axiom,
% 8.01/5.77 ! [I: int,J: int] :
% 8.01/5.77 ( ( nil_int
% 8.01/5.77 = ( upto @ I @ J ) )
% 8.01/5.77 = ( ord_less_int @ J @ I ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_Nil2
% 8.01/5.77 thf(fact_10053_upto__empty,axiom,
% 8.01/5.77 ! [J: int,I: int] :
% 8.01/5.77 ( ( ord_less_int @ J @ I )
% 8.01/5.77 => ( ( upto @ I @ J )
% 8.01/5.77 = nil_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_empty
% 8.01/5.77 thf(fact_10054_upto__single,axiom,
% 8.01/5.77 ! [I: int] :
% 8.01/5.77 ( ( upto @ I @ I )
% 8.01/5.77 = ( cons_int @ I @ nil_int ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_single
% 8.01/5.77 thf(fact_10055_nth__upto,axiom,
% 8.01/5.77 ! [I: int,K: nat,J: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 8.01/5.77 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 8.01/5.77 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % nth_upto
% 8.01/5.77 thf(fact_10056_length__upto,axiom,
% 8.01/5.77 ! [I: int,J: int] :
% 8.01/5.77 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 8.01/5.77 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % length_upto
% 8.01/5.77 thf(fact_10057_upto__rec__numeral_I1_J,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 8.01/5.77 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 = nil_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_rec_numeral(1)
% 8.01/5.77 thf(fact_10058_upto__rec__numeral_I2_J,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 8.01/5.77 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 = nil_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_rec_numeral(2)
% 8.01/5.77 thf(fact_10059_upto__rec__numeral_I3_J,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 8.01/5.77 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 8.01/5.77 = nil_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_rec_numeral(3)
% 8.01/5.77 thf(fact_10060_upto__rec__numeral_I4_J,axiom,
% 8.01/5.77 ! [M: num,N: num] :
% 8.01/5.77 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 8.01/5.77 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.01/5.77 = nil_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_rec_numeral(4)
% 8.01/5.77 thf(fact_10061_upto__aux__def,axiom,
% 8.01/5.77 ( upto_aux
% 8.01/5.77 = ( ^ [I2: int,J2: int] : ( append_int @ ( upto @ I2 @ J2 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_aux_def
% 8.01/5.77 thf(fact_10062_upto__code,axiom,
% 8.01/5.77 ( upto
% 8.01/5.77 = ( ^ [I2: int,J2: int] : ( upto_aux @ I2 @ J2 @ nil_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_code
% 8.01/5.77 thf(fact_10063_atLeastAtMost__upto,axiom,
% 8.01/5.77 ( set_or1266510415728281911st_int
% 8.01/5.77 = ( ^ [I2: int,J2: int] : ( set_int2 @ ( upto @ I2 @ J2 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastAtMost_upto
% 8.01/5.77 thf(fact_10064_upto__split2,axiom,
% 8.01/5.77 ! [I: int,J: int,K: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ I @ J )
% 8.01/5.77 => ( ( ord_less_eq_int @ J @ K )
% 8.01/5.77 => ( ( upto @ I @ K )
% 8.01/5.77 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_split2
% 8.01/5.77 thf(fact_10065_upto__split1,axiom,
% 8.01/5.77 ! [I: int,J: int,K: int] :
% 8.01/5.77 ( ( ord_less_eq_int @ I @ J )
% 8.01/5.77 => ( ( ord_less_eq_int @ J @ K )
% 8.01/5.77 => ( ( upto @ I @ K )
% 8.01/5.77 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto_split1
% 8.01/5.77 thf(fact_10066_atLeastLessThan__upto,axiom,
% 8.01/5.77 ( set_or4662586982721622107an_int
% 8.01/5.77 = ( ^ [I2: int,J2: int] : ( set_int2 @ ( upto @ I2 @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % atLeastLessThan_upto
% 8.01/5.77 thf(fact_10067_greaterThanAtMost__upto,axiom,
% 8.01/5.77 ( set_or6656581121297822940st_int
% 8.01/5.77 = ( ^ [I2: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % greaterThanAtMost_upto
% 8.01/5.77 thf(fact_10068_upto_Osimps,axiom,
% 8.01/5.77 ( upto
% 8.01/5.77 = ( ^ [I2: int,J2: int] : ( if_list_int @ ( ord_less_eq_int @ I2 @ J2 ) @ ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) ) @ nil_int ) ) ) ).
% 8.01/5.77
% 8.01/5.77 % upto.simps
% 8.01/5.77 thf(fact_10069_upto_Oelims,axiom,
% 8.01/5.77 ! [X: int,Xa3: int,Y: list_int] :
% 8.01/5.78 ( ( ( upto @ X @ Xa3 )
% 8.01/5.78 = Y )
% 8.01/5.78 => ( ( ( ord_less_eq_int @ X @ Xa3 )
% 8.01/5.78 => ( Y
% 8.01/5.78 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa3 ) ) ) )
% 8.01/5.78 & ( ~ ( ord_less_eq_int @ X @ Xa3 )
% 8.01/5.78 => ( Y = nil_int ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % upto.elims
% 8.01/5.78 thf(fact_10070_upto__rec1,axiom,
% 8.01/5.78 ! [I: int,J: int] :
% 8.01/5.78 ( ( ord_less_eq_int @ I @ J )
% 8.01/5.78 => ( ( upto @ I @ J )
% 8.01/5.78 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % upto_rec1
% 8.01/5.78 thf(fact_10071_upto__rec2,axiom,
% 8.01/5.78 ! [I: int,J: int] :
% 8.01/5.78 ( ( ord_less_eq_int @ I @ J )
% 8.01/5.78 => ( ( upto @ I @ J )
% 8.01/5.78 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % upto_rec2
% 8.01/5.78 thf(fact_10072_greaterThanLessThan__upto,axiom,
% 8.01/5.78 ( set_or5832277885323065728an_int
% 8.01/5.78 = ( ^ [I2: int,J2: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ ( minus_minus_int @ J2 @ one_one_int ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % greaterThanLessThan_upto
% 8.01/5.78 thf(fact_10073_upto__split3,axiom,
% 8.01/5.78 ! [I: int,J: int,K: int] :
% 8.01/5.78 ( ( ord_less_eq_int @ I @ J )
% 8.01/5.78 => ( ( ord_less_eq_int @ J @ K )
% 8.01/5.78 => ( ( upto @ I @ K )
% 8.01/5.78 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % upto_split3
% 8.01/5.78 thf(fact_10074_upto_Opsimps,axiom,
% 8.01/5.78 ! [I: int,J: int] :
% 8.01/5.78 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 8.01/5.78 => ( ( ( ord_less_eq_int @ I @ J )
% 8.01/5.78 => ( ( upto @ I @ J )
% 8.01/5.78 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 8.01/5.78 & ( ~ ( ord_less_eq_int @ I @ J )
% 8.01/5.78 => ( ( upto @ I @ J )
% 8.01/5.78 = nil_int ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % upto.psimps
% 8.01/5.78 thf(fact_10075_sorted__list__of__set__atMost__Suc,axiom,
% 8.01/5.78 ! [K: nat] :
% 8.01/5.78 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 8.01/5.78 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % sorted_list_of_set_atMost_Suc
% 8.01/5.78 thf(fact_10076_sorted__list__of__set__range,axiom,
% 8.01/5.78 ! [M: nat,N: nat] :
% 8.01/5.78 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 8.01/5.78 = ( upt @ M @ N ) ) ).
% 8.01/5.78
% 8.01/5.78 % sorted_list_of_set_range
% 8.01/5.78 thf(fact_10077_sorted__list__of__set__lessThan__Suc,axiom,
% 8.01/5.78 ! [K: nat] :
% 8.01/5.78 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 8.01/5.78 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % sorted_list_of_set_lessThan_Suc
% 8.01/5.78 thf(fact_10078_sorted__list__of__set__greaterThanAtMost,axiom,
% 8.01/5.78 ! [I: nat,J: nat] :
% 8.01/5.78 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 8.01/5.78 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 8.01/5.78 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % sorted_list_of_set_greaterThanAtMost
% 8.01/5.78 thf(fact_10079_sorted__list__of__set__greaterThanLessThan,axiom,
% 8.01/5.78 ! [I: nat,J: nat] :
% 8.01/5.78 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 8.01/5.78 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 8.01/5.78 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % sorted_list_of_set_greaterThanLessThan
% 8.01/5.78 thf(fact_10080_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 8.01/5.78 ! [N: nat,J: nat,I: nat] :
% 8.01/5.78 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 8.01/5.78 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 8.01/5.78 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % nth_sorted_list_of_set_greaterThanAtMost
% 8.01/5.78 thf(fact_10081_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 8.01/5.78 ! [N: nat,J: nat,I: nat] :
% 8.01/5.78 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 8.01/5.78 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 8.01/5.78 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % nth_sorted_list_of_set_greaterThanLessThan
% 8.01/5.78 thf(fact_10082_upt__filter__extend,axiom,
% 8.01/5.78 ! [U: nat,U3: nat,P: nat > $o] :
% 8.01/5.78 ( ( ord_less_eq_nat @ U @ U3 )
% 8.01/5.78 => ( ! [I3: nat] :
% 8.01/5.78 ( ( ( ord_less_eq_nat @ U @ I3 )
% 8.01/5.78 & ( ord_less_nat @ I3 @ U3 ) )
% 8.01/5.78 => ~ ( P @ I3 ) )
% 8.01/5.78 => ( ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U ) )
% 8.01/5.78 = ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U3 ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % upt_filter_extend
% 8.01/5.78 thf(fact_10083_sort__upt,axiom,
% 8.01/5.78 ! [M: nat,N: nat] :
% 8.01/5.78 ( ( linord738340561235409698at_nat
% 8.01/5.78 @ ^ [X2: nat] : X2
% 8.01/5.78 @ ( upt @ M @ N ) )
% 8.01/5.78 = ( upt @ M @ N ) ) ).
% 8.01/5.78
% 8.01/5.78 % sort_upt
% 8.01/5.78 thf(fact_10084_sort__upto,axiom,
% 8.01/5.78 ! [I: int,J: int] :
% 8.01/5.78 ( ( linord1735203802627413978nt_int
% 8.01/5.78 @ ^ [X2: int] : X2
% 8.01/5.78 @ ( upto @ I @ J ) )
% 8.01/5.78 = ( upto @ I @ J ) ) ).
% 8.01/5.78
% 8.01/5.78 % sort_upto
% 8.01/5.78 thf(fact_10085_tl__upt,axiom,
% 8.01/5.78 ! [M: nat,N: nat] :
% 8.01/5.78 ( ( tl_nat @ ( upt @ M @ N ) )
% 8.01/5.78 = ( upt @ ( suc @ M ) @ N ) ) ).
% 8.01/5.78
% 8.01/5.78 % tl_upt
% 8.01/5.78 thf(fact_10086_hd__upt,axiom,
% 8.01/5.78 ! [I: nat,J: nat] :
% 8.01/5.78 ( ( ord_less_nat @ I @ J )
% 8.01/5.78 => ( ( hd_nat @ ( upt @ I @ J ) )
% 8.01/5.78 = I ) ) ).
% 8.01/5.78
% 8.01/5.78 % hd_upt
% 8.01/5.78 thf(fact_10087_csqrt_Osimps_I1_J,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( re @ ( csqrt @ Z ) )
% 8.01/5.78 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % csqrt.simps(1)
% 8.01/5.78 thf(fact_10088_complex__Re__numeral,axiom,
% 8.01/5.78 ! [V: num] :
% 8.01/5.78 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 8.01/5.78 = ( numeral_numeral_real @ V ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_Re_numeral
% 8.01/5.78 thf(fact_10089_Re__divide__of__nat,axiom,
% 8.01/5.78 ! [Z: complex,N: nat] :
% 8.01/5.78 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 8.01/5.78 = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_divide_of_nat
% 8.01/5.78 thf(fact_10090_Re__divide__of__real,axiom,
% 8.01/5.78 ! [Z: complex,R2: real] :
% 8.01/5.78 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 8.01/5.78 = ( divide_divide_real @ ( re @ Z ) @ R2 ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_divide_of_real
% 8.01/5.78 thf(fact_10091_Re__sgn,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( re @ ( sgn_sgn_complex @ Z ) )
% 8.01/5.78 = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_sgn
% 8.01/5.78 thf(fact_10092_Re__divide__numeral,axiom,
% 8.01/5.78 ! [Z: complex,W: num] :
% 8.01/5.78 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 8.01/5.78 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_divide_numeral
% 8.01/5.78 thf(fact_10093_cos__Arg__i__mult__zero,axiom,
% 8.01/5.78 ! [Y: complex] :
% 8.01/5.78 ( ( Y != zero_zero_complex )
% 8.01/5.78 => ( ( ( re @ Y )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 => ( ( cos_real @ ( arg @ Y ) )
% 8.01/5.78 = zero_zero_real ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % cos_Arg_i_mult_zero
% 8.01/5.78 thf(fact_10094_scaleR__complex_Osimps_I1_J,axiom,
% 8.01/5.78 ! [R2: real,X: complex] :
% 8.01/5.78 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 8.01/5.78 = ( times_times_real @ R2 @ ( re @ X ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % scaleR_complex.simps(1)
% 8.01/5.78 thf(fact_10095_one__complex_Osimps_I1_J,axiom,
% 8.01/5.78 ( ( re @ one_one_complex )
% 8.01/5.78 = one_one_real ) ).
% 8.01/5.78
% 8.01/5.78 % one_complex.simps(1)
% 8.01/5.78 thf(fact_10096_imaginary__unit_Osimps_I1_J,axiom,
% 8.01/5.78 ( ( re @ imaginary_unit )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % imaginary_unit.simps(1)
% 8.01/5.78 thf(fact_10097_zero__complex_Osimps_I1_J,axiom,
% 8.01/5.78 ( ( re @ zero_zero_complex )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % zero_complex.simps(1)
% 8.01/5.78 thf(fact_10098_Re__csqrt,axiom,
% 8.01/5.78 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_csqrt
% 8.01/5.78 thf(fact_10099_cmod__plus__Re__le__0__iff,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 8.01/5.78 = ( ( re @ Z )
% 8.01/5.78 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % cmod_plus_Re_le_0_iff
% 8.01/5.78 thf(fact_10100_cos__n__Re__cis__pow__n,axiom,
% 8.01/5.78 ! [N: nat,A: real] :
% 8.01/5.78 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 8.01/5.78 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % cos_n_Re_cis_pow_n
% 8.01/5.78 thf(fact_10101_csqrt_Ocode,axiom,
% 8.01/5.78 ( csqrt
% 8.01/5.78 = ( ^ [Z6: complex] :
% 8.01/5.78 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.01/5.78 @ ( times_times_real
% 8.01/5.78 @ ( if_real
% 8.01/5.78 @ ( ( im @ Z6 )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 @ one_one_real
% 8.01/5.78 @ ( sgn_sgn_real @ ( im @ Z6 ) ) )
% 8.01/5.78 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % csqrt.code
% 8.01/5.78 thf(fact_10102_csqrt_Osimps_I2_J,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( im @ ( csqrt @ Z ) )
% 8.01/5.78 = ( times_times_real
% 8.01/5.78 @ ( if_real
% 8.01/5.78 @ ( ( im @ Z )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 @ one_one_real
% 8.01/5.78 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 8.01/5.78 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % csqrt.simps(2)
% 8.01/5.78 thf(fact_10103_complex__Im__fact,axiom,
% 8.01/5.78 ! [N: nat] :
% 8.01/5.78 ( ( im @ ( semiri5044797733671781792omplex @ N ) )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % complex_Im_fact
% 8.01/5.78 thf(fact_10104_complex__Im__of__int,axiom,
% 8.01/5.78 ! [Z: int] :
% 8.01/5.78 ( ( im @ ( ring_17405671764205052669omplex @ Z ) )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % complex_Im_of_int
% 8.01/5.78 thf(fact_10105_Im__complex__of__real,axiom,
% 8.01/5.78 ! [Z: real] :
% 8.01/5.78 ( ( im @ ( real_V4546457046886955230omplex @ Z ) )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % Im_complex_of_real
% 8.01/5.78 thf(fact_10106_Im__power__real,axiom,
% 8.01/5.78 ! [X: complex,N: nat] :
% 8.01/5.78 ( ( ( im @ X )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 => ( ( im @ ( power_power_complex @ X @ N ) )
% 8.01/5.78 = zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_power_real
% 8.01/5.78 thf(fact_10107_complex__Im__numeral,axiom,
% 8.01/5.78 ! [V: num] :
% 8.01/5.78 ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % complex_Im_numeral
% 8.01/5.78 thf(fact_10108_complex__Im__of__nat,axiom,
% 8.01/5.78 ! [N: nat] :
% 8.01/5.78 ( ( im @ ( semiri8010041392384452111omplex @ N ) )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % complex_Im_of_nat
% 8.01/5.78 thf(fact_10109_Im__divide__of__real,axiom,
% 8.01/5.78 ! [Z: complex,R2: real] :
% 8.01/5.78 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 8.01/5.78 = ( divide_divide_real @ ( im @ Z ) @ R2 ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_divide_of_real
% 8.01/5.78 thf(fact_10110_Im__sgn,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( im @ ( sgn_sgn_complex @ Z ) )
% 8.01/5.78 = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_sgn
% 8.01/5.78 thf(fact_10111_Re__power__real,axiom,
% 8.01/5.78 ! [X: complex,N: nat] :
% 8.01/5.78 ( ( ( im @ X )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 => ( ( re @ ( power_power_complex @ X @ N ) )
% 8.01/5.78 = ( power_power_real @ ( re @ X ) @ N ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_power_real
% 8.01/5.78 thf(fact_10112_Im__divide__numeral,axiom,
% 8.01/5.78 ! [Z: complex,W: num] :
% 8.01/5.78 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 8.01/5.78 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_divide_numeral
% 8.01/5.78 thf(fact_10113_Im__divide__of__nat,axiom,
% 8.01/5.78 ! [Z: complex,N: nat] :
% 8.01/5.78 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 8.01/5.78 = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_divide_of_nat
% 8.01/5.78 thf(fact_10114_csqrt__of__real__nonneg,axiom,
% 8.01/5.78 ! [X: complex] :
% 8.01/5.78 ( ( ( im @ X )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 8.01/5.78 => ( ( csqrt @ X )
% 8.01/5.78 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % csqrt_of_real_nonneg
% 8.01/5.78 thf(fact_10115_csqrt__minus,axiom,
% 8.01/5.78 ! [X: complex] :
% 8.01/5.78 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 8.01/5.78 | ( ( ( im @ X )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 8.01/5.78 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 8.01/5.78 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % csqrt_minus
% 8.01/5.78 thf(fact_10116_csqrt__of__real__nonpos,axiom,
% 8.01/5.78 ! [X: complex] :
% 8.01/5.78 ( ( ( im @ X )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 8.01/5.78 => ( ( csqrt @ X )
% 8.01/5.78 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % csqrt_of_real_nonpos
% 8.01/5.78 thf(fact_10117_complex__is__Int__iff,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( member_complex @ Z @ ring_1_Ints_complex )
% 8.01/5.78 = ( ( ( im @ Z )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 & ? [I2: int] :
% 8.01/5.78 ( ( re @ Z )
% 8.01/5.78 = ( ring_1_of_int_real @ I2 ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_is_Int_iff
% 8.01/5.78 thf(fact_10118_imaginary__unit_Osimps_I2_J,axiom,
% 8.01/5.78 ( ( im @ imaginary_unit )
% 8.01/5.78 = one_one_real ) ).
% 8.01/5.78
% 8.01/5.78 % imaginary_unit.simps(2)
% 8.01/5.78 thf(fact_10119_one__complex_Osimps_I2_J,axiom,
% 8.01/5.78 ( ( im @ one_one_complex )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % one_complex.simps(2)
% 8.01/5.78 thf(fact_10120_zero__complex_Osimps_I2_J,axiom,
% 8.01/5.78 ( ( im @ zero_zero_complex )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % zero_complex.simps(2)
% 8.01/5.78 thf(fact_10121_scaleR__complex_Osimps_I2_J,axiom,
% 8.01/5.78 ! [R2: real,X: complex] :
% 8.01/5.78 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 8.01/5.78 = ( times_times_real @ R2 @ ( im @ X ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % scaleR_complex.simps(2)
% 8.01/5.78 thf(fact_10122_times__complex_Osimps_I2_J,axiom,
% 8.01/5.78 ! [X: complex,Y: complex] :
% 8.01/5.78 ( ( im @ ( times_times_complex @ X @ Y ) )
% 8.01/5.78 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % times_complex.simps(2)
% 8.01/5.78 thf(fact_10123_cmod__eq__Re,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( ( im @ Z )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 => ( ( real_V1022390504157884413omplex @ Z )
% 8.01/5.78 = ( abs_abs_real @ ( re @ Z ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % cmod_eq_Re
% 8.01/5.78 thf(fact_10124_cmod__eq__Im,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( ( re @ Z )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 => ( ( real_V1022390504157884413omplex @ Z )
% 8.01/5.78 = ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % cmod_eq_Im
% 8.01/5.78 thf(fact_10125_Im__eq__0,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( ( abs_abs_real @ ( re @ Z ) )
% 8.01/5.78 = ( real_V1022390504157884413omplex @ Z ) )
% 8.01/5.78 => ( ( im @ Z )
% 8.01/5.78 = zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_eq_0
% 8.01/5.78 thf(fact_10126_times__complex_Osimps_I1_J,axiom,
% 8.01/5.78 ! [X: complex,Y: complex] :
% 8.01/5.78 ( ( re @ ( times_times_complex @ X @ Y ) )
% 8.01/5.78 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % times_complex.simps(1)
% 8.01/5.78 thf(fact_10127_scaleR__complex_Ocode,axiom,
% 8.01/5.78 ( real_V2046097035970521341omplex
% 8.01/5.78 = ( ^ [R5: real,X2: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X2 ) ) @ ( times_times_real @ R5 @ ( im @ X2 ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % scaleR_complex.code
% 8.01/5.78 thf(fact_10128_csqrt__principal,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 8.01/5.78 | ( ( ( re @ ( csqrt @ Z ) )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % csqrt_principal
% 8.01/5.78 thf(fact_10129_sin__n__Im__cis__pow__n,axiom,
% 8.01/5.78 ! [N: nat,A: real] :
% 8.01/5.78 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 8.01/5.78 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % sin_n_Im_cis_pow_n
% 8.01/5.78 thf(fact_10130_Re__exp,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( re @ ( exp_complex @ Z ) )
% 8.01/5.78 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_exp
% 8.01/5.78 thf(fact_10131_Im__exp,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( im @ ( exp_complex @ Z ) )
% 8.01/5.78 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_exp
% 8.01/5.78 thf(fact_10132_times__complex_Ocode,axiom,
% 8.01/5.78 ( times_times_complex
% 8.01/5.78 = ( ^ [X2: complex,Y6: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y6 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y6 ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % times_complex.code
% 8.01/5.78 thf(fact_10133_cmod__power2,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.01/5.78 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % cmod_power2
% 8.01/5.78 thf(fact_10134_Im__power2,axiom,
% 8.01/5.78 ! [X: complex] :
% 8.01/5.78 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.01/5.78 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_power2
% 8.01/5.78 thf(fact_10135_Re__power2,axiom,
% 8.01/5.78 ! [X: complex] :
% 8.01/5.78 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.01/5.78 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_power2
% 8.01/5.78 thf(fact_10136_complex__eq__0,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( Z = zero_zero_complex )
% 8.01/5.78 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.01/5.78 = zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_eq_0
% 8.01/5.78 thf(fact_10137_norm__complex__def,axiom,
% 8.01/5.78 ( real_V1022390504157884413omplex
% 8.01/5.78 = ( ^ [Z6: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % norm_complex_def
% 8.01/5.78 thf(fact_10138_inverse__complex_Osimps_I1_J,axiom,
% 8.01/5.78 ! [X: complex] :
% 8.01/5.78 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 8.01/5.78 = ( 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 ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % inverse_complex.simps(1)
% 8.01/5.78 thf(fact_10139_complex__neq__0,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( Z != zero_zero_complex )
% 8.01/5.78 = ( 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 ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_neq_0
% 8.01/5.78 thf(fact_10140_Re__divide,axiom,
% 8.01/5.78 ! [X: complex,Y: complex] :
% 8.01/5.78 ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 8.01/5.78 = ( 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 ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_divide
% 8.01/5.78 thf(fact_10141_csqrt__square,axiom,
% 8.01/5.78 ! [B: complex] :
% 8.01/5.78 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 8.01/5.78 | ( ( ( re @ B )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 8.01/5.78 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.01/5.78 = B ) ) ).
% 8.01/5.78
% 8.01/5.78 % csqrt_square
% 8.01/5.78 thf(fact_10142_csqrt__unique,axiom,
% 8.01/5.78 ! [W: complex,Z: complex] :
% 8.01/5.78 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.01/5.78 = Z )
% 8.01/5.78 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 8.01/5.78 | ( ( ( re @ W )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 8.01/5.78 => ( ( csqrt @ Z )
% 8.01/5.78 = W ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % csqrt_unique
% 8.01/5.78 thf(fact_10143_inverse__complex_Osimps_I2_J,axiom,
% 8.01/5.78 ! [X: complex] :
% 8.01/5.78 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 8.01/5.78 = ( 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 ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % inverse_complex.simps(2)
% 8.01/5.78 thf(fact_10144_Im__divide,axiom,
% 8.01/5.78 ! [X: complex,Y: complex] :
% 8.01/5.78 ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 8.01/5.78 = ( 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 ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_divide
% 8.01/5.78 thf(fact_10145_complex__abs__le__norm,axiom,
% 8.01/5.78 ! [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 ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_abs_le_norm
% 8.01/5.78 thf(fact_10146_complex__unit__circle,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( Z != zero_zero_complex )
% 8.01/5.78 => ( ( 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 ) ) ) )
% 8.01/5.78 = one_one_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_unit_circle
% 8.01/5.78 thf(fact_10147_inverse__complex_Ocode,axiom,
% 8.01/5.78 ( invers8013647133539491842omplex
% 8.01/5.78 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % inverse_complex.code
% 8.01/5.78 thf(fact_10148_Complex__divide,axiom,
% 8.01/5.78 ( divide1717551699836669952omplex
% 8.01/5.78 = ( ^ [X2: complex,Y6: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Complex_divide
% 8.01/5.78 thf(fact_10149_Im__Reals__divide,axiom,
% 8.01/5.78 ! [R2: complex,Z: complex] :
% 8.01/5.78 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 8.01/5.78 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 8.01/5.78 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_Reals_divide
% 8.01/5.78 thf(fact_10150_Re__Reals__divide,axiom,
% 8.01/5.78 ! [R2: complex,Z: complex] :
% 8.01/5.78 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 8.01/5.78 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 8.01/5.78 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_Reals_divide
% 8.01/5.78 thf(fact_10151_Re__divide__Reals,axiom,
% 8.01/5.78 ! [R2: complex,Z: complex] :
% 8.01/5.78 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 8.01/5.78 => ( ( re @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 8.01/5.78 = ( divide_divide_real @ ( re @ Z ) @ ( re @ R2 ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_divide_Reals
% 8.01/5.78 thf(fact_10152_real__eq__imaginary__iff,axiom,
% 8.01/5.78 ! [Y: complex,X: complex] :
% 8.01/5.78 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 8.01/5.78 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 8.01/5.78 => ( ( X
% 8.01/5.78 = ( times_times_complex @ imaginary_unit @ Y ) )
% 8.01/5.78 = ( ( X = zero_zero_complex )
% 8.01/5.78 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % real_eq_imaginary_iff
% 8.01/5.78 thf(fact_10153_imaginary__eq__real__iff,axiom,
% 8.01/5.78 ! [Y: complex,X: complex] :
% 8.01/5.78 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 8.01/5.78 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 8.01/5.78 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 8.01/5.78 = X )
% 8.01/5.78 = ( ( X = zero_zero_complex )
% 8.01/5.78 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % imaginary_eq_real_iff
% 8.01/5.78 thf(fact_10154_Im__divide__Reals,axiom,
% 8.01/5.78 ! [R2: complex,Z: complex] :
% 8.01/5.78 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 8.01/5.78 => ( ( im @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 8.01/5.78 = ( divide_divide_real @ ( im @ Z ) @ ( re @ R2 ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_divide_Reals
% 8.01/5.78 thf(fact_10155_complex__is__Real__iff,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( member_complex @ Z @ real_V2521375963428798218omplex )
% 8.01/5.78 = ( ( im @ Z )
% 8.01/5.78 = zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_is_Real_iff
% 8.01/5.78 thf(fact_10156_Complex__in__Reals,axiom,
% 8.01/5.78 ! [X: real] : ( member_complex @ ( complex2 @ X @ zero_zero_real ) @ real_V2521375963428798218omplex ) ).
% 8.01/5.78
% 8.01/5.78 % Complex_in_Reals
% 8.01/5.78 thf(fact_10157_complex__mult__cnj,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 8.01/5.78 = ( 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 ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_mult_cnj
% 8.01/5.78 thf(fact_10158_card__UNIV__unit,axiom,
% 8.01/5.78 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 8.01/5.78 = one_one_nat ) ).
% 8.01/5.78
% 8.01/5.78 % card_UNIV_unit
% 8.01/5.78 thf(fact_10159_card__Collect__less__nat,axiom,
% 8.01/5.78 ! [N: nat] :
% 8.01/5.78 ( ( finite_card_nat
% 8.01/5.78 @ ( collect_nat
% 8.01/5.78 @ ^ [I2: nat] : ( ord_less_nat @ I2 @ N ) ) )
% 8.01/5.78 = N ) ).
% 8.01/5.78
% 8.01/5.78 % card_Collect_less_nat
% 8.01/5.78 thf(fact_10160_card__atMost,axiom,
% 8.01/5.78 ! [U: nat] :
% 8.01/5.78 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 8.01/5.78 = ( suc @ U ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_atMost
% 8.01/5.78 thf(fact_10161_complex__cnj__zero,axiom,
% 8.01/5.78 ( ( cnj @ zero_zero_complex )
% 8.01/5.78 = zero_zero_complex ) ).
% 8.01/5.78
% 8.01/5.78 % complex_cnj_zero
% 8.01/5.78 thf(fact_10162_complex__cnj__zero__iff,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( ( cnj @ Z )
% 8.01/5.78 = zero_zero_complex )
% 8.01/5.78 = ( Z = zero_zero_complex ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_cnj_zero_iff
% 8.01/5.78 thf(fact_10163_complex__cnj__one__iff,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( ( cnj @ Z )
% 8.01/5.78 = one_one_complex )
% 8.01/5.78 = ( Z = one_one_complex ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_cnj_one_iff
% 8.01/5.78 thf(fact_10164_complex__cnj__one,axiom,
% 8.01/5.78 ( ( cnj @ one_one_complex )
% 8.01/5.78 = one_one_complex ) ).
% 8.01/5.78
% 8.01/5.78 % complex_cnj_one
% 8.01/5.78 thf(fact_10165_card__Collect__le__nat,axiom,
% 8.01/5.78 ! [N: nat] :
% 8.01/5.78 ( ( finite_card_nat
% 8.01/5.78 @ ( collect_nat
% 8.01/5.78 @ ^ [I2: nat] : ( ord_less_eq_nat @ I2 @ N ) ) )
% 8.01/5.78 = ( suc @ N ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_Collect_le_nat
% 8.01/5.78 thf(fact_10166_card__UNIV__bool,axiom,
% 8.01/5.78 ( ( finite_card_o @ top_top_set_o )
% 8.01/5.78 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_UNIV_bool
% 8.01/5.78 thf(fact_10167_card__atLeastAtMost,axiom,
% 8.01/5.78 ! [L: nat,U: nat] :
% 8.01/5.78 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 8.01/5.78 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_atLeastAtMost
% 8.01/5.78 thf(fact_10168_card__greaterThanLessThan,axiom,
% 8.01/5.78 ! [L: nat,U: nat] :
% 8.01/5.78 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 8.01/5.78 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_greaterThanLessThan
% 8.01/5.78 thf(fact_10169_complex__In__mult__cnj__zero,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 8.01/5.78 = zero_zero_real ) ).
% 8.01/5.78
% 8.01/5.78 % complex_In_mult_cnj_zero
% 8.01/5.78 thf(fact_10170_card__atLeastAtMost__int,axiom,
% 8.01/5.78 ! [L: int,U: int] :
% 8.01/5.78 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 8.01/5.78 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_atLeastAtMost_int
% 8.01/5.78 thf(fact_10171_card__greaterThanLessThan__int,axiom,
% 8.01/5.78 ! [L: int,U: int] :
% 8.01/5.78 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 8.01/5.78 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_greaterThanLessThan_int
% 8.01/5.78 thf(fact_10172_subset__card__intvl__is__intvl,axiom,
% 8.01/5.78 ! [A2: set_nat,K: nat] :
% 8.01/5.78 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 8.01/5.78 => ( A2
% 8.01/5.78 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % subset_card_intvl_is_intvl
% 8.01/5.78 thf(fact_10173_card__less__Suc2,axiom,
% 8.01/5.78 ! [M7: set_nat,I: nat] :
% 8.01/5.78 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 8.01/5.78 => ( ( finite_card_nat
% 8.01/5.78 @ ( collect_nat
% 8.01/5.78 @ ^ [K3: nat] :
% 8.01/5.78 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 8.01/5.78 & ( ord_less_nat @ K3 @ I ) ) ) )
% 8.01/5.78 = ( finite_card_nat
% 8.01/5.78 @ ( collect_nat
% 8.01/5.78 @ ^ [K3: nat] :
% 8.01/5.78 ( ( member_nat @ K3 @ M7 )
% 8.01/5.78 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_less_Suc2
% 8.01/5.78 thf(fact_10174_card__less__Suc,axiom,
% 8.01/5.78 ! [M7: set_nat,I: nat] :
% 8.01/5.78 ( ( member_nat @ zero_zero_nat @ M7 )
% 8.01/5.78 => ( ( suc
% 8.01/5.78 @ ( finite_card_nat
% 8.01/5.78 @ ( collect_nat
% 8.01/5.78 @ ^ [K3: nat] :
% 8.01/5.78 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 8.01/5.78 & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 8.01/5.78 = ( finite_card_nat
% 8.01/5.78 @ ( collect_nat
% 8.01/5.78 @ ^ [K3: nat] :
% 8.01/5.78 ( ( member_nat @ K3 @ M7 )
% 8.01/5.78 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_less_Suc
% 8.01/5.78 thf(fact_10175_card__less,axiom,
% 8.01/5.78 ! [M7: set_nat,I: nat] :
% 8.01/5.78 ( ( member_nat @ zero_zero_nat @ M7 )
% 8.01/5.78 => ( ( finite_card_nat
% 8.01/5.78 @ ( collect_nat
% 8.01/5.78 @ ^ [K3: nat] :
% 8.01/5.78 ( ( member_nat @ K3 @ M7 )
% 8.01/5.78 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 8.01/5.78 != zero_zero_nat ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_less
% 8.01/5.78 thf(fact_10176_card__atLeastZeroLessThan__int,axiom,
% 8.01/5.78 ! [U: int] :
% 8.01/5.78 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 8.01/5.78 = ( nat2 @ U ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_atLeastZeroLessThan_int
% 8.01/5.78 thf(fact_10177_Re__complex__div__eq__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 8.01/5.78 = zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_complex_div_eq_0
% 8.01/5.78 thf(fact_10178_Im__complex__div__eq__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.01/5.78 = zero_zero_real )
% 8.01/5.78 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 8.01/5.78 = zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_complex_div_eq_0
% 8.01/5.78 thf(fact_10179_subset__eq__atLeast0__lessThan__card,axiom,
% 8.01/5.78 ! [N4: set_nat,N: nat] :
% 8.01/5.78 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.01/5.78 => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 8.01/5.78
% 8.01/5.78 % subset_eq_atLeast0_lessThan_card
% 8.01/5.78 thf(fact_10180_card__le__Suc__Max,axiom,
% 8.01/5.78 ! [S3: set_nat] :
% 8.01/5.78 ( ( finite_finite_nat @ S3 )
% 8.01/5.78 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_le_Suc_Max
% 8.01/5.78 thf(fact_10181_card__UNIV__char,axiom,
% 8.01/5.78 ( ( finite_card_char @ top_top_set_char )
% 8.01/5.78 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_UNIV_char
% 8.01/5.78 thf(fact_10182_card__sum__le__nat__sum,axiom,
% 8.01/5.78 ! [S3: set_nat] :
% 8.01/5.78 ( ord_less_eq_nat
% 8.01/5.78 @ ( groups3542108847815614940at_nat
% 8.01/5.78 @ ^ [X2: nat] : X2
% 8.01/5.78 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 8.01/5.78 @ ( groups3542108847815614940at_nat
% 8.01/5.78 @ ^ [X2: nat] : X2
% 8.01/5.78 @ S3 ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_sum_le_nat_sum
% 8.01/5.78 thf(fact_10183_card__nth__roots,axiom,
% 8.01/5.78 ! [C: complex,N: nat] :
% 8.01/5.78 ( ( C != zero_zero_complex )
% 8.01/5.78 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.78 => ( ( finite_card_complex
% 8.01/5.78 @ ( collect_complex
% 8.01/5.78 @ ^ [Z6: complex] :
% 8.01/5.78 ( ( power_power_complex @ Z6 @ N )
% 8.01/5.78 = C ) ) )
% 8.01/5.78 = N ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_nth_roots
% 8.01/5.78 thf(fact_10184_card__roots__unity__eq,axiom,
% 8.01/5.78 ! [N: nat] :
% 8.01/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.01/5.78 => ( ( finite_card_complex
% 8.01/5.78 @ ( collect_complex
% 8.01/5.78 @ ^ [Z6: complex] :
% 8.01/5.78 ( ( power_power_complex @ Z6 @ N )
% 8.01/5.78 = one_one_complex ) ) )
% 8.01/5.78 = N ) ) ).
% 8.01/5.78
% 8.01/5.78 % card_roots_unity_eq
% 8.01/5.78 thf(fact_10185_Re__complex__div__lt__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.01/5.78 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_complex_div_lt_0
% 8.01/5.78 thf(fact_10186_Re__complex__div__gt__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.01/5.78 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_complex_div_gt_0
% 8.01/5.78 thf(fact_10187_Re__complex__div__le__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.01/5.78 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_complex_div_le_0
% 8.01/5.78 thf(fact_10188_Re__complex__div__ge__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.01/5.78 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Re_complex_div_ge_0
% 8.01/5.78 thf(fact_10189_Im__complex__div__lt__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.01/5.78 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_complex_div_lt_0
% 8.01/5.78 thf(fact_10190_Im__complex__div__gt__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.01/5.78 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_complex_div_gt_0
% 8.01/5.78 thf(fact_10191_Im__complex__div__le__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.01/5.78 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_complex_div_le_0
% 8.01/5.78 thf(fact_10192_Im__complex__div__ge__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.01/5.78 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % Im_complex_div_ge_0
% 8.01/5.78 thf(fact_10193_complex__mod__mult__cnj,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 8.01/5.78 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_mod_mult_cnj
% 8.01/5.78 thf(fact_10194_complex__div__gt__0,axiom,
% 8.01/5.78 ! [A: complex,B: complex] :
% 8.01/5.78 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.01/5.78 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 8.01/5.78 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.01/5.78 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_div_gt_0
% 8.01/5.78 thf(fact_10195_complex__norm__square,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.01/5.78 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_norm_square
% 8.01/5.78 thf(fact_10196_complex__add__cnj,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 8.01/5.78 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_add_cnj
% 8.01/5.78 thf(fact_10197_complex__diff__cnj,axiom,
% 8.01/5.78 ! [Z: complex] :
% 8.01/5.78 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 8.01/5.78 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_diff_cnj
% 8.01/5.78 thf(fact_10198_complex__div__cnj,axiom,
% 8.01/5.78 ( divide1717551699836669952omplex
% 8.01/5.78 = ( ^ [A3: complex,B4: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B4 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % complex_div_cnj
% 8.01/5.78 thf(fact_10199_cnj__add__mult__eq__Re,axiom,
% 8.01/5.78 ! [Z: complex,W: complex] :
% 8.01/5.78 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 8.01/5.78 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 8.01/5.78
% 8.01/5.78 % cnj_add_mult_eq_Re
% 8.01/5.78 thf(fact_10200_card__num0,axiom,
% 8.01/5.78 ( ( finite6454714172617411596l_num0 @ top_to3689904424835650196l_num0 )
% 8.01/5.78 = zero_zero_nat ) ).
% 8.01/5.78
% 8.01/5.78 % card_num0
% 8.01/5.78 thf(fact_10201_card__num1,axiom,
% 8.01/5.78 ( ( finite6454714172617411597l_num1 @ top_to3689904429138878997l_num1 )
% 8.01/5.78 = one_one_nat ) ).
% 8.01/5.78
% 8.01/5.78 % card_num1
% 8.01/5.78 thf(fact_10202_card__nat,axiom,
% 8.01/5.78 ( ( finite_card_nat @ top_top_set_nat )
% 8.01/5.78 = zero_zero_nat ) ).
% 8.01/5.78
% 8.01/5.78 % card_nat
% 8.01/5.78 thf(fact_10203_card__literal,axiom,
% 8.01/5.78 ( ( finite_card_literal @ top_top_set_literal )
% 8.01/5.78 = zero_zero_nat ) ).
% 8.01/5.78
% 8.01/5.78 % card_literal
% 8.01/5.78 thf(fact_10204_distinct__upt,axiom,
% 8.01/5.78 ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 8.01/5.78
% 8.01/5.78 % distinct_upt
% 8.01/5.78 thf(fact_10205_distinct__upto,axiom,
% 8.01/5.78 ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 8.01/5.78
% 8.01/5.78 % distinct_upto
% 8.01/5.78
% 8.01/5.78 % Helper facts (46)
% 8.01/5.78 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 8.01/5.78 ! [X: int,Y: int] :
% 8.01/5.78 ( ( if_int @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 8.01/5.78 ! [X: int,Y: int] :
% 8.01/5.78 ( ( if_int @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 8.01/5.78 ! [X: nat,Y: nat] :
% 8.01/5.78 ( ( if_nat @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 8.01/5.78 ! [X: nat,Y: nat] :
% 8.01/5.78 ( ( if_nat @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 8.01/5.78 ! [X: num,Y: num] :
% 8.01/5.78 ( ( if_num @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 8.01/5.78 ! [X: num,Y: num] :
% 8.01/5.78 ( ( if_num @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 8.01/5.78 ! [X: rat,Y: rat] :
% 8.01/5.78 ( ( if_rat @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 8.01/5.78 ! [X: rat,Y: rat] :
% 8.01/5.78 ( ( if_rat @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 8.01/5.78 ! [X: real,Y: real] :
% 8.01/5.78 ( ( if_real @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 8.01/5.78 ! [X: real,Y: real] :
% 8.01/5.78 ( ( if_real @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Uint32__Ouint32_T,axiom,
% 8.01/5.78 ! [X: uint32,Y: uint32] :
% 8.01/5.78 ( ( if_uint32 @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Uint32__Ouint32_T,axiom,
% 8.01/5.78 ! [X: uint32,Y: uint32] :
% 8.01/5.78 ( ( if_uint32 @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 8.01/5.78 ! [P: real > $o] :
% 8.01/5.78 ( ( P @ ( fChoice_real @ P ) )
% 8.01/5.78 = ( ? [X7: real] : ( P @ X7 ) ) ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 8.01/5.78 ! [X: assn,Y: assn] :
% 8.01/5.78 ( ( if_assn @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 8.01/5.78 ! [X: assn,Y: assn] :
% 8.01/5.78 ( ( if_assn @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 8.01/5.78 ! [X: complex,Y: complex] :
% 8.01/5.78 ( ( if_complex @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 8.01/5.78 ! [X: complex,Y: complex] :
% 8.01/5.78 ( ( if_complex @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 8.01/5.78 ! [X: extended_enat,Y: extended_enat] :
% 8.01/5.78 ( ( if_Extended_enat @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 8.01/5.78 ! [X: extended_enat,Y: extended_enat] :
% 8.01/5.78 ( ( if_Extended_enat @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 8.01/5.78 ! [X: code_integer,Y: code_integer] :
% 8.01/5.78 ( ( if_Code_integer @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 8.01/5.78 ! [X: code_integer,Y: code_integer] :
% 8.01/5.78 ( ( if_Code_integer @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 8.01/5.78 ! [X: set_int,Y: set_int] :
% 8.01/5.78 ( ( if_set_int @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 8.01/5.78 ! [X: set_int,Y: set_int] :
% 8.01/5.78 ( ( if_set_int @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 8.01/5.78 ! [X: set_nat,Y: set_nat] :
% 8.01/5.78 ( ( if_set_nat @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 8.01/5.78 ! [X: set_nat,Y: set_nat] :
% 8.01/5.78 ( ( if_set_nat @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 8.01/5.78 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 8.01/5.78 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 8.01/5.78 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 8.01/5.78 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 8.01/5.78 ! [X: list_int,Y: list_int] :
% 8.01/5.78 ( ( if_list_int @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 8.01/5.78 ! [X: list_int,Y: list_int] :
% 8.01/5.78 ( ( if_list_int @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 8.01/5.78 ! [X: list_nat,Y: list_nat] :
% 8.01/5.78 ( ( if_list_nat @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 8.01/5.78 ! [X: list_nat,Y: list_nat] :
% 8.01/5.78 ( ( if_list_nat @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.01/5.78 ! [X: int > int,Y: int > int] :
% 8.01/5.78 ( ( if_int_int @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.01/5.78 ! [X: int > int,Y: int > int] :
% 8.01/5.78 ( ( if_int_int @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 8.01/5.78 ! [X: option_nat,Y: option_nat] :
% 8.01/5.78 ( ( if_option_nat @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 8.01/5.78 ! [X: option_nat,Y: option_nat] :
% 8.01/5.78 ( ( if_option_nat @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 8.01/5.78 ! [X: option_num,Y: option_num] :
% 8.01/5.78 ( ( if_option_num @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 8.01/5.78 ! [X: option_num,Y: option_num] :
% 8.01/5.78 ( ( if_option_num @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.01/5.78 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 8.01/5.78 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.01/5.78 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 8.01/5.78 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.01/5.78 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.01/5.78 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.01/5.78 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.01/5.78 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 8.01/5.78 ! [X: nat > int > int,Y: nat > int > int] :
% 8.01/5.78 ( ( if_nat_int_int @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 8.01/5.78 ! [X: nat > int > int,Y: nat > int > int] :
% 8.01/5.78 ( ( if_nat_int_int @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.01/5.78 ! [P: $o] :
% 8.01/5.78 ( ( P = $true )
% 8.01/5.78 | ( P = $false ) ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.01/5.78 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 8.01/5.78 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 8.01/5.78 = Y ) ).
% 8.01/5.78
% 8.01/5.78 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.01/5.78 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 8.01/5.78 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 8.01/5.78 = X ) ).
% 8.01/5.78
% 8.01/5.78 % Conjectures (1)
% 8.01/5.78 thf(conj_0,conjecture,
% 8.01/5.78 ( entails
% 8.01/5.78 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ xa @ x ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( replicate_VEBT_VEBT @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ na @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ x ) ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ na ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ xb ) )
% 8.01/5.78 @ ( pure_assn
% 8.01/5.78 @ ( xc
% 8.01/5.78 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ na ) ) @ xa @ xb ) ) ) )
% 8.01/5.78 @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ ( suc @ ( suc @ na ) ) ) @ xc ) ) ).
% 8.01/5.78
% 8.01/5.78 %------------------------------------------------------------------------------
% 9.16/7.07 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.NFB1DyDFGn/cvc5---1.0.5_13006.p...
% 9.16/7.07 (declare-sort $$unsorted 0)
% 9.16/7.07 (declare-sort tptp.option2860828798490689354et_nat 0)
% 9.16/7.07 (declare-sort tptp.produc2732055786443039994et_nat 0)
% 9.16/7.07 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 9.16/7.07 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 9.16/7.07 (declare-sort tptp.option5190343406534369742et_nat 0)
% 9.16/7.07 (declare-sort tptp.produc3925858234332021118et_nat 0)
% 9.16/7.07 (declare-sort tptp.produc1193250871479095198on_num 0)
% 9.16/7.07 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 9.16/7.07 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 9.16/7.07 (declare-sort tptp.itself8794530163899892676l_num1 0)
% 9.16/7.07 (declare-sort tptp.produc7036089656553540234on_num 0)
% 9.16/7.07 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 9.16/7.07 (declare-sort tptp.produc3658429121746597890et_nat 0)
% 9.16/7.07 (declare-sort tptp.produc3447558737645232053on_num 0)
% 9.16/7.07 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 9.16/7.07 (declare-sort tptp.produc3625547720036274456_VEBTi 0)
% 9.16/7.07 (declare-sort tptp.produc8923325533196201883nteger 0)
% 9.16/7.07 (declare-sort tptp.option2661157926820139483um_num 0)
% 9.16/7.07 (declare-sort tptp.option4927543243414619207at_nat 0)
% 9.16/7.07 (declare-sort tptp.option4624381673175914239nt_int 0)
% 9.16/7.07 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 9.16/7.07 (declare-sort tptp.heap_T8145700208782473153_VEBTi 0)
% 9.16/7.07 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 9.16/7.07 (declare-sort tptp.set_li6976499617229504675nteger 0)
% 9.16/7.07 (declare-sort tptp.heap_e7401611519738050253t_unit 0)
% 9.16/7.07 (declare-sort tptp.product_prod_num_num 0)
% 9.16/7.07 (declare-sort tptp.product_prod_nat_nat 0)
% 9.16/7.07 (declare-sort tptp.product_prod_int_int 0)
% 9.16/7.07 (declare-sort tptp.set_list_complex 0)
% 9.16/7.07 (declare-sort tptp.array_VEBT_VEBTi 0)
% 9.16/7.07 (declare-sort tptp.list_VEBT_VEBTi 0)
% 9.16/7.07 (declare-sort tptp.set_VEBT_VEBTi 0)
% 9.16/7.07 (declare-sort tptp.set_list_real 0)
% 9.16/7.07 (declare-sort tptp.list_VEBT_VEBT 0)
% 9.16/7.07 (declare-sort tptp.heap_Time_Heap_nat 0)
% 9.16/7.07 (declare-sort tptp.set_list_nat 0)
% 9.16/7.07 (declare-sort tptp.set_list_int 0)
% 9.16/7.07 (declare-sort tptp.list_Code_integer 0)
% 9.16/7.07 (declare-sort tptp.set_VEBT_VEBT 0)
% 9.16/7.07 (declare-sort tptp.set_set_nat 0)
% 9.16/7.07 (declare-sort tptp.set_Code_integer 0)
% 9.16/7.07 (declare-sort tptp.set_Product_unit 0)
% 9.16/7.07 (declare-sort tptp.set_Numeral_num1 0)
% 9.16/7.07 (declare-sort tptp.set_Numeral_num0 0)
% 9.16/7.07 (declare-sort tptp.itself_Numeral_num1 0)
% 9.16/7.07 (declare-sort tptp.itself_Numeral_num0 0)
% 9.16/7.07 (declare-sort tptp.list_complex 0)
% 9.16/7.07 (declare-sort tptp.set_list_o 0)
% 9.16/7.07 (declare-sort tptp.set_complex 0)
% 9.16/7.07 (declare-sort tptp.option_real 0)
% 9.16/7.07 (declare-sort tptp.filter_real 0)
% 9.16/7.07 (declare-sort tptp.set_literal 0)
% 9.16/7.07 (declare-sort tptp.itself_finite_3 0)
% 9.16/7.07 (declare-sort tptp.itself_finite_2 0)
% 9.16/7.07 (declare-sort tptp.itself_finite_1 0)
% 9.16/7.07 (declare-sort tptp.option_rat 0)
% 9.16/7.07 (declare-sort tptp.option_num 0)
% 9.16/7.07 (declare-sort tptp.option_nat 0)
% 9.16/7.07 (declare-sort tptp.option_int 0)
% 9.16/7.07 (declare-sort tptp.filter_nat 0)
% 9.16/7.07 (declare-sort tptp.vEBT_VEBTi 0)
% 9.16/7.07 (declare-sort tptp.set_char 0)
% 9.16/7.07 (declare-sort tptp.list_real 0)
% 9.16/7.07 (declare-sort tptp.set_real 0)
% 9.16/7.07 (declare-sort tptp.list_nat 0)
% 9.16/7.07 (declare-sort tptp.list_int 0)
% 9.16/7.07 (declare-sort tptp.vEBT_VEBT 0)
% 9.16/7.07 (declare-sort tptp.set_rat 0)
% 9.16/7.07 (declare-sort tptp.set_num 0)
% 9.16/7.07 (declare-sort tptp.set_nat 0)
% 9.16/7.07 (declare-sort tptp.set_int 0)
% 9.16/7.07 (declare-sort tptp.code_integer 0)
% 9.16/7.07 (declare-sort tptp.extended_enat 0)
% 9.16/7.07 (declare-sort tptp.list_o 0)
% 9.16/7.07 (declare-sort tptp.complex 0)
% 9.16/7.07 (declare-sort tptp.assn 0)
% 9.16/7.07 (declare-sort tptp.set_o 0)
% 9.16/7.07 (declare-sort tptp.uint32 0)
% 9.16/7.07 (declare-sort tptp.char 0)
% 9.16/7.07 (declare-sort tptp.real 0)
% 9.16/7.07 (declare-sort tptp.rat 0)
% 9.16/7.07 (declare-sort tptp.num 0)
% 9.16/7.07 (declare-sort tptp.nat 0)
% 9.16/7.07 (declare-sort tptp.int 0)
% 9.16/7.07 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 9.16/7.07 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 9.16/7.07 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 9.16/7.07 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 9.16/7.07 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 9.16/7.07 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 9.16/7.07 (declare-fun tptp.rep_assn (tptp.assn tptp.produc3658429121746597890et_nat) Bool)
% 9.16/7.07 (declare-fun tptp.entails (tptp.assn tptp.assn) Bool)
% 9.16/7.07 (declare-fun tptp.ex_ass463751140784270563_VEBTi ((-> tptp.list_VEBT_VEBTi tptp.assn)) tptp.assn)
% 9.16/7.07 (declare-fun tptp.pure_assn (Bool) tptp.assn)
% 9.16/7.07 (declare-fun tptp.snga_assn_VEBT_VEBTi (tptp.array_VEBT_VEBTi tptp.list_VEBT_VEBTi) tptp.assn)
% 9.16/7.07 (declare-fun tptp.fI_QUERY (tptp.assn tptp.assn tptp.assn) Bool)
% 9.16/7.07 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_bi6516823479961619367ts_int ((-> tptp.nat Bool)) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_wf_set_bits_int ((-> tptp.nat Bool)) Bool)
% 9.16/7.07 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 9.16/7.07 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 9.16/7.07 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.bit_ri7632146776885996613nteger (tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se3928097537394005634nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se1080825931792720795nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se7788150548672797655nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 9.16/7.07 (declare-fun tptp.bit_Sh3965577149348748681tl_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bit_Sh2154871086232339855tr_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.bits_Bit_integer (tptp.code_integer Bool) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.bits_b8758750999018896077nteger (tptp.code_integer) Bool)
% 9.16/7.07 (declare-fun tptp.bits_b2549910563261871055nteger (tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.code_dup (tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 9.16/7.07 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 9.16/7.07 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 9.16/7.07 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 9.16/7.07 (declare-fun tptp.im (tptp.complex) tptp.real)
% 9.16/7.07 (declare-fun tptp.re (tptp.complex) tptp.real)
% 9.16/7.07 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.imaginary_unit () tptp.complex)
% 9.16/7.07 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 9.16/7.07 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 9.16/7.07 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 9.16/7.07 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 9.16/7.07 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 9.16/7.07 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 9.16/7.07 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 9.16/7.07 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 9.16/7.07 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 9.16/7.07 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 9.16/7.07 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 9.16/7.07 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 9.16/7.07 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 9.16/7.07 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 9.16/7.07 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 9.16/7.07 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 9.16/7.07 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 9.16/7.07 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 9.16/7.07 (declare-fun tptp.at_top_real () tptp.filter_real)
% 9.16/7.07 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 9.16/7.07 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 9.16/7.07 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 9.16/7.07 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 9.16/7.07 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 9.16/7.07 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 9.16/7.07 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 9.16/7.07 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 9.16/7.07 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.finite6454714172617411596l_num0 (tptp.set_Numeral_num0) tptp.nat)
% 9.16/7.07 (declare-fun tptp.finite6454714172617411597l_num1 (tptp.set_Numeral_num1) tptp.nat)
% 9.16/7.07 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 9.16/7.07 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 9.16/7.07 (declare-fun tptp.finite_card_literal (tptp.set_literal) tptp.nat)
% 9.16/7.07 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 9.16/7.07 (declare-fun tptp.finite6017078050557962740nteger (tptp.set_Code_integer) Bool)
% 9.16/7.07 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 9.16/7.07 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 9.16/7.07 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 9.16/7.07 (declare-fun tptp.finite1283093830868386564nteger (tptp.set_li6976499617229504675nteger) Bool)
% 9.16/7.07 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 9.16/7.07 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 9.16/7.07 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 9.16/7.07 (declare-fun tptp.finite306553202115118035t_real (tptp.set_list_real) Bool)
% 9.16/7.07 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 9.16/7.07 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 9.16/7.07 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 9.16/7.07 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 9.16/7.07 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 9.16/7.07 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 9.16/7.07 (declare-fun tptp.comp_nat_o_nat ((-> tptp.nat Bool) (-> tptp.nat tptp.nat) tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 9.16/7.07 (declare-fun tptp.inj_on_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.generi2397576812484419408nteger (tptp.code_integer tptp.nat Bool) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.generi8991105624351003935it_int (tptp.int tptp.nat Bool) tptp.int)
% 9.16/7.07 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.minus_2355218937544613996nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 9.16/7.07 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.minus_5127226145743854075T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.one_one_assn () tptp.assn)
% 9.16/7.07 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.one_one_complex () tptp.complex)
% 9.16/7.07 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.one_one_int () tptp.int)
% 9.16/7.07 (declare-fun tptp.one_one_nat () tptp.nat)
% 9.16/7.07 (declare-fun tptp.one_one_rat () tptp.rat)
% 9.16/7.07 (declare-fun tptp.one_one_real () tptp.real)
% 9.16/7.07 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.times_times_assn (tptp.assn tptp.assn) tptp.assn)
% 9.16/7.07 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 9.16/7.07 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.zero_zero_int () tptp.int)
% 9.16/7.07 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 9.16/7.07 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 9.16/7.07 (declare-fun tptp.zero_zero_real () tptp.real)
% 9.16/7.07 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 9.16/7.07 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.groups1304777262505850412r_assn ((-> tptp.code_integer tptp.assn) tptp.set_Code_integer) tptp.assn)
% 9.16/7.07 (declare-fun tptp.groups862514429393162674omplex ((-> tptp.code_integer tptp.complex) tptp.set_Code_integer) tptp.complex)
% 9.16/7.07 (declare-fun tptp.groups3188404863801439024er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 9.16/7.07 (declare-fun tptp.groups3190895334310489300er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 9.16/7.07 (declare-fun tptp.groups2555765274223993564er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 9.16/7.07 (declare-fun tptp.groups9004974159866482096r_real ((-> tptp.code_integer tptp.real) tptp.set_Code_integer) tptp.real)
% 9.16/7.07 (declare-fun tptp.groups4150731942483176573x_assn ((-> tptp.complex tptp.assn) tptp.set_complex) tptp.assn)
% 9.16/7.07 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 9.16/7.07 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 9.16/7.07 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 9.16/7.07 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 9.16/7.07 (declare-fun tptp.groups7882442080178216443t_assn ((-> tptp.int tptp.assn) tptp.set_int) tptp.assn)
% 9.16/7.07 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 9.16/7.07 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 9.16/7.07 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 9.16/7.07 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 9.16/7.07 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 9.16/7.07 (declare-fun tptp.groups6906906614972039071t_assn ((-> tptp.nat tptp.assn) tptp.set_nat) tptp.assn)
% 9.16/7.07 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 9.16/7.07 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 9.16/7.07 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.groups1155561341820557179l_assn ((-> tptp.real tptp.assn) tptp.set_real) tptp.assn)
% 9.16/7.07 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 9.16/7.07 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 9.16/7.07 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 9.16/7.07 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 9.16/7.07 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 9.16/7.07 (declare-fun tptp.groups569574905686396791T_assn ((-> tptp.vEBT_VEBT tptp.assn) tptp.set_VEBT_VEBT) tptp.assn)
% 9.16/7.07 (declare-fun tptp.groups127312072573709053omplex ((-> tptp.vEBT_VEBT tptp.complex) tptp.set_VEBT_VEBT) tptp.complex)
% 9.16/7.07 (declare-fun tptp.groups6359315924273963643BT_int ((-> tptp.vEBT_VEBT tptp.int) tptp.set_VEBT_VEBT) tptp.int)
% 9.16/7.07 (declare-fun tptp.groups6361806394783013919BT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.groups5726676334696518183BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 9.16/7.07 (declare-fun tptp.groups2703838992350267259T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 9.16/7.07 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 9.16/7.07 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 9.16/7.07 (declare-fun tptp.undefi2040150642751712519uint32 ((-> tptp.code_integer tptp.uint32) tptp.code_integer) tptp.uint32)
% 9.16/7.07 (declare-fun tptp.size_a6397454172108246045_VEBTi ((-> tptp.vEBT_VEBTi tptp.nat) tptp.array_VEBT_VEBTi) tptp.nat)
% 9.16/7.07 (declare-fun tptp.heap_Time_return_nat (tptp.nat) tptp.heap_Time_Heap_nat)
% 9.16/7.07 (declare-fun tptp.heap_T3630416162098727440_VEBTi (tptp.vEBT_VEBTi) tptp.heap_T8145700208782473153_VEBTi)
% 9.16/7.07 (declare-fun tptp.hoare_3067605981109127869le_nat (tptp.assn tptp.heap_Time_Heap_nat (-> tptp.nat tptp.assn)) Bool)
% 9.16/7.07 (declare-fun tptp.hoare_1429296392585015714_VEBTi (tptp.assn tptp.heap_T8145700208782473153_VEBTi (-> tptp.vEBT_VEBTi tptp.assn)) Bool)
% 9.16/7.07 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.if_nat_int_int (Bool (-> tptp.nat tptp.int tptp.int) (-> tptp.nat tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.if_assn (Bool tptp.assn tptp.assn) tptp.assn)
% 9.16/7.07 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 9.16/7.07 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 9.16/7.07 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 9.16/7.07 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 9.16/7.07 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.if_uint32 (Bool tptp.uint32 tptp.uint32) tptp.uint32)
% 9.16/7.07 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 9.16/7.07 (declare-fun tptp.ring_1_Ints_complex () tptp.set_complex)
% 9.16/7.07 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 9.16/7.07 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 9.16/7.07 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 9.16/7.07 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 9.16/7.07 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 9.16/7.07 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.least_7544222001954398261nteger (tptp.code_integer) Bool)
% 9.16/7.07 (declare-fun tptp.least_4859182151741483524sb_int (tptp.int) Bool)
% 9.16/7.07 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 9.16/7.07 (declare-fun tptp.append_o (tptp.list_o tptp.list_o) tptp.list_o)
% 9.16/7.07 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 9.16/7.07 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 9.16/7.07 (declare-fun tptp.filter_nat2 ((-> tptp.nat Bool) tptp.list_nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.foldr_o_nat ((-> Bool tptp.nat tptp.nat) tptp.list_o tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.foldr_int_nat ((-> tptp.int tptp.nat tptp.nat) tptp.list_int tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.foldr_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.foldr_real_nat ((-> tptp.real tptp.nat tptp.nat) tptp.list_real tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.foldr_real_real ((-> tptp.real tptp.real tptp.real) tptp.list_real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.cons_o (Bool tptp.list_o) tptp.list_o)
% 9.16/7.07 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.nil_o () tptp.list_o)
% 9.16/7.07 (declare-fun tptp.nil_int () tptp.list_int)
% 9.16/7.07 (declare-fun tptp.nil_nat () tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.map_o_o ((-> Bool Bool) tptp.list_o) tptp.list_o)
% 9.16/7.07 (declare-fun tptp.map_o_nat ((-> Bool tptp.nat) tptp.list_o) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.map_o_real ((-> Bool tptp.real) tptp.list_o) tptp.list_real)
% 9.16/7.07 (declare-fun tptp.map_o_VEBT_VEBT ((-> Bool tptp.vEBT_VEBT) tptp.list_o) tptp.list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.map_complex_complex ((-> tptp.complex tptp.complex) tptp.list_complex) tptp.list_complex)
% 9.16/7.07 (declare-fun tptp.map_complex_real ((-> tptp.complex tptp.real) tptp.list_complex) tptp.list_real)
% 9.16/7.07 (declare-fun tptp.map_int_o ((-> tptp.int Bool) tptp.list_int) tptp.list_o)
% 9.16/7.07 (declare-fun tptp.map_int_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.map_int_nat ((-> tptp.int tptp.nat) tptp.list_int) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.map_int_real ((-> tptp.int tptp.real) tptp.list_int) tptp.list_real)
% 9.16/7.07 (declare-fun tptp.map_int_VEBT_VEBT ((-> tptp.int tptp.vEBT_VEBT) tptp.list_int) tptp.list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.map_nat_o ((-> tptp.nat Bool) tptp.list_nat) tptp.list_o)
% 9.16/7.07 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.map_nat_real ((-> tptp.nat tptp.real) tptp.list_nat) tptp.list_real)
% 9.16/7.07 (declare-fun tptp.map_nat_VEBT_VEBT ((-> tptp.nat tptp.vEBT_VEBT) tptp.list_nat) tptp.list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.map_real_o ((-> tptp.real Bool) tptp.list_real) tptp.list_o)
% 9.16/7.07 (declare-fun tptp.map_real_nat ((-> tptp.real tptp.nat) tptp.list_real) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.map_real_real ((-> tptp.real tptp.real) tptp.list_real) tptp.list_real)
% 9.16/7.07 (declare-fun tptp.map_real_VEBT_VEBT ((-> tptp.real tptp.vEBT_VEBT) tptp.list_real) tptp.list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.map_VEBT_VEBTi_int ((-> tptp.vEBT_VEBTi tptp.int) tptp.list_VEBT_VEBTi) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.map_VEBT_VEBTi_nat ((-> tptp.vEBT_VEBTi tptp.nat) tptp.list_VEBT_VEBTi) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.map_VE483055756984248624_VEBTi ((-> tptp.vEBT_VEBTi tptp.vEBT_VEBTi) tptp.list_VEBT_VEBTi) tptp.list_VEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.map_VE7998069337340375161T_VEBT ((-> tptp.vEBT_VEBTi tptp.vEBT_VEBT) tptp.list_VEBT_VEBTi) tptp.list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.map_VEBT_VEBT_int ((-> tptp.vEBT_VEBT tptp.int) tptp.list_VEBT_VEBT) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.map_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.map_VEBT_VEBT_real ((-> tptp.vEBT_VEBT tptp.real) tptp.list_VEBT_VEBT) tptp.list_real)
% 9.16/7.07 (declare-fun tptp.map_VE7029150624388687525_VEBTi ((-> tptp.vEBT_VEBT tptp.vEBT_VEBTi) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.map_VE8901447254227204932T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 9.16/7.07 (declare-fun tptp.set_Code_integer2 (tptp.list_Code_integer) tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 9.16/7.07 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.set_VEBT_VEBTi2 (tptp.list_VEBT_VEBTi) tptp.set_VEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 9.16/7.07 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 9.16/7.07 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 9.16/7.07 (declare-fun tptp.list_u6098035379799741383_VEBTi (tptp.list_VEBT_VEBTi tptp.nat tptp.vEBT_VEBTi) tptp.list_VEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 9.16/7.07 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 9.16/7.07 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.nth_VEBT_VEBTi (tptp.list_VEBT_VEBTi tptp.nat) tptp.vEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 9.16/7.07 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 9.16/7.07 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 9.16/7.07 (declare-fun tptp.replicate_VEBT_VEBTi (tptp.nat tptp.vEBT_VEBTi) tptp.list_VEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 9.16/7.07 (declare-fun tptp.slice_o (tptp.nat tptp.nat tptp.list_o) tptp.list_o)
% 9.16/7.07 (declare-fun tptp.slice_int (tptp.nat tptp.nat tptp.list_int) tptp.list_int)
% 9.16/7.07 (declare-fun tptp.slice_nat (tptp.nat tptp.nat tptp.list_nat) tptp.list_nat)
% 9.16/7.07 (declare-fun tptp.slice_real (tptp.nat tptp.nat tptp.list_real) tptp.list_real)
% 9.16/7.07 (declare-fun tptp.slice_VEBT_VEBTi (tptp.nat tptp.nat tptp.list_VEBT_VEBTi) tptp.list_VEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.slice_VEBT_VEBT (tptp.nat tptp.nat tptp.list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 9.16/7.07 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 9.16/7.07 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 9.16/7.07 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_s7982070591426661849_VEBTi (tptp.list_VEBT_VEBTi) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_uint32 (tptp.uint32) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_VEBT_VEBTi (tptp.vEBT_VEBTi) tptp.nat)
% 9.16/7.07 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.inc (tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.one () tptp.num)
% 9.16/7.07 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 9.16/7.07 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 9.16/7.07 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 9.16/7.07 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 9.16/7.07 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 9.16/7.07 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 9.16/7.07 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 9.16/7.07 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 9.16/7.07 (declare-fun tptp.none_nat () tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.none_num () tptp.option_num)
% 9.16/7.07 (declare-fun tptp.none_P199884684680593241et_nat () tptp.option2860828798490689354et_nat)
% 9.16/7.07 (declare-fun tptp.none_P4972525538344268765et_nat () tptp.option5190343406534369742et_nat)
% 9.16/7.07 (declare-fun tptp.none_P2377608414092835994nt_int () tptp.option4624381673175914239nt_int)
% 9.16/7.07 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 9.16/7.07 (declare-fun tptp.none_P4394680061957285238um_num () tptp.option2661157926820139483um_num)
% 9.16/7.07 (declare-fun tptp.some_int (tptp.int) tptp.option_int)
% 9.16/7.07 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 9.16/7.07 (declare-fun tptp.some_P1630309045189364437et_nat (tptp.produc2732055786443039994et_nat) tptp.option2860828798490689354et_nat)
% 9.16/7.07 (declare-fun tptp.some_P750831030444334937et_nat (tptp.produc3925858234332021118et_nat) tptp.option5190343406534369742et_nat)
% 9.16/7.07 (declare-fun tptp.some_P4184893108420464158nt_int (tptp.product_prod_int_int) tptp.option4624381673175914239nt_int)
% 9.16/7.07 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 9.16/7.07 (declare-fun tptp.some_P6201964756284913402um_num (tptp.product_prod_num_num) tptp.option2661157926820139483um_num)
% 9.16/7.07 (declare-fun tptp.some_rat (tptp.rat) tptp.option_rat)
% 9.16/7.07 (declare-fun tptp.some_real (tptp.real) tptp.option_real)
% 9.16/7.07 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 9.16/7.07 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 9.16/7.07 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 9.16/7.07 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 9.16/7.07 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 9.16/7.07 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 9.16/7.07 (declare-fun tptp.bot_bot_assn () tptp.assn)
% 9.16/7.07 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 9.16/7.07 (declare-fun tptp.bot_bo3990330152332043303nteger () tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 9.16/7.07 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 9.16/7.07 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 9.16/7.07 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 9.16/7.07 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 9.16/7.07 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 9.16/7.07 (declare-fun tptp.ord_less_complex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_VEBT_VEBT_o ((-> tptp.vEBT_VEBT Bool) (-> tptp.vEBT_VEBT Bool)) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_option_int (tptp.option_int tptp.option_int) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_option_nat (tptp.option_nat tptp.option_nat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_option_num (tptp.option_num tptp.option_num) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_option_rat (tptp.option_rat tptp.option_rat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_option_real (tptp.option_real tptp.option_real) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le3480810397992357184T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_char (tptp.char tptp.char) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le5914376470875661696on_nat (tptp.option_nat tptp.option_nat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le6622620407824499402on_num (tptp.option_num tptp.option_num) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le6592769550269828683_VEBTi (tptp.set_VEBT_VEBTi tptp.set_VEBT_VEBTi) Bool)
% 9.16/7.07 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.ord_less_eq_char (tptp.char tptp.char) Bool)
% 9.16/7.07 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 9.16/7.07 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 9.16/7.07 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.top_top_assn () tptp.assn)
% 9.16/7.07 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 9.16/7.07 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.top_to3689904424835650196l_num0 () tptp.set_Numeral_num0)
% 9.16/7.07 (declare-fun tptp.top_to3689904429138878997l_num1 () tptp.set_Numeral_num1)
% 9.16/7.07 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 9.16/7.07 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 9.16/7.07 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 9.16/7.07 (declare-fun tptp.top_top_set_literal () tptp.set_literal)
% 9.16/7.07 (declare-fun tptp.power_power_assn (tptp.assn tptp.nat) tptp.assn)
% 9.16/7.07 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 9.16/7.07 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 9.16/7.07 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 9.16/7.07 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 9.16/7.07 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 9.16/7.07 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 9.16/7.07 (declare-fun tptp.produc2245416461498447860et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 9.16/7.07 (declare-fun tptp.produc5001842942810119800et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat)
% 9.16/7.07 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 9.16/7.07 (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)
% 9.16/7.07 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 9.16/7.07 (declare-fun tptp.produc7507926704131184380et_nat (tptp.heap_e7401611519738050253t_unit tptp.set_nat) tptp.produc3658429121746597890et_nat)
% 9.16/7.07 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 9.16/7.07 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 9.16/7.07 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 9.16/7.07 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 9.16/7.07 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 9.16/7.07 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 9.16/7.07 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 9.16/7.07 (declare-fun tptp.produc6084888613844515218_VEBTi (tptp.vEBT_VEBT tptp.vEBT_VEBTi) tptp.produc3625547720036274456_VEBTi)
% 9.16/7.07 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 9.16/7.07 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 9.16/7.07 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 9.16/7.07 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 9.16/7.07 (declare-fun tptp.type_N8448461349408098053l_num1 () tptp.itself8794530163899892676l_num1)
% 9.16/7.07 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 9.16/7.07 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 9.16/7.07 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 9.16/7.07 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 9.16/7.07 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 9.16/7.07 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 9.16/7.07 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 9.16/7.07 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 9.16/7.07 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.dvd_dvd_assn (tptp.assn tptp.assn) Bool)
% 9.16/7.07 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 9.16/7.07 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 9.16/7.07 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 9.16/7.07 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 9.16/7.07 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 9.16/7.07 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 9.16/7.07 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 9.16/7.07 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 9.16/7.07 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 9.16/7.07 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 9.16/7.07 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 9.16/7.07 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 9.16/7.07 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 9.16/7.07 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 9.16/7.07 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 9.16/7.07 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 9.16/7.07 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 9.16/7.07 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 9.16/7.07 (declare-fun tptp.collec3483841146883906114nteger ((-> tptp.list_Code_integer Bool)) tptp.set_li6976499617229504675nteger)
% 9.16/7.07 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 9.16/7.07 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 9.16/7.07 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 9.16/7.07 (declare-fun tptp.collect_list_real ((-> tptp.list_real Bool)) tptp.set_list_real)
% 9.16/7.07 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 9.16/7.07 (declare-fun tptp.collect_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool)) tptp.set_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.image_4470545334726330049nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 9.16/7.07 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.image_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.insert_o (Bool tptp.set_o) tptp.set_o)
% 9.16/7.07 (declare-fun tptp.insert_Code_integer (tptp.code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 9.16/7.07 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 9.16/7.07 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 9.16/7.07 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.insert_VEBT_VEBTi (tptp.vEBT_VEBTi tptp.set_VEBT_VEBTi) tptp.set_VEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.set_fo1959793692361082170t_assn ((-> tptp.nat tptp.assn tptp.assn) tptp.nat tptp.nat tptp.assn) tptp.assn)
% 9.16/7.07 (declare-fun tptp.set_fo1084959871951514735nteger ((-> tptp.nat tptp.code_integer tptp.code_integer) tptp.nat tptp.nat tptp.code_integer) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 9.16/7.07 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.set_or189985376899183464nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 9.16/7.07 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 9.16/7.07 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 9.16/7.07 (declare-fun tptp.set_or8404916559141939852nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.set_or1222409239386451017an_num (tptp.num tptp.num) tptp.set_num)
% 9.16/7.07 (declare-fun tptp.set_or4029947393144176647an_rat (tptp.rat tptp.rat) tptp.set_rat)
% 9.16/7.07 (declare-fun tptp.set_or66887138388493659n_real (tptp.real tptp.real) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.set_or3540276404033026485et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 9.16/7.07 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.set_or2715278749043346189nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.set_or4266950643985792945nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 9.16/7.07 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 9.16/7.07 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 9.16/7.07 (declare-fun tptp.signed6714573509424544716de_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.signed6292675348222524329lo_int (tptp.int tptp.int) tptp.int)
% 9.16/7.07 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 9.16/7.07 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 9.16/7.07 (declare-fun tptp.size_char (tptp.char) tptp.nat)
% 9.16/7.07 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 9.16/7.07 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 9.16/7.07 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 9.16/7.07 (declare-fun tptp.syntax7398250324933576852n_assn (tptp.assn tptp.assn) Bool)
% 9.16/7.07 (declare-fun tptp.time_htt_nat (tptp.assn tptp.heap_Time_Heap_nat (-> tptp.nat tptp.assn) tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.time_time_VEBT_VEBTi (tptp.heap_T8145700208782473153_VEBTi tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 9.16/7.07 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 9.16/7.07 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 9.16/7.07 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 9.16/7.07 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 9.16/7.07 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 9.16/7.07 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 9.16/7.07 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.pi () tptp.real)
% 9.16/7.07 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 9.16/7.07 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 9.16/7.07 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 9.16/7.07 (declare-fun tptp.type_l31302759751748491nite_1 (tptp.itself_finite_1) tptp.nat)
% 9.16/7.07 (declare-fun tptp.type_l31302759751748492nite_2 (tptp.itself_finite_2) tptp.nat)
% 9.16/7.07 (declare-fun tptp.type_l31302759751748493nite_3 (tptp.itself_finite_3) tptp.nat)
% 9.16/7.07 (declare-fun tptp.type_l796852477590012082l_num1 (tptp.itself8794530163899892676l_num1) tptp.nat)
% 9.16/7.07 (declare-fun tptp.type_l4264026598287037464l_num0 (tptp.itself_Numeral_num0) tptp.nat)
% 9.16/7.07 (declare-fun tptp.type_l4264026598287037465l_num1 (tptp.itself_Numeral_num1) tptp.nat)
% 9.16/7.07 (declare-fun tptp.uint322 (tptp.code_integer) tptp.uint32)
% 9.16/7.07 (declare-fun tptp.uint32_signed (tptp.code_integer) tptp.uint32)
% 9.16/7.07 (declare-fun tptp.vEBT_T_i_n_s_e_r_t (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T_i_n_s_e_r_t2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T5076183648494686801_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T9217963907923527482_t_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T_m_a_x_t (tptp.vEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T_m_a_x_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T_m_e_m_b_e_r (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T_m_e_m_b_e_r2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T8099345112685741742_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T5837161174952499735_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T_m_i_n_N_u_l_l (tptp.vEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T5462971552011256508_l_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T_m_i_n_t (tptp.vEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T_m_i_n_t_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T_p_r_e_d (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T_p_r_e_d2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T_p_r_e_d_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T_p_r_e_d_rel2 (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T_s_u_c_c (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T_s_u_c_c2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T_s_u_c_c_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T_s_u_c_c_rel2 (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_V441764108873111860ildupi (tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_V2957053500504383685pi_rel (tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_highi (tptp.nat tptp.nat) tptp.heap_Time_Heap_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_lowi (tptp.nat tptp.nat) tptp.heap_Time_Heap_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_V739175172307565963ildupi (tptp.nat) tptp.heap_T8145700208782473153_VEBTi)
% 9.16/7.07 (declare-fun tptp.vEBT_Leafi (Bool Bool) tptp.vEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.vEBT_Nodei (tptp.option4927543243414619207at_nat tptp.nat tptp.array_VEBT_VEBTi tptp.vEBT_VEBTi) tptp.vEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.vEBT_size_VEBTi (tptp.vEBT_VEBTi) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_assn_raw (tptp.vEBT_VEBT tptp.vEBT_VEBTi) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_v8524038756793281170aw_rel (tptp.produc3625547720036274456_VEBTi tptp.produc3625547720036274456_VEBTi) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_T_d_e_l_e_t_e (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_T8441311223069195367_e_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_V1232361888498592333_e_t_e (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_V6368547301243506412_e_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_delete (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_delete_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_height (tptp.vEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_height_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_L1528199826722428489_VEBTi (tptp.set_nat (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn) tptp.list_VEBT_VEBT tptp.list_VEBT_VEBTi) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L7363604446928714179sn_o_o ((-> Bool Bool tptp.assn) tptp.list_o tptp.list_o) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L4785011123346445925_o_nat ((-> Bool tptp.nat tptp.assn) tptp.list_o tptp.list_nat) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L4725278957065240257o_real ((-> Bool tptp.real tptp.assn) tptp.list_o tptp.list_real) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L4260503343685368993omplex ((-> tptp.complex tptp.complex tptp.assn) tptp.list_complex tptp.list_complex) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L134985006839036959ex_int ((-> tptp.complex tptp.int tptp.assn) tptp.list_complex tptp.list_int) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L137475477348087235ex_nat ((-> tptp.complex tptp.nat tptp.assn) tptp.list_complex tptp.list_nat) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L2479436891206192927x_real ((-> tptp.complex tptp.real tptp.assn) tptp.list_complex tptp.list_real) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L8524933119956041985T_VEBT ((-> tptp.complex tptp.vEBT_VEBT tptp.assn) tptp.list_complex tptp.list_VEBT_VEBT) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L6066640139021943271_int_o ((-> tptp.int Bool tptp.assn) tptp.list_int tptp.list_o) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L8288995350762215837t_real ((-> tptp.int tptp.real tptp.assn) tptp.list_int tptp.list_real) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L7887682484454631235_nat_o ((-> tptp.nat Bool tptp.assn) tptp.list_nat tptp.list_o) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L6102073776069194049t_real ((-> tptp.nat tptp.real tptp.assn) tptp.list_nat tptp.list_real) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L6234343332106409831real_o ((-> tptp.real Bool tptp.assn) tptp.list_real tptp.list_o) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L1446010312343316929al_nat ((-> tptp.real tptp.nat tptp.assn) tptp.list_real tptp.list_nat) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L1930518968523514909l_real ((-> tptp.real tptp.real tptp.assn) tptp.list_real tptp.list_real) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L2162147798726695391omplex ((-> tptp.vEBT_VEBT tptp.complex tptp.assn) tptp.list_VEBT_VEBT tptp.list_complex) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L8294436054247626077BT_int ((-> tptp.vEBT_VEBT tptp.int tptp.assn) tptp.list_VEBT_VEBT tptp.list_int) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L8296926524756676353BT_nat ((-> tptp.vEBT_VEBT tptp.nat tptp.assn) tptp.list_VEBT_VEBT tptp.list_nat) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L5781919052683127133T_real ((-> tptp.vEBT_VEBT tptp.real tptp.assn) tptp.list_VEBT_VEBT tptp.list_real) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L6296928887356842470_VEBTi ((-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn) tptp.list_VEBT_VEBT tptp.list_VEBT_VEBTi) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_L1279224858307276611T_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn) tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.assn)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 9.16/7.07 (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)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_V8646137997579335489_i_l_d (tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_V8346862874174094_d_u_p (tptp.nat) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_V1247956027447740395_p_rel (tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_V5144397997797733112_d_rel (tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_cnt (tptp.vEBT_VEBT) tptp.real)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_cnt2 (tptp.vEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_cnt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_cnt_rel2 (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_space (tptp.vEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_space2 (tptp.vEBT_VEBT) tptp.nat)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_space_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_VEBT_space_rel2 (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 9.16/7.07 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 9.16/7.07 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 9.16/7.07 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 9.16/7.07 (declare-fun tptp.accp_P7675410724331315407_VEBTi ((-> tptp.produc3625547720036274456_VEBTi tptp.produc3625547720036274456_VEBTi Bool) tptp.produc3625547720036274456_VEBTi) Bool)
% 9.16/7.07 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 9.16/7.07 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 9.16/7.07 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 9.16/7.07 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 9.16/7.07 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 9.16/7.07 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 9.16/7.07 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 9.16/7.07 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 9.16/7.07 (declare-fun tptp.member_list_real (tptp.list_real tptp.set_list_real) Bool)
% 9.16/7.07 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 9.16/7.07 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 9.16/7.07 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 9.16/7.07 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 9.16/7.07 (declare-fun tptp.member_VEBT_VEBTi (tptp.vEBT_VEBTi tptp.set_VEBT_VEBTi) Bool)
% 9.16/7.07 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 9.16/7.07 (declare-fun tptp.na () tptp.nat)
% 9.16/7.07 (declare-fun tptp.x () tptp.list_VEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.xa () tptp.array_VEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.xb () tptp.vEBT_VEBTi)
% 9.16/7.07 (declare-fun tptp.xc () tptp.vEBT_VEBTi)
% 9.16/7.07 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.array_VEBT_VEBTi) (X14 tptp.vEBT_VEBTi) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.array_VEBT_VEBTi) (Y14 tptp.vEBT_VEBTi)) (= (= (@ (@ (@ (@ tptp.vEBT_Nodei X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Nodei Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))))
% 9.16/7.07 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (Tree_is tptp.list_VEBT_VEBTi) (X13 tptp.array_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) TreeList) Tree_is))) (let ((_let_2 (@ (@ tptp.snga_assn_VEBT_VEBTi X13) Tree_is))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))) (@ (@ tptp.entails (@ (@ tptp.times_times_assn _let_1) (@ (@ tptp.times_times_assn _let_2) _let_3))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn _let_3) _let_2)) _let_1)))))))
% 9.16/7.07 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.na)))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((P tptp.assn) (B Bool) (Q tptp.assn)) (= (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B))) Q) (=> B (@ (@ tptp.entails P) Q)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.power_8256067586552552935nteger (@ _let_2 N)) _let_1)))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_assn A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_assn A) (@ (@ tptp.power_power_assn (@ _let_2 N)) _let_1)))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1)))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1)))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1)))))))
% 9.16/7.07 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.times_times_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (and A B)))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_assn A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_assn (@ _let_2 N)) _let_1))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1))))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_8256067586552552935nteger (@ _let_2 N)) _let_1))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N)))))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.power_power_assn X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn X) X)) X)) X))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) X)) X))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((P Bool) (Q Bool)) (= (= (@ tptp.pure_assn P) (@ tptp.pure_assn Q)) (= P Q))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ (@ tptp.power_8256067586552552935nteger (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ (@ tptp.power_power_assn (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N))) (@ _let_1 N)))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N)) (not (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ (@ tptp.divide_divide_nat N) _let_1))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N) _let_1)))))))
% 9.16/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)))))
% 9.16/7.07 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) N)))))
% 9.16/7.07 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)))))
% 9.16/7.07 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) N)))))
% 9.16/7.07 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 9.16/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 9.16/7.07 (assert (forall ((B tptp.int) (A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2))))))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2))))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)) A)))))
% 9.16/7.07 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn P))) (= (@ (@ tptp.times_times_assn (@ _let_1 Q)) R) (@ _let_1 (@ (@ tptp.times_times_assn Q) R))))))
% 9.16/7.07 (assert (= tptp.times_times_assn (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (@ (@ tptp.times_times_assn Q2) P2))))
% 9.16/7.07 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 Q) (=> (@ (@ tptp.entails Q) R) (@ _let_1 R))))))
% 9.16/7.07 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails P) P)))
% 9.16/7.07 (assert (forall ((A2 tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entails A2) B3) (=> (@ (@ tptp.entails B3) A2) (= A2 B3)))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((X tptp.assn) (Y tptp.assn) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn X) N))) (let ((_let_2 (@ tptp.times_times_assn Y))) (=> (= (@ (@ tptp.times_times_assn X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_assn _let_1) Y) (@ _let_2 _let_1)))))))
% 9.16/7.07 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) N))) (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)))))))
% 9.16/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N))) (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)))))))
% 9.16/7.07 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N))) (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)))))))
% 9.16/7.07 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger X) N))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger Y))) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ _let_2 _let_1)))))))
% 9.16/7.07 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) N))) (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)))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (B tptp.assn) (N tptp.nat)) (= (@ (@ tptp.power_power_assn (@ (@ tptp.times_times_assn A) B)) N) (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn A) N)) (@ (@ tptp.power_power_assn B) N)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn A) N))) (= (@ (@ tptp.times_times_assn _let_1) A) (@ (@ tptp.times_times_assn A) _let_1)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) A) (@ (@ tptp.times_3573771949741848930nteger A) _let_1)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_real (@ _let_1 M)) N)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_int (@ _let_1 M)) N)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_8256067586552552935nteger (@ _let_1 M)) N)))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_assn (@ _let_1 M)) N)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q3)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q3)))))
% 9.16/7.07 (assert (forall ((P tptp.assn) (P3 tptp.assn) (Q tptp.assn) (Q4 tptp.assn)) (=> (@ (@ tptp.entails P) P3) (=> (@ (@ tptp.entails Q) Q4) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) Q)) (@ (@ tptp.times_times_assn P3) Q4))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_assn (@ _let_1 N)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_assn A) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 9.16/7.07 (assert (forall ((A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (@ (@ tptp.member_VEBT_VEBT A) (@ tptp.collect_VEBT_VEBT P)) (@ P A))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 9.16/7.07 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 9.16/7.07 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 9.16/7.07 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A2))) A2)))
% 9.16/7.07 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (= (@ tptp.collect_VEBT_VEBT (lambda ((X2 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X2) A2))) A2)))
% 9.16/7.07 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A2))) A2)))
% 9.16/7.07 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A2))) A2)))
% 9.16/7.07 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A2))) A2)))
% 9.16/7.07 (assert (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.member_set_nat X2) A2))) A2)))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 9.16/7.07 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_assn A) A))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_3573771949741848930nteger A) A))))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))))
% 9.16/7.07 (assert (= (lambda ((Y2 tptp.nat) (Z2 tptp.nat)) (= Y2 Z2)) (lambda ((A3 tptp.nat) (B4 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 B4)) (= (@ (@ tptp.divide_divide_nat A3) _let_1) (@ (@ tptp.divide_divide_nat B4) _let_1))))))))
% 9.16/7.07 (assert (= (lambda ((Y2 tptp.int) (Z2 tptp.int)) (= Y2 Z2)) (lambda ((A3 tptp.int) (B4 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 B4)) (= (@ (@ tptp.divide_divide_int A3) _let_1) (@ (@ tptp.divide_divide_int B4) _let_1))))))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 9.16/7.07 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 9.16/7.07 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Z)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Z))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))))
% 9.16/7.07 (assert (forall ((X tptp.nat)) (=> (forall ((N2 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N2) N2)))) (not (forall ((N2 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N2) (@ tptp.suc N2)))))))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) A)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) A)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) A)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) A)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 9.16/7.07 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 9.16/7.07 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L2 tptp.nat) (D tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D))) L2))))
% 9.16/7.07 (assert (forall ((V tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger V))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger B) _let_1))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B)) (@ _let_1 B)))))
% 9.16/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))))
% 9.16/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) E)) C))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 C))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 C))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 C))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 C))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 B))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 B))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 B))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 B))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C)))))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 9.16/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 9.16/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 9.16/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 9.16/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_assn (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p5714425477246183910nteger Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p5714425477246183910nteger Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 9.16/7.07 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) B)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ _let_1 C))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) C) (@ _let_1 C))))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 9.16/7.07 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) _let_2) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_2)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) X)) Y)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn B) A) (not (forall ((K2 tptp.assn)) (not (= A (@ (@ tptp.times_times_assn B) K2))))))))
% 9.16/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K2 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K2))))))))
% 9.16/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K2))))))))
% 9.16/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K2))))))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K2))))))))
% 9.16/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (not (forall ((K2 tptp.complex)) (not (= A (@ (@ tptp.times_times_complex B) K2))))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (B tptp.assn) (K tptp.assn)) (=> (= A (@ (@ tptp.times_times_assn B) K)) (@ (@ tptp.dvd_dvd_assn B) A))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (K tptp.complex)) (=> (= A (@ (@ tptp.times_times_complex B) K)) (@ (@ tptp.dvd_dvd_complex B) A))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_assn (lambda ((B4 tptp.assn) (A3 tptp.assn)) (exists ((K3 tptp.assn)) (= A3 (@ (@ tptp.times_times_assn B4) K3))))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_real (lambda ((B4 tptp.real) (A3 tptp.real)) (exists ((K3 tptp.real)) (= A3 (@ (@ tptp.times_times_real B4) K3))))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_nat (lambda ((B4 tptp.nat) (A3 tptp.nat)) (exists ((K3 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B4) K3))))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_int (lambda ((B4 tptp.int) (A3 tptp.int)) (exists ((K3 tptp.int)) (= A3 (@ (@ tptp.times_times_int B4) K3))))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B4 tptp.code_integer) (A3 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A3 (@ (@ tptp.times_3573771949741848930nteger B4) K3))))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_complex (lambda ((B4 tptp.complex) (A3 tptp.complex)) (exists ((K3 tptp.complex)) (= A3 (@ (@ tptp.times_times_complex B4) K3))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.dvd_dvd_assn A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.dvd_dvd_assn A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A) B)) C) (@ (@ tptp.dvd_dvd_assn A) C))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real A) C))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex A) C))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.dvd_dvd_assn A) (@ (@ tptp.times_times_assn A) B))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex A) B))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn A) B) (=> (@ (@ tptp.dvd_dvd_assn C) D2) (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A) C)) (@ (@ tptp.times_times_assn B) D2))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex A) B) (=> (@ (@ tptp.dvd_dvd_complex C) D2) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) D2))))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A) B)) C) (@ (@ tptp.dvd_dvd_assn B) C))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real B) C))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex B) C))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.dvd_dvd_assn A) (@ (@ tptp.times_times_assn B) A))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex B) A))))
% 9.16/7.07 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (= A B)))))))
% 9.16/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (= A B)))))))
% 9.16/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (= A B)))))))
% 9.16/7.07 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (= A B)))))))
% 9.16/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (= A B)))))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 9.16/7.07 (assert (forall ((D2 tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D2) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D2)) (@ (@ tptp.divide_divide_nat B) D2)) (@ _let_1 B)))))))
% 9.16/7.07 (assert (forall ((D2 tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D2) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D2)) (@ (@ tptp.divide_divide_int B) D2)) (@ _let_1 B)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger tptp.one)) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.numera6620942414471956472nteger tptp.one)) A)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))))
% 9.16/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))))
% 9.16/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 9.16/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 9.16/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))))
% 9.16/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))))
% 9.16/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 9.16/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 9.16/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))
% 9.16/7.07 (assert (forall ((B tptp.nat) (A tptp.nat) (D2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D2) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))
% 9.16/7.07 (assert (forall ((B tptp.int) (A tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D2) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat N) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.suc _let_3))) (let ((_let_6 (@ tptp.vEBT_V441764108873111860ildupi _let_5))) (let ((_let_7 (@ (@ tptp.times_times_nat _let_6) _let_4))) (let ((_let_8 (@ tptp.bit0 _let_1))) (let ((_let_9 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_8)))) (let ((_let_10 (@ tptp.vEBT_V441764108873111860ildupi (@ tptp.suc (@ tptp.suc N))))) (let ((_let_11 (@ (@ tptp.dvd_dvd_nat _let_2) N))) (and (=> _let_11 (= _let_10 (@ tptp.suc (@ tptp.suc (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_6) (@ (@ tptp.plus_plus_nat (@ _let_9 _let_4)) (@ (@ tptp.times_times_nat _let_2) _let_7)))))))) (=> (not _let_11) (= _let_10 (@ tptp.suc (@ tptp.suc (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.vEBT_V441764108873111860ildupi (@ tptp.suc _let_5))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_8))) _let_4)) (@ _let_9 _let_7))))))))))))))))))))))
% 9.16/7.07 (assert (= tptp.nat_triangle (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N3) (@ tptp.suc N3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((D2 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 D2))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D2)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D2))) (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 D2))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D2)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D2)))))))))))))))))
% 9.16/7.07 (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))))))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))))
% 9.16/7.07 (assert (= tptp.vEBT_VEBT_highi (lambda ((X2 tptp.nat) (N3 tptp.nat)) (@ tptp.heap_Time_return_nat (@ (@ tptp.divide_divide_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 9.16/7.07 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y22)) (= X22 Y22))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.07 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (M tptp.num) (N tptp.num) (B tptp.assn)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (M tptp.num) (N tptp.num) (B tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 9.16/7.07 (assert (forall ((A tptp.assn) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 9.16/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat A) B) (not (= A B))) (not (and (@ (@ tptp.dvd_dvd_nat B) A) (not (= B A)))))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ _let_1 C))))))
% 9.16/7.07 (assert (= (lambda ((Y2 tptp.nat) (Z2 tptp.nat)) (= Y2 Z2)) (lambda ((A3 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat A3) B4) (@ (@ tptp.dvd_dvd_nat B4) A3)))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat A) A) (not (= A A))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= A B)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (and (@ _let_1 B) (not (= A B))) (=> (and (@ (@ tptp.dvd_dvd_nat B) C) (not (= B C))) (and (@ _let_1 C) (not (= A C))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (and (@ (@ tptp.dvd_dvd_nat B) C) (not (= B C))) (and (@ _let_1 C) (not (= A C))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (and (@ _let_1 B) (not (= A B))) (=> (@ (@ tptp.dvd_dvd_nat B) C) (and (@ _let_1 C) (not (= A C))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (= (and _let_1 (not (= A B))) (and _let_1 (not (@ (@ tptp.dvd_dvd_nat B) A)))))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (let ((_let_1 (= A3 B4))) (or (and (@ (@ tptp.dvd_dvd_nat A3) B4) (not _let_1)) _let_1)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (and (@ (@ tptp.dvd_dvd_nat A) B) (not (= A B))))) (= _let_1 _let_1))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (=> (and _let_1 (not (= A B))) _let_1))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (not (= A B)))) (=> (and (@ (@ tptp.dvd_dvd_nat A) B) _let_1) _let_1))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (not (= A B)))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat A) B))) (=> _let_1 (=> _let_2 (and _let_2 _let_1)))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 9.16/7.07 (assert (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B5 tptp.nat) (C2 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B5) C2)) (@ (@ tptp.dvd_dvd_nat B5) B) (@ (@ tptp.dvd_dvd_nat C2) C))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B5 tptp.int) (C2 tptp.int)) (and (= A (@ (@ tptp.times_times_int B5) C2)) (@ (@ tptp.dvd_dvd_int B5) B) (@ (@ tptp.dvd_dvd_int C2) C))))))
% 9.16/7.07 (assert (forall ((P4 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P4) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P4 (@ (@ tptp.times_times_nat X3) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 9.16/7.07 (assert (forall ((P4 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P4) (@ (@ tptp.times_times_int A) B)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P4 (@ (@ tptp.times_times_int X3) Y3)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 9.16/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 9.16/7.07 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N) Y)))))
% 9.16/7.07 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M))))))
% 9.16/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (not (= Y _let_1)))) (=> (= (@ tptp.vEBT_V441764108873111860ildupi X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_2) (=> (=> (= X _let_1) _let_2) (not (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat N2) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.suc _let_3))) (let ((_let_6 (@ tptp.vEBT_V441764108873111860ildupi _let_5))) (let ((_let_7 (@ (@ tptp.times_times_nat _let_6) _let_4))) (let ((_let_8 (@ tptp.bit0 _let_1))) (let ((_let_9 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_8)))) (let ((_let_10 (@ (@ tptp.dvd_dvd_nat _let_2) N2))) (=> (= X (@ tptp.suc (@ tptp.suc N2))) (not (and (=> _let_10 (= Y (@ tptp.suc (@ tptp.suc (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_6) (@ (@ tptp.plus_plus_nat (@ _let_9 _let_4)) (@ (@ tptp.times_times_nat _let_2) _let_7)))))))) (=> (not _let_10) (= Y (@ tptp.suc (@ tptp.suc (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.vEBT_V441764108873111860ildupi (@ tptp.suc _let_5))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_8))) _let_4)) (@ _let_9 _let_7))))))))))))))))))))))))))))))
% 9.16/7.07 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.pow K) L)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y22)) (= X22 Y22))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (= tptp.vEBT_VEBT_lowi (lambda ((X2 tptp.nat) (N3 tptp.nat)) (@ tptp.heap_Time_return_nat (@ (@ tptp.modulo_modulo_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))))
% 9.16/7.07 (assert (forall ((P (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (P3 (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (L tptp.list_VEBT_VEBT) (L3 tptp.list_VEBT_VEBTi)) (=> (forall ((X3 tptp.vEBT_VEBT) (X4 tptp.vEBT_VEBTi)) (@ (@ tptp.entails (@ (@ P X3) X4)) (@ (@ P3 X3) X4))) (@ (@ tptp.entails (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi P) L) L3)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi P3) L) L3)))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) tptp.one_one_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) tptp.one_one_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) B))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B) _let_1))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (= (@ (@ tptp.modulo_modulo_int _let_1) B) _let_1))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 9.16/7.07 (assert (= (@ tptp.pure_assn true) tptp.one_one_assn))
% 9.16/7.07 (assert (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.one_one_assn) P)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M) N))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M) N))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M) N))))
% 9.16/7.07 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M) N))))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 9.16/7.07 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 9.16/7.07 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger) (or (= A tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (= A B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= A B)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 9.16/7.07 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn A) tptp.one_one_assn) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger tptp.one_one_Code_integer) N) tptp.one_one_Code_integer)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_assn tptp.one_one_assn) N) tptp.one_one_assn)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 9.16/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 9.16/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 9.16/7.07 (assert (forall ((B Bool) (Q tptp.assn)) (= (@ (@ tptp.entails (@ tptp.pure_assn B)) Q) (=> B (@ (@ tptp.entails tptp.one_one_assn) Q)))))
% 9.16/7.07 (assert (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger C) B)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger C) A) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) A) B))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) A))))
% 9.16/7.07 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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)))))))))
% 9.16/7.07 (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)))))))))
% 9.16/7.07 (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)))))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))))
% 9.16/7.07 (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)))))))))
% 9.16/7.07 (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)))))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) (@ tptp.suc N)) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 9.16/7.07 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 9.16/7.07 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numeral_numeral_nat K)) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 9.16/7.07 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))))
% 9.16/7.07 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 9.16/7.07 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 9.16/7.07 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 9.16/7.07 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 9.16/7.07 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.07 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 9.16/7.07 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 9.16/7.07 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 9.16/7.07 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N)) (and (= M _let_1) (= N _let_1))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N) M) (= N tptp.one_one_nat)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))))
% 9.16/7.07 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 9.16/7.07 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N)))))))))
% 9.16/7.07 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))))))
% 9.16/7.07 (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))))))))
% 9.16/7.07 (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))))))))
% 9.16/7.07 (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))))))))
% 9.16/7.07 (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))))))))
% 9.16/7.07 (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))))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.07 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) N) tptp.zero_z3403309356797280102nteger) (and (= A tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N)) N) M))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M)) N) M))))
% 9.16/7.07 (assert (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N) K)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 9.16/7.07 (assert (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 9.16/7.07 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 9.16/7.07 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 9.16/7.07 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 9.16/7.07 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 9.16/7.07 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 9.16/7.07 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 9.16/7.07 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 9.16/7.07 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 9.16/7.07 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.07 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 9.16/7.07 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 9.16/7.07 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 9.16/7.07 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 9.16/7.07 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 9.16/7.07 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ _let_2 A))))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ _let_2 A))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (= (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ _let_2 A))))))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ (@ tptp.modulo_modulo_nat M) _let_1)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.07 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 9.16/7.07 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 9.16/7.07 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 9.16/7.07 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (not (@ _let_1 A))))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (not (@ _let_1 A))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 9.16/7.07 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.zero_z3403309356797280102nteger) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) _let_1)) tptp.zero_z3403309356797280102nteger) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (W tptp.num)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (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_8256067586552552935nteger A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_z3403309356797280102nteger))) (and (not _let_3) (@ _let_1 A)))))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A)))))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D2) tptp.zero_zero_nat) (exists ((Q5 tptp.nat)) (= M (@ (@ tptp.times_times_nat D2) Q5))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 9.16/7.07 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M2 tptp.nat)) (@ (@ P M2) tptp.zero_zero_nat)) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ P N2) (@ (@ tptp.modulo_modulo_nat M2) N2)) (@ (@ P M2) N2)))) (@ (@ P M) N)))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 9.16/7.07 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 9.16/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N2) (@ P M3))) (@ P N2))) (@ P N))))
% 9.16/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N2) (not (@ P M3)))))) (@ P N))))
% 9.16/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P N2)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N2) (not (@ P M3))))))) (@ P N)))))
% 9.16/7.07 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 9.16/7.07 (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)))))))))
% 9.16/7.07 (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)))))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))))
% 9.16/7.07 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((X5 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X5))))
% 9.16/7.07 (assert (forall ((X5 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X5))))
% 9.16/7.07 (assert (forall ((X5 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X5) X_1))))
% 9.16/7.07 (assert (forall ((X5 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X5) X_1))))
% 9.16/7.07 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B3) N))))))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 9.16/7.07 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) M)))))
% 9.16/7.07 (assert (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))))
% 9.16/7.07 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((X tptp.assn)) (= (= tptp.one_one_assn X) (= X tptp.one_one_assn))))
% 9.16/7.07 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 9.16/7.07 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 9.16/7.07 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 9.16/7.07 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 9.16/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B)) B))))
% 9.16/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B)) B))))
% 9.16/7.07 (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))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 9.16/7.07 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 9.16/7.07 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 9.16/7.07 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 9.16/7.07 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 9.16/7.07 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 9.16/7.07 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 9.16/7.07 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 9.16/7.07 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 9.16/7.07 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 9.16/7.07 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 9.16/7.07 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N)) (not (@ (@ tptp.dvd_dvd_nat N) M)))))
% 9.16/7.07 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N))) M) tptp.one_one_nat))))
% 9.16/7.07 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P4 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P4) (=> (@ (@ tptp.ord_less_nat M) P4) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) P4) (=> (@ P N2) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N2)) P4))))) (@ P M)))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_real (@ F N)) (@ F N5))))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N5))))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_num (@ F N)) (@ F N5))))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N5))))))
% 9.16/7.07 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_int (@ F N)) (@ F N5))))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B4) A3) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B4) A3) tptp.zero_zero_int))))
% 9.16/7.07 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A3 tptp.code_integer) (B4 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B4) A3) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.07 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 9.16/7.07 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 9.16/7.07 (assert (forall ((M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger M) N)))))))
% 9.16/7.07 (assert (forall ((M tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M) N)))))))
% 9.16/7.07 (assert (forall ((M tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M) N)))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 9.16/7.07 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M) N)))))))
% 9.16/7.07 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 9.16/7.07 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) A)) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.07 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 9.16/7.07 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 9.16/7.07 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (@ _let_1 B)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (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)))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (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)))))))
% 9.16/7.07 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (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))))))
% 9.16/7.07 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 9.16/7.07 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J2 tptp.nat)) (and (= M (@ tptp.suc J2)) (@ (@ tptp.ord_less_nat J2) N)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M2 tptp.nat)) (= N (@ tptp.suc M2))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (@ P tptp.zero_zero_nat) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P (@ tptp.suc I2))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (or (@ P tptp.zero_zero_nat) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P (@ tptp.suc I2))))))))
% 9.16/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) tptp.zero_zero_nat) tptp.one_one_Code_integer)))
% 9.16/7.08 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) tptp.zero_zero_nat) tptp.one_one_assn)))
% 9.16/7.08 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I) K2) J))))))
% 9.16/7.08 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 9.16/7.08 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 9.16/7.08 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 9.16/7.08 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn A) tptp.one_one_assn) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) _let_1))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N))) tptp.one_one_Code_integer)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) tptp.one_one_real)))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I2)) J2)) (@ P J2))))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (X tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X) (@ (@ tptp.power_power_rat X) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N)))))
% 9.16/7.08 (assert (forall ((N tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((N tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((N tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 9.16/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 9.16/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M)) M) (= N tptp.one_one_nat)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N)) M) (= N tptp.one_one_nat)))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.power_8256067586552552935nteger A) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger A) _let_1))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) (or (not (= X tptp.zero_z3403309356797280102nteger)) (not (= Y tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N)))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N)))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))))
% 9.16/7.08 (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))))))))))))
% 9.16/7.08 (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))))))))))))
% 9.16/7.08 (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))))))))))))
% 9.16/7.08 (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))))))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C3)))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C3)))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C3 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N) K)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A4) B6)) C))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A4) B6)) C))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) B6)) C))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A4) B6)) C))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A4) B6)) C))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A4) B6)) C))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M) N))))))
% 9.16/7.08 (assert (forall ((Q3 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q3)) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N) Q3))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N)) B))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N)) B))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) B))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N)))))))
% 9.16/7.08 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N)))))))
% 9.16/7.08 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N)))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K (@ tptp.suc J3))))))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (not (= K (@ tptp.suc J3)))))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (or (@ P N) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (@ P N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M5 tptp.nat)) (and (= M (@ tptp.suc M5)) (@ (@ tptp.ord_less_nat N) M5))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I3 tptp.nat)) (@ (@ P I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J3) (=> (@ (@ tptp.ord_less_nat J3) K2) (=> (@ _let_1 J3) (=> (@ (@ P J3) K2) (@ _let_1 K2))))))) (@ (@ P I) J))))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I3 tptp.nat)) (=> (= J (@ tptp.suc I3)) (@ P I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ P (@ tptp.suc I3)) (@ P I3)))) (@ P I))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 9.16/7.08 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 9.16/7.08 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger)) (and (not (= A tptp.zero_z3403309356797280102nteger)) (not (= B tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger) (or (= A tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (not (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (= A B)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.assn)) (@ (@ tptp.dvd_dvd_assn tptp.one_one_assn) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int)))))
% 9.16/7.08 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (not (= (@ (@ tptp.power_8256067586552552935nteger A) N) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N2 tptp.nat)) (not (= X (@ tptp.suc N2))))))))
% 9.16/7.08 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 9.16/7.08 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 9.16/7.08 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc N2)))) (@ P N)))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X3) Y3) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P M) N))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 9.16/7.08 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M2 tptp.nat)) (= N (@ tptp.suc M2))))))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 9.16/7.08 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 9.16/7.08 (assert (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B4 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B4 tptp.zero_zero_complex)))))
% 9.16/7.08 (assert (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B4 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B4 tptp.zero_zero_real)))))
% 9.16/7.08 (assert (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B4 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B4 tptp.zero_zero_rat)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B2 tptp.nat)) (= (@ (@ P A5) B2) (@ (@ P B2) A5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) tptp.zero_zero_nat)) (=> (forall ((A5 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A5) B2))))) (@ (@ P A) B))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 9.16/7.08 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) P) P)))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 9.16/7.08 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (let ((_let_1 (not (= A tptp.zero_zero_nat)))) (= _let_1 (and (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat) _let_1)))))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 9.16/7.08 (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)))))))))))))
% 9.16/7.08 (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)))))))))))))
% 9.16/7.08 (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)))))))))))))
% 9.16/7.08 (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)))))))))))))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B2 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B2) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B2)))))))))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B2 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B2) tptp.one_one_nat) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_nat A) B2) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B2)))))))))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B2 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B2) tptp.one_one_int) (=> (= (@ _let_1 A) B2) (=> (= (@ _let_1 B2) A) (=> (= (@ (@ tptp.times_times_int A) B2) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B2)))))))))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I2)) J2)) (@ P I2))))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_z3403309356797280102nteger))) (and (not _let_2) (@ _let_1 A))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((Q3 tptp.num) (N 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 N))) _let_1))))))
% 9.16/7.08 (assert (forall ((Q3 tptp.num) (N 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 N))) _let_1))))))
% 9.16/7.08 (assert (forall ((Q3 tptp.num) (N 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 N))) _let_1))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 9.16/7.08 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N)) N)) (@ (@ tptp.modulo_modulo_nat A2) N)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 9.16/7.08 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 9.16/7.08 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 9.16/7.08 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 9.16/7.08 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 9.16/7.08 (assert (= tptp.ord_less_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (exists ((K3 tptp.nat)) (= N3 (@ tptp.suc (@ (@ tptp.plus_plus_nat M4) K3)))))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q5 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q5)))))))))
% 9.16/7.08 (assert (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))))
% 9.16/7.08 (assert (forall ((X tptp.assn) (Y tptp.assn) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_assn X) Y) tptp.one_one_assn) (= (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn X) N)) (@ (@ tptp.power_power_assn Y) N)) tptp.one_one_assn))))
% 9.16/7.08 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) N)) tptp.one_one_real))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))))
% 9.16/7.08 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)) tptp.one_one_Code_integer))))
% 9.16/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) N)) tptp.one_one_complex))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 9.16/7.08 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_complex A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 9.16/7.08 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I))))
% 9.16/7.08 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 9.16/7.08 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 9.16/7.08 (assert (= tptp.suc (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))) (or (not (= X tptp.zero_z3403309356797280102nteger)) (not (= Y tptp.zero_z3403309356797280102nteger)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ P N))))))
% 9.16/7.08 (assert (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ tptp.vEBT_V441764108873111860ildupi _let_1) _let_1)))
% 9.16/7.08 (assert (= (@ tptp.vEBT_V441764108873111860ildupi tptp.zero_zero_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q3)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N)) Q3))) (@ _let_1 N)))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real B4) A3))))
% 9.16/7.08 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat B4) A3))))
% 9.16/7.08 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A3))))
% 9.16/7.08 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A3))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 9.16/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 9.16/7.08 (assert (= tptp.times_times_assn (lambda ((A3 tptp.assn) (B4 tptp.assn)) (@ (@ tptp.times_times_assn B4) A3))))
% 9.16/7.08 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B4 tptp.real)) (@ (@ tptp.times_times_real B4) A3))))
% 9.16/7.08 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.times_times_nat B4) A3))))
% 9.16/7.08 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B4 tptp.int)) (@ (@ tptp.times_times_int B4) A3))))
% 9.16/7.08 (assert (= tptp.times_3573771949741848930nteger (lambda ((A3 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger B4) A3))))
% 9.16/7.08 (assert (= tptp.times_times_complex (lambda ((A3 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.times_times_complex B4) A3))))
% 9.16/7.08 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn B))) (let ((_let_2 (@ tptp.times_times_assn A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 9.16/7.08 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D2) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D2) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D2) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D2)))))))))
% 9.16/7.08 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 9.16/7.08 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 9.16/7.08 (assert (= (@ (@ tptp.power_8256067586552552935nteger tptp.one_one_Code_integer) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 9.16/7.08 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 9.16/7.08 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 9.16/7.08 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 9.16/7.08 (assert (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 9.16/7.08 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 9.16/7.08 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_z3403309356797280102nteger)) (not (= (@ _let_1 M) tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_z3403309356797280102nteger)) (not (= (@ _let_1 N) tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_Code_integer))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_nat))))))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B2)) tptp.one_one_int))))))))
% 9.16/7.08 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N)) (@ _let_1 M)))))))))
% 9.16/7.08 (assert (forall ((Y tptp.nat) (N tptp.nat) (X tptp.nat) (M tptp.nat) (Sz tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (=> (@ (@ tptp.ord_less_nat Y) _let_2) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 M)) (=> (= Sz (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat X) _let_2)) Y)) (@ _let_1 Sz)))))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (X tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X Y))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) N) (= (@ (@ tptp.modulo_modulo_nat A) N) A))))
% 9.16/7.08 (assert (forall ((C tptp.nat) (R2 tptp.nat) (B tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (=> (@ (@ tptp.ord_less_nat R2) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat Q3) C))) R2)) (@ _let_1 C)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M)) N) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat M) N)) K)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (= (@ (@ tptp.divide_divide_int A) B) A) (= B tptp.one_one_int)))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 9.16/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.power_power_int _let_1) N))) tptp.one_one_int))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A2) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ tptp.divide_divide_int B3) N))))))))
% 9.16/7.08 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N2)) Y))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((M tptp.int) (A tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int M) N))) M) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) M)) N)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N)) A))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_1)) _let_1))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_1)) _let_1))))
% 9.16/7.08 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (and (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) X)) X)) _let_1) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.zero_zero_int) X)) X)) _let_1) tptp.zero_zero_int)))))
% 9.16/7.08 (assert (forall ((N tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int N) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (or (= _let_1 tptp.zero_zero_int) (= _let_1 tptp.one_one_int)))))
% 9.16/7.08 (assert (forall ((K tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 9.16/7.08 (assert (forall ((A2 tptp.int) (N tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N)) N)) (@ (@ tptp.modulo_modulo_int A2) N)))))
% 9.16/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X) N2))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N) A)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X3) (= (@ (@ tptp.power_power_real X3) N) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N) A)) (= Y4 X3)))))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.times_times_int _let_1))) (let ((_let_4 (@ tptp.plus_plus_int tptp.one_one_int))) (= (@ (@ tptp.modulo_modulo_int (@ _let_4 (@ _let_3 B))) (@ _let_3 _let_2)) (@ _let_4 (@ _let_3 (@ (@ tptp.modulo_modulo_int B) _let_2))))))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.times_times_int _let_1))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ _let_3 B)) tptp.one_one_int)) (@ _let_3 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ (@ tptp.modulo_modulo_int B) _let_2))) tptp.one_one_int)))))))
% 9.16/7.08 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) B)) tptp.one_one_int)) _let_1) tptp.one_one_int))))
% 9.16/7.08 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (and (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) X)) X)) _let_1) X) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.zero_zero_int) X)) X)) _let_1) X)))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (not (@ (@ tptp.ord_less_real T) X5)))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (not (@ (@ tptp.ord_less_rat T) X5)))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (not (@ (@ tptp.ord_less_num T) X5)))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (@ (@ tptp.ord_less_nat T) X5)))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (not (@ (@ tptp.ord_less_int T) X5)))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X5))) (=> (@ _let_1 Z3) (@ _let_1 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z4) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (@ (@ tptp.ord_less_real T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (@ (@ tptp.ord_less_rat T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (@ (@ tptp.ord_less_num T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (@ (@ tptp.ord_less_nat T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (@ (@ tptp.ord_less_int T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (not (@ (@ tptp.ord_less_real X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (not (@ (@ tptp.ord_less_rat X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (not (@ (@ tptp.ord_less_num X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (@ (@ tptp.ord_less_nat X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (not (@ (@ tptp.ord_less_int X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (not (= X5 T)))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.real Bool)) (P3 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q4 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.rat Bool)) (P3 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.num Bool)) (P3 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.int Bool)) (P3 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ P3 X5) (@ Q4 X5))))))))))
% 9.16/7.08 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va))))))))))
% 9.16/7.08 (assert (forall ((B tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) N))) (=> (@ (@ tptp.ord_less_nat B) N) (=> (= _let_1 (@ (@ tptp.modulo_modulo_nat B) N)) (= _let_1 B))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (X tptp.nat) (M tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) X)) M) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) X)) M)) (= (@ (@ tptp.modulo_modulo_nat A) M) (@ (@ tptp.modulo_modulo_nat B) M)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X5) S)))) (=> (@ (@ tptp.ord_less_real Z3) X5) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X5) S)))) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X5) S)))) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X5) S)))) (=> (@ (@ tptp.ord_less_int Z3) X5) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X5) S))))) (=> (@ (@ tptp.ord_less_real Z3) X5) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X5) S))))) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X5) S))))) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X5) S))))) (=> (@ (@ tptp.ord_less_int Z3) X5) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X5) S)))) (=> (@ (@ tptp.ord_less_real X5) Z3) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X5) S)))) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X5) S)))) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X5) S)))) (=> (@ (@ tptp.ord_less_int X5) Z3) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.real) (S tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D2) (@ (@ tptp.plus_plus_real X5) S))))) (=> (@ (@ tptp.ord_less_real X5) Z3) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.rat) (S tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X5) S))))) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.nat) (S tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X5) S))))) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((D2 tptp.int) (S tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X5) S))))) (=> (@ (@ tptp.ord_less_int X5) Z3) (= _let_1 _let_1)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_nat B) N) (= (@ (@ tptp.modulo_modulo_nat B) N) B)))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M)) N) (@ (@ tptp.modulo_modulo_nat M) N))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) B)) tptp.one_one_int)) _let_1) B))))
% 9.16/7.08 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A) C)) B)))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N) X)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((L tptp.nat) (K tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat D2))) (=> (= (@ (@ tptp.plus_plus_nat L) K) (@ _let_1 (@ (@ tptp.modulo_modulo_nat K) L))) (=> (@ (@ tptp.ord_less_nat N) L) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 N)) L) N))))))
% 9.16/7.08 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 9.16/7.08 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 9.16/7.08 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 9.16/7.08 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (A4 tptp.nat) (B tptp.nat) (B6 tptp.nat) (N4 tptp.nat)) (=> (= A A4) (=> (@ (@ tptp.ord_less_nat B) B6) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) N4)) B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A4) N4)) B6))))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (D2 tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D2)) (@ (@ tptp.vEBT_VEBT_low X) D2)) D2) X)))
% 9.16/7.08 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 9.16/7.08 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 9.16/7.08 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.08 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 9.16/7.08 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 9.16/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 9.16/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 9.16/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 9.16/7.08 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 9.16/7.08 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 9.16/7.08 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.08 (assert (forall ((M tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D2) tptp.zero_zero_int) (exists ((Q5 tptp.int)) (= M (@ (@ tptp.times_times_int D2) Q5))))))
% 9.16/7.08 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M) N))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((M tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D2) tptp.zero_zero_int) (exists ((Q6 tptp.int)) (= M (@ (@ tptp.times_times_int D2) Q6))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))))
% 9.16/7.08 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 9.16/7.08 (assert (forall ((N tptp.int) (M tptp.int) (K tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int N) M) K) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int N) A)) M) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int K) A)) M)))))
% 9.16/7.08 (assert (forall ((B tptp.int) (B6 tptp.int) (X tptp.int) (X6 tptp.int) (Y tptp.int) (Y5 tptp.int) (Z5 tptp.int)) (=> (= B B6) (=> (= (@ (@ tptp.modulo_modulo_int X) B6) (@ (@ tptp.modulo_modulo_int X6) B6)) (=> (= (@ (@ tptp.modulo_modulo_int Y) B6) (@ (@ tptp.modulo_modulo_int Y5) B6)) (=> (= (@ (@ tptp.plus_plus_int X6) Y5) Z5) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int X) Y)) B) (@ (@ tptp.modulo_modulo_int Z5) B6))))))))
% 9.16/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 9.16/7.08 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I))))))
% 9.16/7.08 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 9.16/7.08 (assert (forall ((L tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L) L)))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N2 tptp.extended_enat)) (=> (forall ((M3 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M3) N2) (@ P M3))) (@ P N2))) (@ P N))))
% 9.16/7.08 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 9.16/7.08 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.08 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N) (not (@ (@ tptp.dvd_dvd_int N) M))))))
% 9.16/7.08 (assert (= tptp.neg_numeral_dbl_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real X2) X2))))
% 9.16/7.08 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat X2) X2))))
% 9.16/7.08 (assert (= tptp.neg_numeral_dbl_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int X2) X2))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N)) (@ _let_1 N)))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (A2 tptp.nat) (B tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) A2) (=> (@ (@ tptp.ord_less_nat B) N4) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) N4)) B)) (@ (@ tptp.times_times_nat A2) N4))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (A4 tptp.nat) (B tptp.nat) (N4 tptp.nat) (B6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) A4) (=> (@ (@ tptp.ord_less_nat B) N4) (=> (@ (@ tptp.ord_less_nat B6) N4) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) N4)) B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A4) N4)) B6)))))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc X)) (@ P I2))) (and (@ P tptp.zero_zero_nat) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) X) (@ P (@ tptp.suc I2))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc tptp.zero_zero_nat)) (@ P I2))) (@ P tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ tptp.suc X))) (@ P I2))) (and (@ P tptp.zero_zero_nat) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc X)) (@ P (@ tptp.suc I2))))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D2)))))))))
% 9.16/7.08 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D2)))))))))
% 9.16/7.08 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D2)))))))))
% 9.16/7.08 (assert (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D2)))))))))
% 9.16/7.08 (assert (forall ((R2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger R2))) (=> (not (= R2 tptp.zero_z3403309356797280102nteger)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ _let_1 C)) (@ (@ tptp.plus_p5714425477246183910nteger B) (@ _let_1 D2)))))))))
% 9.16/7.08 (assert (forall ((R2 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D2)))))))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 9.16/7.08 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 9.16/7.08 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 9.16/7.08 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 9.16/7.08 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 9.16/7.08 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 9.16/7.08 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 9.16/7.08 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 9.16/7.08 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 9.16/7.08 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 9.16/7.08 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 9.16/7.08 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 9.16/7.08 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 9.16/7.08 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N) (@ tptp.zero_n2687167440665602831ol_nat (not (= N _let_1)))))))
% 9.16/7.08 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P4))) P4)))
% 9.16/7.08 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P4))) P4)))
% 9.16/7.08 (assert (forall ((P4 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P4))) P4)))
% 9.16/7.08 (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)))
% 9.16/7.08 (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)))
% 9.16/7.08 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.08 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 9.16/7.08 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 9.16/7.08 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 9.16/7.08 (assert (forall ((P4 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P4) (@ tptp.zero_n2687167440665602831ol_nat Q3)) (= P4 Q3))))
% 9.16/7.08 (assert (forall ((P4 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P4) (@ tptp.zero_n2684676970156552555ol_int Q3)) (= P4 Q3))))
% 9.16/7.08 (assert (forall ((P4 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P4) (@ tptp.zero_n356916108424825756nteger Q3)) (= P4 Q3))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n1201886186963655149omplex (and P Q)) (@ (@ tptp.times_times_complex (@ tptp.zero_n1201886186963655149omplex P)) (@ tptp.zero_n1201886186963655149omplex Q)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 9.16/7.08 (assert (forall ((P (-> tptp.complex Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P4)) (not (or (and P4 (not (@ P tptp.one_one_complex))) (and (not P4) (not (@ P tptp.zero_zero_complex))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.real Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P4)) (not (or (and P4 (not (@ P tptp.one_one_real))) (and (not P4) (not (@ P tptp.zero_zero_real))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.rat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P4)) (not (or (and P4 (not (@ P tptp.one_one_rat))) (and (not P4) (not (@ P tptp.zero_zero_rat))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P4)) (not (or (and P4 (not (@ P tptp.one_one_nat))) (and (not P4) (not (@ P tptp.zero_zero_nat))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.int Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P4)) (not (or (and P4 (not (@ P tptp.one_one_int))) (and (not P4) (not (@ P tptp.zero_zero_int))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.code_integer Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P4)) (not (or (and P4 (not (@ P tptp.one_one_Code_integer))) (and (not P4) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.complex Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P4)) (and (=> P4 (@ P tptp.one_one_complex)) (=> (not P4) (@ P tptp.zero_zero_complex))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.real Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P4)) (and (=> P4 (@ P tptp.one_one_real)) (=> (not P4) (@ P tptp.zero_zero_real))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.rat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P4)) (and (=> P4 (@ P tptp.one_one_rat)) (=> (not P4) (@ P tptp.zero_zero_rat))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P4)) (and (=> P4 (@ P tptp.one_one_nat)) (=> (not P4) (@ P tptp.zero_zero_nat))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.int Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P4)) (and (=> P4 (@ P tptp.one_one_int)) (=> (not P4) (@ P tptp.zero_zero_int))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.code_integer Bool)) (P4 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P4)) (and (=> P4 (@ P tptp.one_one_Code_integer)) (=> (not P4) (@ P tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.08 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))))
% 9.16/7.08 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))))
% 9.16/7.08 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))))
% 9.16/7.08 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))
% 9.16/7.08 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))
% 9.16/7.08 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B2)) (@ (@ tptp.times_times_nat _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 9.16/7.08 (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) (B2 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B2)) (@ (@ tptp.times_times_int _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 9.16/7.08 (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) (B2 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B2)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 9.16/7.08 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 9.16/7.08 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 9.16/7.08 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 9.16/7.08 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_rat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_real (@ _let_2 D2)) (@ _let_1 C)))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_nat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_int (@ _let_2 D2)) (@ _let_1 C)))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 D2)) (@ _let_1 C)))))))))
% 9.16/7.08 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_complex (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_complex (@ _let_2 D2)) (@ _let_1 C)))))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((W tptp.code_integer) (Y tptp.code_integer) (X tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger X))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger W))) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) tptp.zero_zero_nat) (@ P I4))))
% 9.16/7.08 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (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_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) _let_1)) tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (and _let_2 (= A tptp.zero_z3403309356797280102nteger)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 (@ tptp.suc K)))) (let ((_let_3 (@ (@ tptp.plus_plus_int A) (@ _let_1 K)))) (=> (@ (@ tptp.ord_less_int _let_3) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int _let_3) _let_2)) (@ (@ tptp.modulo_modulo_int _let_3) _let_2))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (assert (forall ((X tptp.option_nat)) (not (@ (@ tptp.ord_less_option_nat X) tptp.none_nat))))
% 9.16/7.08 (assert (forall ((X tptp.option_num)) (not (@ (@ tptp.ord_less_option_num X) tptp.none_num))))
% 9.16/7.08 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) Xs) (@ (@ tptp.ord_less_eq_nat X2) Y6)))))))
% 9.16/7.08 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Xs) (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.member_nat Y6) Xs) (@ (@ tptp.ord_less_eq_nat Y6) X2)))))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 9.16/7.08 (assert (forall ((X tptp.option_nat)) (@ (@ tptp.ord_le5914376470875661696on_nat tptp.none_nat) X)))
% 9.16/7.08 (assert (forall ((X tptp.option_num)) (@ (@ tptp.ord_le6622620407824499402on_num tptp.none_num) X)))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 9.16/7.08 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 9.16/7.08 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((B tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 9.16/7.08 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 9.16/7.08 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 9.16/7.08 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (= X Y))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (W tptp.num)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (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_8256067586552552935nteger A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N)) (@ F N5))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N5))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N5))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N5))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N5))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N5)) (@ F N))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N))))))
% 9.16/7.08 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 9.16/7.08 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 9.16/7.08 (assert (forall ((A tptp.int) (X tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X) (= A X) (@ (@ tptp.ord_less_eq_int X) A))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((X tptp.option_nat)) (@ (@ tptp.ord_le5914376470875661696on_nat tptp.none_nat) X)))
% 9.16/7.08 (assert (forall ((X tptp.option_num)) (@ (@ tptp.ord_le6622620407824499402on_num tptp.none_num) X)))
% 9.16/7.08 (assert (forall ((X tptp.option_nat)) (=> (@ (@ tptp.ord_le5914376470875661696on_nat X) tptp.none_nat) (= X tptp.none_nat))))
% 9.16/7.08 (assert (forall ((X tptp.option_num)) (=> (@ (@ tptp.ord_le6622620407824499402on_num X) tptp.none_num) (= X tptp.none_num))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 9.16/7.08 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 9.16/7.08 (assert (forall ((B6 tptp.real) (A4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B6) A4)) (@ (@ tptp.ord_less_real A4) B6))))
% 9.16/7.08 (assert (forall ((B6 tptp.rat) (A4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B6) A4)) (@ (@ tptp.ord_less_rat A4) B6))))
% 9.16/7.08 (assert (forall ((B6 tptp.num) (A4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B6) A4)) (@ (@ tptp.ord_less_num A4) B6))))
% 9.16/7.08 (assert (forall ((B6 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B6) A4)) (@ (@ tptp.ord_less_nat A4) B6))))
% 9.16/7.08 (assert (forall ((B6 tptp.int) (A4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B6) A4)) (@ (@ tptp.ord_less_int A4) B6))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (not (@ (@ tptp.ord_less_eq_real X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (not (@ (@ tptp.ord_less_eq_rat X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (not (@ (@ tptp.ord_less_eq_num X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (not (@ (@ tptp.ord_less_eq_int X5) T)))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (@ (@ tptp.ord_less_eq_real T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (@ (@ tptp.ord_less_eq_rat T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (@ (@ tptp.ord_less_eq_num T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (@ (@ tptp.ord_less_eq_nat T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (@ (@ tptp.ord_less_eq_int T) X5))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (@ (@ tptp.ord_less_eq_real X5) T))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (@ (@ tptp.ord_less_eq_rat X5) T))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (@ (@ tptp.ord_less_eq_num X5) T))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (@ (@ tptp.ord_less_eq_nat X5) T))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (@ (@ tptp.ord_less_eq_int X5) T))))))
% 9.16/7.08 (assert (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (not (@ (@ tptp.ord_less_eq_real T) X5)))))))
% 9.16/7.08 (assert (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (not (@ (@ tptp.ord_less_eq_rat T) X5)))))))
% 9.16/7.08 (assert (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (not (@ (@ tptp.ord_less_eq_num T) X5)))))))
% 9.16/7.08 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))))
% 9.16/7.08 (assert (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (not (@ (@ tptp.ord_less_eq_int T) X5)))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (exists ((C4 tptp.nat)) (= B4 (@ (@ tptp.plus_plus_nat A3) C4))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 9.16/7.08 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M6) (exists ((M2 tptp.nat)) (= M6 (@ tptp.suc M2))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M3)) N2) (@ P M3))) (@ P N2))) (@ P N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X3 tptp.nat)) (@ (@ R X3) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((N2 tptp.nat)) (@ (@ R N2) (@ tptp.suc N2))) (@ (@ R M) N)))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (=> (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N6) N) (not (@ P N6)))) (@ P N)) (exists ((N7 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat N7) N) (@ P N7))))))
% 9.16/7.08 (assert (= tptp.ord_less_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M4) N3) (not (= M4 N3))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.08 (assert (= tptp.ord_less_eq_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (or (@ (@ tptp.ord_less_nat M4) N3) (= M4 N3)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J3) (@ (@ tptp.ord_less_nat (@ F I3)) (@ F J3)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 9.16/7.08 (assert (= tptp.ord_less_eq_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (exists ((K3 tptp.nat)) (= N3 (@ (@ tptp.plus_plus_nat M4) K3))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N2 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N2))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 9.16/7.08 (assert (= tptp.ord_less_eq_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y6) (= X2 Y6)))))
% 9.16/7.08 (assert (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P3)) (= (and (@ _let_1 X) P) (and _let_2 P3))))))))
% 9.16/7.08 (assert (forall ((X tptp.int) (X6 tptp.int) (P Bool) (P3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X6))) (=> (= X X6) (=> (=> _let_2 (= P P3)) (= (=> (@ _let_1 X) P) (=> _let_2 P3))))))))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 9.16/7.08 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 9.16/7.08 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 9.16/7.08 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 9.16/7.08 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N4)) (@ _let_1 N))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 9.16/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 9.16/7.08 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger Z))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 9.16/7.08 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 9.16/7.08 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 9.16/7.08 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 9.16/7.08 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 9.16/7.08 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) A))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) B))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ _let_1 B)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ _let_1 B))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 9.16/7.08 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N2) (@ P Nn))) (@ P (@ tptp.suc N2)))) (@ P N)))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N2) (@ P Nn))) (@ P (@ tptp.suc N2)))) (@ P N)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc A))) (= (and (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat B) _let_1)) (= B _let_1)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat B) (@ tptp.suc A))) (= B A))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P (@ tptp.suc N2)) (@ P N2))))) (@ P I))))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P N2) (@ P (@ tptp.suc N2)))))) (@ P J))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K2) (not (@ P I4)))) (@ P K2)))))))
% 9.16/7.08 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_nat (@ F M2)) (@ F N2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 9.16/7.08 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) X) (not (= X tptp.zero_zero_nat)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 9.16/7.08 (assert (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) M))))))
% 9.16/7.08 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) M))))))
% 9.16/7.08 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) M))))))
% 9.16/7.08 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) M))))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (A4 tptp.nat) (B tptp.nat) (B6 tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) A4) (=> (@ (@ tptp.ord_less_eq_nat B) B6) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) N4)) B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A4) N4)) B6))))))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 9.16/7.08 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N)) M)))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N))) M)))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)))
% 9.16/7.08 (assert (forall ((K tptp.int) (I tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_int M) N) (=> (@ (@ tptp.dvd_dvd_int N) M) (= M N))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 9.16/7.08 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger Y) X)) X)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Y)) X)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) A)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.one_one_real)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer)))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_8256067586552552935nteger A) _let_2) (@ (@ tptp.power_8256067586552552935nteger B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) _let_1)) (@ (@ tptp.power_8256067586552552935nteger B) _let_1)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K2) (not (@ P I4)))) (@ P (@ tptp.suc K2))))))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I) (@ _let_1 (@ (@ tptp.power_power_nat I) N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M)))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N)) (and (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N))))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 9.16/7.08 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 9.16/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 9.16/7.08 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 9.16/7.08 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L)) tptp.zero_zero_int))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((N tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int B) N)) (= (@ (@ tptp.modulo_modulo_int B) N) B)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (N tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) N) (=> (= _let_1 (@ (@ tptp.modulo_modulo_int B) N)) (= _let_1 B)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.modulo_modulo_int A) N))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N) Q3)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (forall ((S2 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q3) S2))))))))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N) Q3)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (forall ((S2 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q3) S2))))))))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q5 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N) Q5))))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) A)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.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)))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B6 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) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B6)) (@ _let_1 B))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B6 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) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B6))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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) (and (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ _let_1 (@ (@ tptp.divide_divide_int A) B))))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (=> (@ (@ tptp.ord_less_real Z3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 9.16/7.08 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (=> (@ (@ tptp.ord_less_rat Z3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V) Y))) A)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))))))))
% 9.16/7.08 (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)))))))))))
% 9.16/7.08 (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))))))))))))
% 9.16/7.08 (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))))))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) A)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N))) A)))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (= (@ (@ tptp.power_8256067586552552935nteger A) N) (@ (@ tptp.power_8256067586552552935nteger B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_8256067586552552935nteger A) N) (@ (@ tptp.power_8256067586552552935nteger B) N)) (= A B))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))))
% 9.16/7.08 (assert (forall ((X tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 9.16/7.08 (assert (forall ((X tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (Q3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q3)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q3))) (= (@ (@ tptp.divide_divide_nat M) N) Q3))))))
% 9.16/7.08 (assert (forall ((Q3 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N) Q3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q3)) N)))))
% 9.16/7.08 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) C)) A) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.divide_divide_nat A) C))))))
% 9.16/7.08 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.08 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 9.16/7.08 (assert (forall ((X tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ _let_1 tptp.one_one_int)) (@ _let_1 X)))))))
% 9.16/7.08 (assert (forall ((B6 tptp.int) (Q7 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 B6) Q7)) R4)) (=> (@ (@ tptp.ord_less_int R4) B6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B6) (@ _let_1 Q7)))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (Q3 tptp.int) (R2 tptp.int) (B6 tptp.int) (Q7 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 B6) Q7)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B6) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int Q3) Q7)))))))))))
% 9.16/7.08 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D2)))) (=> (@ (@ 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) D2))))))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (Q3 tptp.int) (R2 tptp.int) (B6 tptp.int) (Q7 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B6) Q7)) 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) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int Q7) Q3))))))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (Q7 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 Q7)) 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 Q7) Q3))))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (Q7 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 Q7)) 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) Q7)))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((B tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) N)) (@ (@ tptp.modulo_modulo_int B) N))))))
% 9.16/7.08 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.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))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V) Y))) A)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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))))))))))))
% 9.16/7.08 (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))))))))))))
% 9.16/7.08 (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)))))))))))))
% 9.16/7.08 (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)))))))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_8256067586552552935nteger X) _let_2) (@ (@ tptp.power_8256067586552552935nteger Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q6 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q6)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q6))) (@ P Q6))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.08 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I2 tptp.int) (J2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J2) (@ (@ tptp.ord_less_int J2) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J2))) (@ P J2)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I2 tptp.int) (J2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J2) (@ (@ tptp.ord_less_eq_int J2) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J2))) (@ P J2))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I2 tptp.int) (J2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J2) (@ (@ tptp.ord_less_int J2) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J2))) (@ P I2)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I2 tptp.int) (J2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J2) (@ (@ tptp.ord_less_eq_int J2) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J2))) (@ P I2))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ _let_1 N))) (let ((_let_3 (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 M)))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 9.16/7.08 (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))))))))
% 9.16/7.08 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (@ (@ tptp.ord_le6747313008572928689nteger X) Y))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (@ _let_1 A))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ _let_1 A))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (@ _let_1 A))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N)))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N)))))
% 9.16/7.08 (assert (forall ((V tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat V) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) (@ _let_1 M))) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 9.16/7.08 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A) C))) (@ (@ tptp.times_times_real B) D2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D2) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 9.16/7.08 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N))))))
% 9.16/7.08 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N))))))
% 9.16/7.08 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I2 tptp.int) (J2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J2) (@ (@ tptp.ord_less_int J2) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J2))) (@ (@ P I2) J2)))))))
% 9.16/7.08 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I2 tptp.int) (J2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J2) (@ (@ tptp.ord_less_eq_int J2) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I2)) J2))) (@ (@ P I2) J2)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (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)))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 9.16/7.08 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 9.16/7.08 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (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))))))))))
% 9.16/7.08 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (and _let_1 (= A tptp.zero_z3403309356797280102nteger))))))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat N) M) (@ tptp.suc tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M))))))
% 9.16/7.08 (assert (forall ((N5 tptp.nat) (N tptp.nat) (K4 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.times_times_nat (@ _let_1 N)) K))) (let ((_let_3 (@ tptp.times_times_nat (@ _let_1 N5)))) (=> (@ (@ tptp.ord_less_eq_nat N5) N) (=> (@ (@ tptp.ord_less_nat (@ _let_3 K4)) _let_2) (@ (@ tptp.ord_less_eq_nat (@ _let_3 (@ (@ tptp.plus_plus_nat K4) tptp.one_one_nat))) _let_2))))))))
% 9.16/7.08 (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)))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((N tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ _let_2 N) (=> (@ _let_2 D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D2) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 N)) D2) (@ _let_1 (@ (@ tptp.modulo_modulo_int N) D2))))))))))
% 9.16/7.08 (assert (forall ((N tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 N) (=> (@ _let_1 D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D2) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int N) tptp.one_one_int)) D2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int N) D2)) tptp.one_one_int))))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt (@ tptp.vEBT_vebt_buildup N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.power_power_real _let_1) N))))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real _let_1) N))))))
% 9.16/7.08 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.vEBT_VEBT_cnt T))))
% 9.16/7.08 (assert (forall ((K tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) K))) (let ((_let_3 (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_3) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) _let_2)) (@ (@ tptp.times_times_int _let_1) _let_2))) _let_3)))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 (@ tptp.suc K)))) (let ((_let_3 (@ _let_1 K))) (let ((_let_4 (@ (@ tptp.plus_plus_int A) _let_3))) (=> (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int _let_4) _let_2)) (@ (@ tptp.modulo_modulo_int _let_4) _let_2)))))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 9.16/7.08 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 9.16/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 9.16/7.08 (assert (forall ((B tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int B)) B)))
% 9.16/7.08 (assert (forall ((B tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real B)) B)))
% 9.16/7.08 (assert (forall ((B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger B)) B)))
% 9.16/7.08 (assert (forall ((B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex B)) B)))
% 9.16/7.08 (assert (forall ((B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat B)) B)))
% 9.16/7.08 (assert (forall ((X32 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X32) (@ tptp.bit1 Y32)) (= X32 Y32))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 9.16/7.08 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N)) (= M N))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 9.16/7.08 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 9.16/7.08 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 9.16/7.08 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.08 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 9.16/7.08 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 9.16/7.08 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.08 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 9.16/7.08 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 9.16/7.08 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.08 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 9.16/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) A) B)))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M N))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M N))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 9.16/7.08 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M N))))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 9.16/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 9.16/7.08 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 9.16/7.08 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 9.16/7.08 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 9.16/7.08 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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)))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))))
% 9.16/7.08 (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))))
% 9.16/7.08 (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))))
% 9.16/7.08 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.dvd_dvd_int X) Y))))
% 9.16/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y) (@ (@ tptp.dvd_dvd_real X) Y))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X)) Y) (@ (@ tptp.dvd_dvd_complex X) Y))))
% 9.16/7.09 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X)) Y) (@ (@ tptp.dvd_dvd_rat X) Y))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt (@ tptp.vEBT_vebt_buildup N))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) N)))))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 9.16/7.09 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 9.16/7.09 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 9.16/7.09 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 9.16/7.09 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 9.16/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 9.16/7.09 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((V tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger V))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger B) _let_1))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 9.16/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.09 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 9.16/7.09 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 9.16/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 9.16/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.09 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 9.16/7.09 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 9.16/7.09 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 9.16/7.09 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 9.16/7.09 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 9.16/7.09 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 9.16/7.09 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 9.16/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 9.16/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 9.16/7.09 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 9.16/7.09 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ 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)))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 9.16/7.09 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 9.16/7.09 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 9.16/7.09 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 9.16/7.09 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 9.16/7.09 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 9.16/7.09 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 9.16/7.09 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 9.16/7.09 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 9.16/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 9.16/7.09 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 9.16/7.09 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 9.16/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 9.16/7.09 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 9.16/7.09 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 9.16/7.09 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 9.16/7.09 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 9.16/7.09 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 9.16/7.09 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 9.16/7.09 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 9.16/7.09 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 9.16/7.09 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 9.16/7.09 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger X) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W) (@ tptp.semiri4939895301339042750nteger X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger M)) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))))
% 9.16/7.09 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 9.16/7.09 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 9.16/7.09 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 9.16/7.09 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 9.16/7.09 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 9.16/7.09 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 9.16/7.09 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 9.16/7.09 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 9.16/7.09 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 9.16/7.09 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 9.16/7.09 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 9.16/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat))))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) tptp.one)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N)))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 9.16/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 9.16/7.09 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N) (@ tptp.semiri4939895301339042750nteger Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.semiri681578069525770553at_rat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))))
% 9.16/7.09 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))))
% 9.16/7.09 (assert (forall ((N tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (= (@ (@ tptp.divide_divide_int A) B) (@ tptp.uminus_uminus_int A)) (= B (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 9.16/7.09 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 9.16/7.09 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))
% 9.16/7.09 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 9.16/7.09 (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))
% 9.16/7.09 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.power_power_complex A) N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real)))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_complex)))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N) tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N) tptp.one_one_real))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N) tptp.one_one_Code_integer))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N) tptp.one_one_complex))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int _let_1) N) _let_1)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real _let_1) N) _let_1)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N) _let_1)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex _let_1) N) _let_1)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat _let_1) N) _let_1)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I)) N)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 9.16/7.09 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (or (@ (@ tptp.ord_less_nat M) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int)) (= N tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 9.16/7.09 (assert (= tptp.vEBT_VEBT_cnt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_cnt2 T2)))))
% 9.16/7.09 (assert (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L) (@ tptp.uminus_uminus_int L))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X3)))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 9.16/7.09 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B4)))))
% 9.16/7.09 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B4)))))
% 9.16/7.09 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B4)))))
% 9.16/7.09 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B4)))))
% 9.16/7.09 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B4)))))
% 9.16/7.09 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B4)))))
% 9.16/7.09 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B4 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B4)))))
% 9.16/7.09 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B4)))))
% 9.16/7.09 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B4)))))
% 9.16/7.09 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B4)))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 C)) B) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) C)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 9.16/7.09 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (=> (= (@ (@ tptp.minus_minus_complex A) B) (@ (@ tptp.minus_minus_complex C) D2)) (= (= A B) (= C D2)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D2)) (= (= A B) (= C D2)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (= A B) (= C D2)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A B) (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A B) (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (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))))))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger X))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ (@ tptp.times_3573771949741848930nteger Y) _let_1)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (= (lambda ((Y2 tptp.rat) (Z2 tptp.rat)) (= Y2 Z2)) (lambda ((A3 tptp.rat) (B4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B4) tptp.zero_zero_rat))))
% 9.16/7.09 (assert (= (lambda ((Y2 tptp.complex) (Z2 tptp.complex)) (= Y2 Z2)) (lambda ((A3 tptp.complex) (B4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B4) tptp.zero_zero_complex))))
% 9.16/7.09 (assert (= (lambda ((Y2 tptp.real) (Z2 tptp.real)) (= Y2 Z2)) (lambda ((A3 tptp.real) (B4 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B4) tptp.zero_zero_real))))
% 9.16/7.09 (assert (= (lambda ((Y2 tptp.int) (Z2 tptp.int)) (= Y2 Z2)) (lambda ((A3 tptp.int) (B4 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B4) tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D2)) (= (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real C) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D2)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real) (D2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real D2) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D2))))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D2) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real) (D2 tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D2) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D2))))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D2) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D2)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D2)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex) (D2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) C)) (@ (@ tptp.plus_plus_complex B) D2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex C) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D2)))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D4))))) (forall ((X5 tptp.real) (K5 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K5) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (forall ((X5 tptp.int) (K5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K5) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.code_integer Bool)) (D4 tptp.code_integer) (Q (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ P X3) (@ P (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D4))))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D4))))) (forall ((X5 tptp.code_integer) (K5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K5) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X3 tptp.complex) (K2 tptp.complex)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K2) D4))))) (=> (forall ((X3 tptp.complex) (K2 tptp.complex)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K2) D4))))) (forall ((X5 tptp.complex) (K5 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K5) D4)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K2) D4))))) (forall ((X5 tptp.real) (K5 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K5) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (forall ((X5 tptp.int) (K5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K5) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.code_integer Bool)) (D4 tptp.code_integer) (Q (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ P X3) (@ P (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D4))))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D4))))) (forall ((X5 tptp.code_integer) (K5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K5) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.complex Bool)) (D4 tptp.complex) (Q (-> tptp.complex Bool))) (=> (forall ((X3 tptp.complex) (K2 tptp.complex)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K2) D4))))) (=> (forall ((X3 tptp.complex) (K2 tptp.complex)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_complex X3) (@ (@ tptp.times_times_complex K2) D4))))) (forall ((X5 tptp.complex) (K5 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K5) D4)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) C)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)))))
% 9.16/7.09 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) C)) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex B) A)) (@ (@ tptp.times_times_complex C) A)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 9.16/7.09 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 9.16/7.09 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 9.16/7.09 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 9.16/7.09 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 9.16/7.09 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_complex Y) Z)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A4) B6)) C))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A4) B6)) C))))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (let ((_let_2 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ _let_2 (@ _let_2 N))) (and (@ _let_1 M) (@ _let_1 N)))))))
% 9.16/7.09 (assert (forall ((J tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 9.16/7.09 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 9.16/7.09 (assert (forall ((B tptp.int) (B6 tptp.int) (X tptp.int) (X6 tptp.int) (Y tptp.int) (Y5 tptp.int) (Z5 tptp.int)) (=> (= B B6) (=> (= (@ (@ tptp.modulo_modulo_int X) B6) (@ (@ tptp.modulo_modulo_int X6) B6)) (=> (= (@ (@ tptp.modulo_modulo_int Y) B6) (@ (@ tptp.modulo_modulo_int Y5) B6)) (=> (= (@ (@ tptp.minus_minus_int X6) Y5) Z5) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int X) Y)) B) (@ (@ tptp.modulo_modulo_int Z5) B6))))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 M)))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N)))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 9.16/7.09 (assert (= tptp.dvd_dvd_int (lambda ((D tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int D)) __flatten_var_0))))
% 9.16/7.09 (assert (= tptp.dvd_dvd_int (lambda ((D tptp.int) (T2 tptp.int)) (@ (@ tptp.dvd_dvd_int D) (@ tptp.uminus_uminus_int T2)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri681578069525770553at_rat N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri5074537144036343181t_real N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri8010041392384452111omplex N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_3 (@ tptp.divide6298287555418463151nteger A))) (= (@ _let_3 (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_3 _let_2)) _let_1)))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat A)) (@ tptp.semiri681578069525770553at_rat B)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat A) B)))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real A)) (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat A) B)))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B)))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat A)) (@ tptp.semiri1316708129612266289at_nat B)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat A) B)))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex A)) (@ tptp.semiri8010041392384452111omplex B)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat A) B)))))
% 9.16/7.09 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B4)) tptp.zero_zero_real))))
% 9.16/7.09 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B4)) tptp.zero_zero_rat))))
% 9.16/7.09 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B4)) tptp.zero_zero_int))))
% 9.16/7.09 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B4)) tptp.zero_zero_real))))
% 9.16/7.09 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B4)) tptp.zero_zero_rat))))
% 9.16/7.09 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B4)) tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N) (@ (@ tptp.ord_less_eq_real I) (@ (@ tptp.minus_minus_real N) K)))))
% 9.16/7.09 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N) (@ (@ tptp.ord_less_eq_rat I) (@ (@ tptp.minus_minus_rat N) K)))))
% 9.16/7.09 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N) K)))))
% 9.16/7.09 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N) K)))))
% 9.16/7.09 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K)) J)))))))))
% 9.16/7.09 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K)) J)))))))))
% 9.16/7.09 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K)) J)))))))))
% 9.16/7.09 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K)) J)))))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))))))))
% 9.16/7.09 (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))))))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger X))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 Y)) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) B))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X) A)) B))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) (@ (@ tptp.minus_8373710615458151222nteger X) Y)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (= C (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D2)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D2))))
% 9.16/7.09 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D2))))
% 9.16/7.09 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D2))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) E)) C) D2))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (E tptp.complex) (C tptp.complex) (B tptp.complex) (D2 tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E)) D2)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) E)) C) D2))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 9.16/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 9.16/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.09 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 9.16/7.09 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 9.16/7.09 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 9.16/7.09 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 9.16/7.09 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 9.16/7.09 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 9.16/7.09 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 9.16/7.09 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 9.16/7.09 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (@ tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y (@ tptp.bit1 X33)))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 9.16/7.09 (assert (= tptp.ord_less_nat (lambda ((N3 tptp.nat) (M4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M4)))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (= tptp.ord_less_eq_nat (lambda ((N3 tptp.nat) (M4 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M4)) tptp.one_one_real)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 9.16/7.09 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 9.16/7.09 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (= (@ tptp.suc N) M) (= N (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 9.16/7.09 (assert (forall ((I tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 9.16/7.09 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 9.16/7.09 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 9.16/7.09 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 9.16/7.09 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 9.16/7.09 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 9.16/7.09 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M) N)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (or (@ (@ tptp.ord_less_nat N) M) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.modulo_modulo_nat N) M))) M) tptp.zero_zero_nat)))
% 9.16/7.09 (assert (forall ((X tptp.nat) (Z tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat X) Y))) (=> (@ (@ tptp.ord_less_nat X) Z) (= (@ (@ tptp.modulo_modulo_nat _let_1) Z) _let_1)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 9.16/7.09 (assert (= tptp.modulo_modulo_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M4) N3)) M4) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M4) N3)) N3)))))
% 9.16/7.09 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 9.16/7.09 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (X tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) X)) (@ (@ tptp.modulo_modulo_nat N) M))) M) (@ (@ tptp.modulo_modulo_nat X) M))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N) Q3)) (@ (@ tptp.dvd_dvd_nat Q3) (@ (@ tptp.minus_minus_nat M) N))))))
% 9.16/7.09 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri681578069525770553at_rat K) tptp.zero_zero_rat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 9.16/7.09 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri5074537144036343181t_real K) tptp.zero_zero_real)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 9.16/7.09 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri1314217659103216013at_int K) tptp.zero_zero_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 9.16/7.09 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri1316708129612266289at_nat K) tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 9.16/7.09 (assert (forall ((K tptp.nat)) (=> (not (= (@ tptp.semiri8010041392384452111omplex K) tptp.zero_zero_complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K))))
% 9.16/7.09 (assert (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) X) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat X) tptp.one_one_nat))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D2))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) E)) C)) D2))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D2))))
% 9.16/7.09 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D2))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 9.16/7.09 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.09 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 9.16/7.09 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) E)) C)) D2))))
% 9.16/7.09 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D2))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D2))))
% 9.16/7.09 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D2))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 9.16/7.09 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 9.16/7.09 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.09 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 9.16/7.09 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 9.16/7.09 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 9.16/7.09 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 9.16/7.09 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 9.16/7.09 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 9.16/7.09 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 9.16/7.09 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 9.16/7.09 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 9.16/7.09 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 9.16/7.09 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((D2 tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D4) (forall ((X5 tptp.rat) (K5 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (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 K5) D4))) T)))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D2) D4) (forall ((X5 tptp.real) (K5 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D2))) (= (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 K5) D4))) T)))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X5 tptp.int) (K5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (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 K5) D4))) T)))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D4) (forall ((X5 tptp.code_integer) (K5 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X5) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K5) D4))) T)))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D2) D4) (forall ((X5 tptp.complex) (K5 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D2))) (= (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 K5) D4))) T)))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D4) (forall ((X5 tptp.rat) (K5 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K5) D4))) T))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D2) D4) (forall ((X5 tptp.real) (K5 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K5) D4))) T))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X5 tptp.int) (K5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K5) D4))) T))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D4) (forall ((X5 tptp.code_integer) (K5 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X5) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K5) D4))) T))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.complex) (D4 tptp.complex) (T tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D2) D4) (forall ((X5 tptp.complex) (K5 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X5) (@ (@ tptp.times_times_complex K5) D4))) T))))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.power_power_real A) N)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ (@ tptp.power_power_complex A) N)))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 9.16/7.09 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N))))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N))))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N))))))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N))))))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N))))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N))))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_1))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_1))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_1))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_1))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_1))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_1))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 9.16/7.09 (assert (forall ((M tptp.num) (Q3 tptp.num) (N 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 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 9.16/7.09 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y4 tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (=> (@ (@ tptp.ord_less_eq_nat K) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat K) (@ tptp.suc tptp.zero_zero_nat))) M)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) M) (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D)) (@ P D)))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D)) (not (@ P D)))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D2) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D2)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D2))))))
% 9.16/7.09 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 9.16/7.09 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D2))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X) D2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X) D2))) _let_1))))))
% 9.16/7.09 (assert (forall ((D2 tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D2))))) (=> (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))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.int) (P3 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D2))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X3) (= (@ P X3) (@ P3 X3))))) (=> (exists ((X_12 tptp.int)) (@ P3 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 9.16/7.09 (assert (forall ((N tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_eq_int N) M) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int N) tptp.one_one_int)) M))))
% 9.16/7.09 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I tptp.int)) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I))))))
% 9.16/7.09 (assert (forall ((B tptp.int) (N tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int B) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int B) N)) _let_1)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (Z tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat X) Y))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat _let_1) Z))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_1) Z))) (=> (@ (@ tptp.ord_less_nat X) Z) (=> (@ (@ tptp.ord_less_nat Y) Z) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) Z)))))))))))
% 9.16/7.09 (assert (forall ((Q3 tptp.nat) (N tptp.nat) (R2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q3))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q3)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q3)))))))))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (D2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) D2) (=> (@ (@ tptp.dvd_dvd_nat B) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B))) (@ (@ tptp.minus_minus_nat D2) B))))))
% 9.16/7.09 (assert (forall ((R2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N) (=> (@ (@ tptp.ord_less_eq_nat R2) M) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M) R2)) (= (@ (@ tptp.modulo_modulo_nat M) N) R2))))))
% 9.16/7.09 (assert (= tptp.modulo_modulo_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.minus_minus_nat M4) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M4) N3)) N3)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.power_power_int _let_1) N)))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.minus_8373710615458151222nteger X) Y)) _let_1) (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.minus_8373710615458151222nteger Y) X)) _let_1)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 9.16/7.09 (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 ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) X)) C))) (= X tptp.zero_zero_real)))))))
% 9.16/7.09 (assert (forall ((N tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((N tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((N tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 9.16/7.09 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn A) A)) A))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger A) A)) A))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 9.16/7.09 (assert (= tptp.plus_plus_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M4 tptp.zero_zero_nat)) N3) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)) N3))))))
% 9.16/7.09 (assert (= tptp.divide_divide_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M4) N3) (= N3 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M4) N3)) N3))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 9.16/7.09 (assert (= tptp.times_times_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N3) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)) N3))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N))))))))
% 9.16/7.09 (assert (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) (@ _let_1 N))) (@ _let_1 M)) (@ (@ tptp.ord_less_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 9.16/7.09 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D2)))) (=> (@ (@ 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) D2))))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int N) M))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int N) tptp.one_one_int)) M))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int M) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) M) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))) (=> (not _let_3) (= _let_2 _let_1)))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.09 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))))))
% 9.16/7.09 (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))))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))))))))
% 9.16/7.09 (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))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_z3403309356797280102nteger)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_nat))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_int))))))
% 9.16/7.09 (assert (forall ((Q3 tptp.num) (N 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 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((Q3 tptp.num) (N 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 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int)))))
% 9.16/7.09 (assert (forall ((Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 9.16/7.09 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M4 tptp.nat)) (@ (@ (@ tptp.if_rat (= M4 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.09 (assert (= tptp.power_power_assn (lambda ((P5 tptp.assn) (M4 tptp.nat)) (@ (@ (@ tptp.if_assn (= M4 tptp.zero_zero_nat)) tptp.one_one_assn) (@ (@ tptp.times_times_assn P5) (@ (@ tptp.power_power_assn P5) (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.09 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M4 tptp.nat)) (@ (@ (@ tptp.if_real (= M4 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.09 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M4 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.09 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M4 tptp.nat)) (@ (@ (@ tptp.if_int (= M4 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.09 (assert (= tptp.power_8256067586552552935nteger (lambda ((P5 tptp.code_integer) (M4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M4 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger P5) (@ (@ tptp.power_8256067586552552935nteger P5) (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.09 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M4 tptp.nat)) (@ (@ (@ tptp.if_complex (= M4 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.assn)) (let ((_let_1 (@ tptp.power_power_assn A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) K))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ _let_1 K)) N)) (@ _let_1 M)))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) K))))
% 9.16/7.09 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))))
% 9.16/7.09 (assert (forall ((X tptp.int) (Z tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X) Y))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int _let_1) Z))) (let ((_let_3 (@ (@ tptp.ord_less_int _let_1) Z))) (let ((_let_4 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) Z) (=> (@ (@ tptp.ord_less_int Y) Z) (=> (@ _let_4 Y) (=> (@ _let_4 X) (=> (@ _let_4 Z) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) Z)))))))))))))))
% 9.16/7.09 (assert (forall ((X tptp.int) (Z tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X) Y))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int _let_1) Z))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int Y) X))) (let ((_let_4 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) Z) (=> (@ (@ tptp.ord_less_int Y) Z) (=> (@ _let_4 Y) (=> (@ _let_4 X) (=> (@ _let_4 Z) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) Z)))))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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)))))))))))))
% 9.16/7.09 (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))))))))))))
% 9.16/7.09 (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))))))))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N))))))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat X))) (=> (@ _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 N)) (@ _let_1 M)))))))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat X))) (=> (@ _let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 N)) (@ _let_1 M))) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (Q3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat (@ _let_1 N)) Q3)) (@ _let_1 M)) (@ (@ tptp.ord_less_nat Q3) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) K))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat (@ _let_1 K)) N)) (@ _let_1 M)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K))))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat X) (@ _let_1 N))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat X) _let_2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) _let_1))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.minus_8373710615458151222nteger X) Y)) _let_2) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_2)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) X)) Y)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))))
% 9.16/7.09 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) K))) (=> (@ (@ tptp.ord_less_eq_int _let_2) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) _let_2)) (@ (@ tptp.times_times_int _let_1) _let_2))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) A)))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_space2 T))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_cnt T)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_V8646137997579335489_i_l_d N))) (@ (@ tptp.times_times_real (@ tptp.vEBT_VEBT_cnt (@ tptp.vEBT_vebt_buildup N))) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_V8346862874174094_d_u_p N))) (@ (@ tptp.times_times_real (@ tptp.vEBT_VEBT_cnt (@ tptp.vEBT_vebt_buildup N))) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))))))
% 9.16/7.09 (assert (forall ((U tptp.nat) (N tptp.nat)) (=> (= U (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_V8346862874174094_d_u_p N)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one)))))) U)))))
% 9.16/7.09 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N)))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)))) E)))))))
% 9.16/7.09 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) E)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.vEBT_V8346862874174094_d_u_p N)) (@ tptp.vEBT_V8646137997579335489_i_l_d N))))
% 9.16/7.09 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 9.16/7.09 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 9.16/7.09 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) (@ tptp.semiri1314217659103216013at_int M))))
% 9.16/7.09 (assert (= tptp.minus_minus_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real Y6)))))
% 9.16/7.09 (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) (B2 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B2) (=> (@ (@ P B2) C3) (=> (@ (@ tptp.ord_less_eq_real A5) B2) (=> (@ (@ tptp.ord_less_eq_real B2) C3) (@ _let_1 C3))))))) (=> (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) (B2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X3) (@ (@ tptp.ord_less_eq_real X3) B2) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B2) A5)) D5)) (@ (@ P A5) B2)))))))) (@ (@ P A) B))))))
% 9.16/7.09 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 9.16/7.09 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N2 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N2))) (=> (forall ((N2 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))) (@ P Z)))))
% 9.16/7.09 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 9.16/7.09 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 9.16/7.09 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 9.16/7.09 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N2 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N2))))))
% 9.16/7.09 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N2 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N2))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((M tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 9.16/7.09 (assert (= tptp.ord_less_int (lambda ((W2 tptp.int) (Z6 tptp.int)) (exists ((N3 tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W2) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N2 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2)))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= K (@ tptp.semiri1314217659103216013at_int N2)))))))
% 9.16/7.09 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N2)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))
% 9.16/7.09 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N2 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N2)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 9.16/7.09 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N2 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 9.16/7.09 (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))))))))))
% 9.16/7.09 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X)))) tptp.one_one_real)))
% 9.16/7.09 (assert (= (@ tptp.vEBT_V8346862874174094_d_u_p tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))
% 9.16/7.09 (assert (= (@ tptp.vEBT_V8646137997579335489_i_l_d tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 9.16/7.09 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 9.16/7.09 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N2 tptp.nat)) (and (not (@ P N2)) (@ P (@ tptp.suc N2))))))))
% 9.16/7.09 (assert (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N2)))))
% 9.16/7.09 (assert (forall ((X tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N2)))))
% 9.16/7.09 (assert (= (@ tptp.vEBT_V8346862874174094_d_u_p (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))
% 9.16/7.09 (assert (= (@ tptp.vEBT_V8646137997579335489_i_l_d (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 9.16/7.09 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) X))))))
% 9.16/7.09 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_nat (@ tptp.vEBT_VEBT_space T)) (@ tptp.vEBT_VEBT_space2 T))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_space2 T))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt T)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_2) N)) (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 _let_1))))))))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt T)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_1) N)) tptp.one_one_real)))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_space2 T)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) U))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_space T)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) U))))))
% 9.16/7.09 (assert (forall ((P Bool) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ (@ tptp.if_nat P) A) B)))) (and (=> P (= _let_1 (@ tptp.semiri1314217659103216013at_int A))) (=> (not P) (= _let_1 (@ tptp.semiri1314217659103216013at_int B)))))))
% 9.16/7.09 (assert (= (lambda ((Y2 tptp.nat) (Z2 tptp.nat)) (= Y2 Z2)) (lambda ((A3 tptp.nat) (B4 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int A3) (@ tptp.semiri1314217659103216013at_int B4)))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat _let_1) (@ tptp.vEBT_VEBT_height T))) (@ (@ tptp.times_times_nat _let_1) N))))))
% 9.16/7.09 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 9.16/7.09 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 9.16/7.09 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))))
% 9.16/7.09 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 9.16/7.09 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 9.16/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K)))))
% 9.16/7.09 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K)))))
% 9.16/7.09 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K)))))
% 9.16/7.09 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 9.16/7.09 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 9.16/7.09 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 9.16/7.09 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 9.16/7.09 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 9.16/7.09 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 9.16/7.09 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 9.16/7.09 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X2 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X2) X2)) tptp.one_one_complex))))
% 9.16/7.09 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X2 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 9.16/7.09 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_d_e_l_e_t_e T) X)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_V1232361888498592333_e_t_e T) X)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y) (or (@ (@ tptp.vEBT_vebt_member T) Y) (= X Y)))))))))
% 9.16/7.09 (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))))))))))
% 9.16/7.09 (assert (forall ((H2 tptp.real) (Z tptp.real) (K6 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K6) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K6) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 9.16/7.09 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K6 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K6) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K6) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 9.16/7.09 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N)))))))))
% 9.16/7.09 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N)))))))))
% 9.16/7.09 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N)))))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N 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))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_1) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_V1232361888498592333_e_t_e T) X))) (@ (@ tptp.plus_plus_real _let_1) (@ _let_2 (@ _let_2 U))))))))))
% 9.16/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 9.16/7.09 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 9.16/7.09 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 9.16/7.09 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 9.16/7.09 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.log _let_2))) (let ((_let_4 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 _let_1))))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_2) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_d_e_l_e_t_e T) X))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_4))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_4)) (@ _let_3 (@ _let_3 U)))))))))))))
% 9.16/7.09 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 9.16/7.09 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 9.16/7.09 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 9.16/7.09 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 9.16/7.09 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 9.16/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 9.16/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 9.16/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 9.16/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N))))))
% 9.16/7.09 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X) N))))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N))))))
% 9.16/7.09 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_complex)))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_real)))))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_rat)))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))))
% 9.16/7.09 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 9.16/7.09 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N)))))
% 9.16/7.09 (assert (forall ((X tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X) N)))))
% 9.16/7.09 (assert (forall ((X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 9.16/7.09 (assert (forall ((X tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N)))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 9.16/7.09 (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)))))))))))
% 9.16/7.09 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 9.16/7.09 (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)))))))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) (@ tptp.semiri5074537144036343181t_real N))))))
% 9.16/7.09 (assert (forall ((X tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X)))))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N)))))
% 9.16/7.09 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X2 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X2) X2)) tptp.one_one_real))))
% 9.16/7.09 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 9.16/7.09 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 9.16/7.09 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((Z tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N))) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((Z tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ _let_1 N))))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N)))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger N)))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N)))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N)))))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N)))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N) K))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N) K))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N) K))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N) K))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N) K))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 9.16/7.09 (assert (forall ((Z tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_rat (@ _let_1 N)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N))) M))))))
% 9.16/7.09 (assert (forall ((Z tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N))) M))))))
% 9.16/7.09 (assert (forall ((Z tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_real (@ _let_1 N)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N))) M))))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_int (@ _let_1 N)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N))) M))))))
% 9.16/7.09 (assert (forall ((Z tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_nat (@ _let_1 N)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N))) M))))))
% 9.16/7.09 (assert (forall ((Z tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.times_times_complex (@ _let_1 N)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N))) M))))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) K) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) K) tptp.zero_zero_rat)))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) K) tptp.zero_zero_real)))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) K) tptp.zero_zero_int)))))
% 9.16/7.09 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) K) tptp.zero_zero_complex)))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex M))) (@ (@ tptp.minus_minus_nat N) M))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 9.16/7.09 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 9.16/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 9.16/7.09 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 9.16/7.09 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))))
% 9.16/7.09 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 9.16/7.09 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 9.16/7.09 (assert (forall ((X tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 9.16/7.09 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.09 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 9.16/7.09 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 9.16/7.09 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 9.16/7.09 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 9.16/7.09 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 9.16/7.09 (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 ((Z6 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z6) (@ (@ tptp.ord_less_nat Z6) X)) (@ (@ tptp.ord_less_eq_nat Z6) Y)))))))
% 9.16/7.09 (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 ((Z6 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z6) (@ (@ tptp.ord_less_nat X) Z6)) (@ (@ tptp.ord_less_eq_nat Y) Z6)))))))
% 9.16/7.09 (assert (forall ((X tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N))))
% 9.16/7.09 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((W tptp.real) (N tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N) (@ (@ tptp.power_power_real Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 9.16/7.09 (assert (forall ((W tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N) (@ (@ tptp.power_power_complex Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N))))
% 9.16/7.09 (assert (forall ((X tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((W tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((W tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D2))))))
% 9.16/7.09 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D2 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D2))))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))))
% 9.16/7.09 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height T)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y)) X))))))))
% 9.16/7.09 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 9.16/7.09 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X2) (@ (@ tptp.vEBT_VEBT_membermima T2) X2)))))
% 9.16/7.09 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 9.16/7.09 (assert (= (@ tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int))
% 9.16/7.09 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 9.16/7.09 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 9.16/7.09 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 9.16/7.09 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B) D2) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B) D2)))) (@ _let_1 D2))))))
% 9.16/7.09 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D2) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D2)))) (@ _let_1 D2))))))
% 9.16/7.09 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D2) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D2)))) (@ _let_1 D2))))))
% 9.16/7.09 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D2) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D2)))) (@ _let_1 D2))))))
% 9.16/7.09 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D2) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D2)))) (@ _let_1 D2))))))
% 9.16/7.09 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ (@ tptp.set_or189985376899183464nteger A) B)) (@ (@ tptp.set_or189985376899183464nteger C) D2)) (and (or (not (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger B) D2) (or (@ (@ tptp.ord_le6747313008572928689nteger C) A) (@ (@ tptp.ord_le6747313008572928689nteger B) D2)))) (@ _let_1 D2))))))
% 9.16/7.09 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D2) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D2)))) (@ _let_1 D2))))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M4) N) (@ P M4))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 9.16/7.09 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N) (@ P M4))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (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))))))))
% 9.16/7.09 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 9.16/7.09 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 9.16/7.09 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))))))
% 9.16/7.09 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.09 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.member_nat Y6) Xs) (@ (@ tptp.ord_less_nat X2) Y6) (forall ((Z6 tptp.nat)) (=> (@ (@ tptp.member_nat Z6) Xs) (=> (@ (@ tptp.ord_less_nat X2) Z6) (@ (@ tptp.ord_less_eq_nat Y6) Z6))))))))
% 9.16/7.09 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X2 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.member_nat Y6) Xs) (@ (@ tptp.ord_less_nat Y6) X2) (forall ((Z6 tptp.nat)) (=> (@ (@ tptp.member_nat Z6) Xs) (=> (@ (@ tptp.ord_less_nat Z6) X2) (@ (@ tptp.ord_less_eq_nat Z6) Y6))))))))
% 9.16/7.09 (assert (forall ((T tptp.vEBT_VEBT) (N 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) N) (=> (= U (@ (@ tptp.power_power_real _let_1) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) 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))))))))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.zero_zero_rat) (= Z tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.zero_zero_int) (= Z tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.zero_zero_real) (= Z tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_rat (@ tptp.ring_1_of_int_rat Z)) (= Z tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z)) (= Z tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z)) (= Z tptp.zero_zero_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_complex (@ tptp.ring_17405671764205052669omplex Z)) (= Z tptp.zero_zero_int))))
% 9.16/7.09 (assert (= (@ tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat))
% 9.16/7.09 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 9.16/7.09 (assert (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real))
% 9.16/7.09 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.zero_zero_int) tptp.zero_zero_complex))
% 9.16/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 9.16/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 9.16/7.09 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 9.16/7.09 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 9.16/7.09 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 9.16/7.09 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 9.16/7.09 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 9.16/7.09 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 9.16/7.09 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.ring_18347121197199848620nteger W)) (@ tptp.ring_18347121197199848620nteger Z)))))
% 9.16/7.09 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 9.16/7.09 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger Z)) N))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B)) W) (@ tptp.ring_18347121197199848620nteger X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger X) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 9.16/7.09 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 9.16/7.09 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 9.16/7.09 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 9.16/7.09 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 9.16/7.09 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 9.16/7.09 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B)) W)) (@ tptp.ring_18347121197199848620nteger X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (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)))))
% 9.16/7.09 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.ring_18347121197199848620nteger B)) W)) (@ tptp.ring_18347121197199848620nteger X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (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))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.09 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.09 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 9.16/7.09 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 9.16/7.10 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 9.16/7.10 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.10 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.10 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z3)))))
% 9.16/7.10 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z3)))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) X))))
% 9.16/7.10 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) X))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.int) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ring_18347121197199848620nteger X))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ (@ tptp.times_3573771949741848930nteger Y) _let_1)))))
% 9.16/7.10 (assert (forall ((X tptp.int) (Y tptp.complex)) (let ((_let_1 (@ tptp.ring_17405671764205052669omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) X))))
% 9.16/7.10 (assert (= tptp.log (lambda ((A3 tptp.real) (X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real A3)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D4))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D4))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X5) D4))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X3) (@ Q (@ (@ tptp.plus_plus_int X3) D4))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X5) D4))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X)))))
% 9.16/7.10 (assert (forall ((D2 tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D2)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D2))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 9.16/7.10 (assert (forall ((X tptp.rat)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 9.16/7.10 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))
% 9.16/7.10 (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)))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 9.16/7.10 (assert (forall ((D2 tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X5))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T)))))))))))
% 9.16/7.10 (assert (forall ((D2 tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X5))) (let ((_let_2 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T))))))))))
% 9.16/7.10 (assert (forall ((D2 tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D4)) T))))))))))
% 9.16/7.10 (assert (forall ((D2 tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D4)) T)))))))))
% 9.16/7.10 (assert (= tptp.ord_less_eq_int (lambda ((N3 tptp.int) (M4 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N3)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M4)) tptp.one_one_real)))))
% 9.16/7.10 (assert (= tptp.ord_less_int (lambda ((N3 tptp.int) (M4 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 M4)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D2))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X) D2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X) D2))) _let_1))))))
% 9.16/7.10 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I2))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I2)))))))
% 9.16/7.10 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I2))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T) (@ (@ tptp.ord_less_eq_rat T) _let_1)) (@ P I2)))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X5 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (= X5 T) (= (@ (@ tptp.minus_minus_int X5) D4) T))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X5 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.minus_minus_int X5) D4) T)))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X5 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_int X5) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X5) D4)) T)))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D4))))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (= X5 T) (= (@ (@ tptp.plus_plus_int X5) D4) T))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.plus_plus_int X5) D4) T)))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_int X5) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X5) D4)) T))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D4)))))))))
% 9.16/7.10 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D2))))) (= (exists ((X7 tptp.int)) (@ P X7)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P X2))))))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X)))) tptp.one_one_real)))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))))))
% 9.16/7.10 (assert (forall ((Q3 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real P4) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P4) Q3)))) Q3)))))
% 9.16/7.10 (assert (forall ((Q3 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat P4) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P4) Q3)))) Q3)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X5 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_eq_int X5) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X5) D4)) T)))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D4))))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_eq_int X5) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X5) D4)) T))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D4)))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P3 (-> 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) (@ P3 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) B3) (@ P (@ (@ tptp.plus_plus_int Y6) X2))))))))))))))
% 9.16/7.10 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P3 (-> 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) (@ P3 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X3 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D4))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P3 X3) (@ P3 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P3 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) A2) (@ P (@ (@ tptp.minus_minus_int Y6) X2))))))))))))))
% 9.16/7.10 (assert (forall ((Q3 tptp.real) (P4 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 P4) Q3)))) tptp.one_one_real)) Q3)) P4))))
% 9.16/7.10 (assert (forall ((Q3 tptp.rat) (P4 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 P4) Q3)))) tptp.one_one_rat)) Q3)) P4))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ 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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_set_nat A2) B3)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N 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.bit0 (@ tptp.bit1 tptp.one)))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_1) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_s_u_c_c 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))))))))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.real) (X tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.log _let_2))) (let ((_let_4 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_1))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_2) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) X))) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_4))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_4)) (@ _let_3 (@ _let_3 U)))))))))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N 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.bit0 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_1) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_p_r_e_d 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))))))))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_s_u_c_c 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.bit0 (@ tptp.bit1 tptp.one))))))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_p_r_e_d 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.bit0 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT) (C tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT C))) (=> (@ (@ tptp.ord_le3480810397992357184T_VEBT A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_less_set_complex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B3) (exists ((B2 tptp.real)) (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B3) A2))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (exists ((B2 tptp.int)) (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B3) A2))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le3480810397992357184T_VEBT A2) B3) (exists ((B2 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT B3) A2))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A2) B3) (exists ((B2 tptp.complex)) (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B3) A2))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (exists ((B2 tptp.nat)) (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B3) A2))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (not (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (@ (@ tptp.ord_less_eq_set_nat B3) A2))))))
% 9.16/7.10 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B7) (not (= A6 B7))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (@ (@ tptp.ord_less_eq_set_nat A2) B3))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C5) (@ _let_1 C5))))))
% 9.16/7.10 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B7) (not (@ (@ tptp.ord_less_eq_set_nat B7) A6))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_set_nat B3) C5) (@ (@ tptp.ord_less_set_nat A2) C5)))))
% 9.16/7.10 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A6) B7) (= A6 B7)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) Y)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t 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.bit0 tptp.one))))))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N 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))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_1) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_s_u_c_c2 T) X))) (@ (@ tptp.plus_plus_real _let_1) (@ _let_2 (@ _let_2 U))))))))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N 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))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_real _let_1) N)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.vEBT_T_p_r_e_d2 T) X))) (@ (@ tptp.plus_plus_real _let_1) (@ _let_2 (@ _let_2 U))))))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 9.16/7.10 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 9.16/7.10 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 9.16/7.10 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 9.16/7.10 (assert (= (@ tptp.tanh_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 9.16/7.10 (assert (= (@ tptp.tanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.tanh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)))))
% 9.16/7.10 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)))))
% 9.16/7.10 (assert (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int))
% 9.16/7.10 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 9.16/7.10 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))))
% 9.16/7.10 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N)) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))))
% 9.16/7.10 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N)) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 9.16/7.10 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 9.16/7.10 (assert (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))))
% 9.16/7.10 (assert (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((L tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L) K))))
% 9.16/7.10 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M4 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) N8) (@ (@ tptp.ord_less_nat X2) M4)))))))
% 9.16/7.10 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N4) (@ (@ tptp.ord_less_nat X3) N))) (@ tptp.finite_finite_nat N4))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.nat_set_decode N))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D2))))))))
% 9.16/7.10 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D2) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D2))))))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D2))))))))
% 9.16/7.10 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D2))))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.one_one_real)))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 9.16/7.10 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D2)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D2))))))
% 9.16/7.10 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D2)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D2))))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D2)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D2))))))
% 9.16/7.10 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D2)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D2))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N4))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X)))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X)))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X) N))))
% 9.16/7.10 (assert (forall ((X tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X) N))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_p_r_e_d2 T) X)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_s_u_c_c2 T) X)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))))))
% 9.16/7.10 (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)))))))))))
% 9.16/7.10 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) N)))))))
% 9.16/7.10 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) N) (= Deg N))))
% 9.16/7.10 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList2) S2))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.powr_real tptp.zero_zero_real) Z) tptp.zero_zero_real)))
% 9.16/7.10 (assert (forall ((W tptp.real) (Z tptp.real)) (= (= (@ (@ tptp.powr_real W) Z) tptp.zero_zero_real) (= W tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 9.16/7.10 (assert (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.arctan X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 9.16/7.10 (assert (= (@ tptp.arctan tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 9.16/7.10 (assert (= (@ tptp.archim6058952711729229775r_real tptp.zero_zero_real) tptp.zero_zero_int))
% 9.16/7.10 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 9.16/7.10 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 9.16/7.10 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 9.16/7.10 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 9.16/7.10 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 9.16/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_real X) Y))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((A tptp.real) (X tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (=> (= X (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (= tptp.abs_abs_int (lambda ((I2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I2)) I2))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((I tptp.int) (D2 tptp.int)) (=> (not (= I tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D2) I) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D2)) (@ tptp.abs_abs_int I))))))
% 9.16/7.10 (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)))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va2)) Vb) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va2)) Vb) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va2 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va2) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va2 tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va2) tptp.one_one_nat)))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) N)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (= tptp.archim7802044766580827645g_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (@ (@ (@ tptp.if_int (= X2 (@ tptp.ring_1_of_int_real _let_1))) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim6058952711729229775r_real X))) tptp.one_one_int)))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N)) M) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 9.16/7.10 (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)))
% 9.16/7.10 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I2))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T) (@ (@ tptp.ord_less_rat T) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I2)))))))
% 9.16/7.10 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I2))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I2)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (K4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K4) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K4) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K4)) (@ _let_1 K))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (K4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K4) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K4)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K4)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((Q3 tptp.rat) (P4 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 P4) Q3)))) Q3)) P4))))
% 9.16/7.10 (assert (forall ((Q3 tptp.real) (P4 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 P4) Q3)))) Q3)) P4))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (K4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K4) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K4) N) (@ (@ tptp.ord_less_nat (@ _let_1 K4)) (@ _let_1 K))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (K4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K4) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K4)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K4)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (@ tptp.binomial N))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_nat I3) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K)))))))))
% 9.16/7.10 (assert (forall ((D2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ 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)) D2))))))
% 9.16/7.10 (assert (forall ((D2 tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D2))) Z)))))
% 9.16/7.10 (assert (forall ((Q3 tptp.rat) (P4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_rat P4) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P4) Q3)))) tptp.one_one_rat)) Q3)))))
% 9.16/7.10 (assert (forall ((Q3 tptp.real) (P4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real P4) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P4) Q3)))) tptp.one_one_real)) Q3)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ F I3) K))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))))
% 9.16/7.10 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)) (@ (@ tptp.ord_less_eq_nat K) N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))))
% 9.16/7.10 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBTi Bool)) (X tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBTi (@ (@ tptp.replicate_VEBT_VEBTi N) X)) I))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X)) I))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 9.16/7.10 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I) X))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ tptp.replicate_VEBT_VEBTi N) X)) I) X))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X)) I) X))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I) X))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R2)) (@ (@ tptp.power_power_nat N) R2)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K))) _let_1))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 9.16/7.10 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) (@ (@ tptp.vEBT_VEBT_high X2) N3))) (@ (@ tptp.vEBT_VEBT_low X2) N3)))))
% 9.16/7.10 (assert (forall ((Xa3 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Xb3 tptp.vEBT_VEBTi) (N tptp.nat) (Xc tptp.vEBT_VEBTi) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Xa3) Tree_is)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) TreeList) Tree_is))) (@ (@ tptp.vEBT_vebt_assn_raw Summary) Xb3))) (@ tptp.pure_assn (and (= tptp.none_P5556105721700978146at_nat tptp.none_P5556105721700978146at_nat) (= N N))))) (@ tptp.pure_assn (= Xc (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) N) Xa3) Xb3))))) H2) (@ (@ tptp.rep_assn (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) N) TreeList) Summary)) Xc)) H2))))
% 9.16/7.10 (assert (forall ((Xa3 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Xb3 tptp.vEBT_VEBTi) (N tptp.nat) (Xc tptp.vEBT_VEBTi) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Xa3) Tree_is)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) TreeList) Tree_is))) (@ (@ tptp.vEBT_vebt_assn_raw Summary) Xb3))) (@ tptp.pure_assn (and (= tptp.none_nat tptp.none_nat) (= N N))))) (@ tptp.pure_assn (= Xc (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) N) Xa3) Xb3))))) H2) (@ (@ tptp.rep_assn (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) N) TreeList) Summary)) Xc)) H2))))
% 9.16/7.10 (assert (forall ((Xa3 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Xb3 tptp.vEBT_VEBTi) (N tptp.nat) (Xc tptp.vEBT_VEBTi) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Xa3) Tree_is)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) TreeList) Tree_is))) (@ (@ tptp.vEBT_vebt_assn_raw Summary) Xb3))) (@ tptp.pure_assn (and (= tptp.none_num tptp.none_num) (= N N))))) (@ tptp.pure_assn (= Xc (@ (@ (@ (@ tptp.vEBT_Nodei tptp.none_P5556105721700978146at_nat) N) Xa3) Xb3))))) H2) (@ (@ tptp.rep_assn (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) N) TreeList) Summary)) Xc)) H2))))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Uu) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Uu) tptp.one_one_nat)))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ tptp.rep_assn X) (@ tptp.rep_assn Y)) (= X Y))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real)) (@ tptp.finite_finite_real (@ tptp.set_real2 Xs2))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs2))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs2))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs2))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_Code_integer)) (@ tptp.finite6017078050557962740nteger (@ tptp.set_Code_integer2 Xs2))))
% 9.16/7.10 (assert (forall ((X tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 9.16/7.10 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 9.16/7.10 (assert (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.real) (P (-> tptp.real Bool))) (= (exists ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.real) (P (-> tptp.real Bool))) (= (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X2))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 9.16/7.10 (assert (forall ((P tptp.assn) (B Bool) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B))) H2) (and (@ (@ tptp.rep_assn P) H2) B))))
% 9.16/7.10 (assert (forall ((P tptp.assn) (Q tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ (@ tptp.times_times_assn Q) (@ tptp.pure_assn B))) (and (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) B)) (@ _let_1 Q))))))
% 9.16/7.10 (assert (forall ((P tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ tptp.pure_assn B)) (and (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) B)) (@ _let_1 tptp.one_one_assn))))))
% 9.16/7.10 (assert (forall ((A tptp.assn) (B tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B)) H2) (not (=> (exists ((X_1 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.rep_assn A) X_1)) (forall ((H_2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn B) H_2))))))))
% 9.16/7.10 (assert (forall ((A2 tptp.assn) (B3 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A2) B3)) H2) (exists ((H1 tptp.produc3658429121746597890et_nat) (H22 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn A2) H1) (@ (@ tptp.rep_assn B3) H22))))))
% 9.16/7.10 (assert (= tptp.entails (lambda ((P2 tptp.assn) (Q2 tptp.assn)) (forall ((H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P2) H) (@ (@ tptp.rep_assn Q2) H))))))
% 9.16/7.10 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (forall ((H3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H3) (@ (@ tptp.rep_assn Q) H3))) (@ (@ tptp.entails P) Q))))
% 9.16/7.10 (assert (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.entails P) Q) (=> (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn Q) H2)))))
% 9.16/7.10 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat) (Q tptp.assn)) (=> (@ (@ tptp.rep_assn P) H2) (=> (@ (@ tptp.entails P) Q) (@ (@ tptp.rep_assn Q) H2)))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (exists ((Xs3 tptp.list_real)) (= (@ tptp.set_real2 Xs3) A2)))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A2) (exists ((Xs3 tptp.list_Code_integer)) (= (@ tptp.set_Code_integer2 Xs3) A2)))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_complex) (Xs4 tptp.list_complex) (Xsi tptp.list_complex) (Xsi2 tptp.list_complex) (A2 (-> tptp.complex tptp.complex tptp.assn)) (A7 (-> tptp.complex tptp.complex tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.complex) (Xi tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs4)) (=> (@ (@ tptp.member_complex Xi) (@ tptp.set_complex2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L4260503343685368993omplex A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L4260503343685368993omplex A7) Xs4) Xsi2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_complex) (Xs4 tptp.list_complex) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT) (A2 (-> tptp.complex tptp.vEBT_VEBT tptp.assn)) (A7 (-> tptp.complex tptp.vEBT_VEBT tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.complex) (Xi tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs4)) (=> (@ (@ tptp.member_VEBT_VEBT Xi) (@ tptp.set_VEBT_VEBT2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L8524933119956041985T_VEBT A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L8524933119956041985T_VEBT A7) Xs4) Xsi2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_complex) (Xs4 tptp.list_complex) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A2 (-> tptp.complex tptp.nat tptp.assn)) (A7 (-> tptp.complex tptp.nat tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.complex) (Xi tptp.nat)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs4)) (=> (@ (@ tptp.member_nat Xi) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L137475477348087235ex_nat A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L137475477348087235ex_nat A7) Xs4) Xsi2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_complex) (Xs4 tptp.list_complex) (Xsi tptp.list_real) (Xsi2 tptp.list_real) (A2 (-> tptp.complex tptp.real tptp.assn)) (A7 (-> tptp.complex tptp.real tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.complex) (Xi tptp.real)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs4)) (=> (@ (@ tptp.member_real Xi) (@ tptp.set_real2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L2479436891206192927x_real A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L2479436891206192927x_real A7) Xs4) Xsi2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_complex) (Xs4 tptp.list_complex) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A2 (-> tptp.complex tptp.int tptp.assn)) (A7 (-> tptp.complex tptp.int tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.complex) (Xi tptp.int)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs4)) (=> (@ (@ tptp.member_int Xi) (@ tptp.set_int2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L134985006839036959ex_int A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L134985006839036959ex_int A7) Xs4) Xsi2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_complex) (Xsi2 tptp.list_complex) (A2 (-> tptp.vEBT_VEBT tptp.complex tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.complex tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.vEBT_VEBT) (Xi tptp.complex)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs4)) (=> (@ (@ tptp.member_complex Xi) (@ tptp.set_complex2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L2162147798726695391omplex A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L2162147798726695391omplex A7) Xs4) Xsi2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_VEBT_VEBT) (Xsi2 tptp.list_VEBT_VEBT) (A2 (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.vEBT_VEBT tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.vEBT_VEBT) (Xi tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs4)) (=> (@ (@ tptp.member_VEBT_VEBT Xi) (@ tptp.set_VEBT_VEBT2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L1279224858307276611T_VEBT A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L1279224858307276611T_VEBT A7) Xs4) Xsi2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_nat) (Xsi2 tptp.list_nat) (A2 (-> tptp.vEBT_VEBT tptp.nat tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.nat tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.vEBT_VEBT) (Xi tptp.nat)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs4)) (=> (@ (@ tptp.member_nat Xi) (@ tptp.set_nat2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L8296926524756676353BT_nat A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L8296926524756676353BT_nat A7) Xs4) Xsi2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_real) (Xsi2 tptp.list_real) (A2 (-> tptp.vEBT_VEBT tptp.real tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.real tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.vEBT_VEBT) (Xi tptp.real)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs4)) (=> (@ (@ tptp.member_real Xi) (@ tptp.set_real2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L5781919052683127133T_real A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L5781919052683127133T_real A7) Xs4) Xsi2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Xs4 tptp.list_VEBT_VEBT) (Xsi tptp.list_int) (Xsi2 tptp.list_int) (A2 (-> tptp.vEBT_VEBT tptp.int tptp.assn)) (A7 (-> tptp.vEBT_VEBT tptp.int tptp.assn))) (=> (= Xs2 Xs4) (=> (= Xsi Xsi2) (=> (forall ((X3 tptp.vEBT_VEBT) (Xi tptp.int)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs4)) (=> (@ (@ tptp.member_int Xi) (@ tptp.set_int2 Xsi2)) (= (@ (@ A2 X3) Xi) (@ (@ A7 X3) Xi))))) (= (@ (@ (@ tptp.vEBT_L8294436054247626077BT_int A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L8294436054247626077BT_int A7) Xs4) Xsi2)))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N 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) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X2 tptp.rat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.archimedean_frac_rat X2))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim3151403230148437115or_rat X2)))))
% 9.16/7.10 (assert (= tptp.archim8280529875227126926d_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.archim2898591450579166408c_real X2))) (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim6058952711729229775r_real X2)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N 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) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((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))))))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X3) (@ tptp.set_VEBT_VEBTi2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBTi Xs2) N))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) N))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) N))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ P X3))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) N)))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.real)) (= (@ tptp.size_size_list_real (@ (@ tptp.replicate_real N) X)) N)))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X)) N)))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X)) N)))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X)) N)))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.zero_zero_complex) (= X tptp.zero_zero_real))))
% 9.16/7.10 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.10 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.zero_zero_real) tptp.zero_zero_complex))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.one_one_complex) (= X tptp.one_one_real))))
% 9.16/7.10 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 9.16/7.10 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X)) N))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X)) N))))
% 9.16/7.10 (assert (forall ((Z tptp.int)) (= (@ tptp.archimedean_frac_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)))
% 9.16/7.10 (assert (forall ((Z tptp.int)) (= (@ tptp.archim2898591450579166408c_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real)))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_real)) (= (@ tptp.size_size_list_real Xs3) N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real) (Ys tptp.list_real)) (=> (not (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_size_list_real Ys))) (not (= Xs2 Ys)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (not (= Xs2 Ys)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.list_real) (Y tptp.list_real)) (=> (not (= (@ tptp.size_size_list_real X) (@ tptp.size_size_list_real Y))) (not (= X Y)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 9.16/7.10 (assert (forall ((P (-> tptp.list_real Bool)) (Xs2 tptp.list_real)) (=> (forall ((Xs3 tptp.list_real)) (=> (forall ((Ys2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_real Ys2)) (@ tptp.size_size_list_real Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs2 tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((M7 tptp.set_list_real)) (=> (@ tptp.finite306553202115118035t_real M7) (exists ((N2 tptp.nat)) (forall ((X5 tptp.list_real)) (=> (@ (@ tptp.member_list_real X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_real X5)) N2)))))))
% 9.16/7.10 (assert (forall ((M7 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M7) (exists ((N2 tptp.nat)) (forall ((X5 tptp.list_o)) (=> (@ (@ tptp.member_list_o X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X5)) N2)))))))
% 9.16/7.10 (assert (forall ((M7 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M7) (exists ((N2 tptp.nat)) (forall ((X5 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X5)) N2)))))))
% 9.16/7.10 (assert (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N2 tptp.nat)) (forall ((X5 tptp.list_int)) (=> (@ (@ tptp.member_list_int X5) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X5)) N2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) (@ (@ tptp.nth_VEBT_VEBT Ys) I3)))) (= Xs2 Ys)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (Ys tptp.list_VEBT_VEBTi)) (=> (= (@ tptp.size_s7982070591426661849_VEBTi Xs2) (@ tptp.size_s7982070591426661849_VEBTi Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (= (@ (@ tptp.nth_VEBT_VEBTi Xs2) I3) (@ (@ tptp.nth_VEBT_VEBTi Ys) I3)))) (= Xs2 Ys)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real) (Ys tptp.list_real)) (=> (= (@ tptp.size_size_list_real Xs2) (@ tptp.size_size_list_real Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I3) (@ (@ tptp.nth_real Ys) I3)))) (= Xs2 Ys)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) (@ (@ tptp.nth_o Ys) I3)))) (= Xs2 Ys)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) (@ (@ tptp.nth_nat Ys) I3)))) (= Xs2 Ys)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) (@ (@ tptp.nth_int Ys) I3)))) (= Xs2 Ys)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 tptp.vEBT_VEBT)) (@ (@ P I2) X7)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_VEBT_VEBT Xs) I2)))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBTi Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 tptp.vEBT_VEBTi)) (@ (@ P I2) X7)))) (exists ((Xs tptp.list_VEBT_VEBTi)) (and (= (@ tptp.size_s7982070591426661849_VEBTi Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_VEBT_VEBTi Xs) I2)))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.real Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 tptp.real)) (@ (@ P I2) X7)))) (exists ((Xs tptp.list_real)) (and (= (@ tptp.size_size_list_real Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_real Xs) I2)))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 Bool)) (@ (@ P I2) X7)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_o Xs) I2)))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 tptp.nat)) (@ (@ P I2) X7)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_nat Xs) I2)))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X7 tptp.int)) (@ (@ P I2) X7)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_int Xs) I2)))))))))
% 9.16/7.10 (assert (= (lambda ((Y2 tptp.list_VEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (= Y2 Z2)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Ys3) I2))))))))
% 9.16/7.10 (assert (= (lambda ((Y2 tptp.list_VEBT_VEBTi) (Z2 tptp.list_VEBT_VEBTi)) (= Y2 Z2)) (lambda ((Xs tptp.list_VEBT_VEBTi) (Ys3 tptp.list_VEBT_VEBTi)) (and (= (@ tptp.size_s7982070591426661849_VEBTi Xs) (@ tptp.size_s7982070591426661849_VEBTi Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s7982070591426661849_VEBTi Xs)) (= (@ (@ tptp.nth_VEBT_VEBTi Xs) I2) (@ (@ tptp.nth_VEBT_VEBTi Ys3) I2))))))))
% 9.16/7.10 (assert (= (lambda ((Y2 tptp.list_real) (Z2 tptp.list_real)) (= Y2 Z2)) (lambda ((Xs tptp.list_real) (Ys3 tptp.list_real)) (and (= (@ tptp.size_size_list_real Xs) (@ tptp.size_size_list_real Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real Xs) I2) (@ (@ tptp.nth_real Ys3) I2))))))))
% 9.16/7.10 (assert (= (lambda ((Y2 tptp.list_o) (Z2 tptp.list_o)) (= Y2 Z2)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I2) (@ (@ tptp.nth_o Ys3) I2))))))))
% 9.16/7.10 (assert (= (lambda ((Y2 tptp.list_nat) (Z2 tptp.list_nat)) (= Y2 Z2)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I2) (@ (@ tptp.nth_nat Ys3) I2))))))))
% 9.16/7.10 (assert (= (lambda ((Y2 tptp.list_int) (Z2 tptp.list_int)) (= Y2 Z2)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I2) (@ (@ tptp.nth_int Ys3) I2))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (P (-> tptp.vEBT_VEBT tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (exists ((Li tptp.vEBT_VEBT)) (@ (@ P Li) I3)))) (not (forall ((L4 tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT L4) N) (not (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ P (@ (@ tptp.nth_VEBT_VEBT L4) I4)) I4))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (P (-> tptp.vEBT_VEBTi tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (exists ((Li tptp.vEBT_VEBTi)) (@ (@ P Li) I3)))) (not (forall ((L4 tptp.list_VEBT_VEBTi)) (=> (= (@ tptp.size_s7982070591426661849_VEBTi L4) N) (not (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ P (@ (@ tptp.nth_VEBT_VEBTi L4) I4)) I4))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (P (-> tptp.real tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (exists ((Li tptp.real)) (@ (@ P Li) I3)))) (not (forall ((L4 tptp.list_real)) (=> (= (@ tptp.size_size_list_real L4) N) (not (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ P (@ (@ tptp.nth_real L4) I4)) I4))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (P (-> Bool tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (exists ((Li Bool)) (@ (@ P Li) I3)))) (not (forall ((L4 tptp.list_o)) (=> (= (@ tptp.size_size_list_o L4) N) (not (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ P (@ (@ tptp.nth_o L4) I4)) I4))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (exists ((Li tptp.nat)) (@ (@ P Li) I3)))) (not (forall ((L4 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat L4) N) (not (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ P (@ (@ tptp.nth_nat L4) I4)) I4))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (P (-> tptp.int tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (exists ((Li tptp.int)) (@ (@ P Li) I3)))) (not (forall ((L4 tptp.list_int)) (=> (= (@ tptp.size_size_list_int L4) N) (not (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ P (@ (@ tptp.nth_int L4) I4)) I4))))))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_complex) (N tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_complex N) X))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N) X))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real) (N tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_real N) X))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_o) (N tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_o N) X))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_nat N) X))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs2)) (= Y3 X))) (= Xs2 (@ (@ tptp.replicate_int N) X))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real) (X tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_real (@ tptp.size_size_list_real Xs2)) X) Xs2))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat) (X tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (= X3 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs2)) X) Xs2))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((A2 (-> tptp.real tptp.real tptp.assn)) (Xs2 tptp.list_real) (Xsi tptp.list_real) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L1930518968523514909l_real A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_real Xs2)))))
% 9.16/7.10 (assert (forall ((A2 (-> Bool tptp.real tptp.assn)) (Xs2 tptp.list_o) (Xsi tptp.list_real) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L4725278957065240257o_real A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_o Xs2)))))
% 9.16/7.10 (assert (forall ((A2 (-> tptp.nat tptp.real tptp.assn)) (Xs2 tptp.list_nat) (Xsi tptp.list_real) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L6102073776069194049t_real A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_nat Xs2)))))
% 9.16/7.10 (assert (forall ((A2 (-> tptp.int tptp.real tptp.assn)) (Xs2 tptp.list_int) (Xsi tptp.list_real) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L8288995350762215837t_real A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_real Xsi) (@ tptp.size_size_list_int Xs2)))))
% 9.16/7.10 (assert (forall ((A2 (-> tptp.real Bool tptp.assn)) (Xs2 tptp.list_real) (Xsi tptp.list_o) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L6234343332106409831real_o A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_o Xsi) (@ tptp.size_size_list_real Xs2)))))
% 9.16/7.10 (assert (forall ((A2 (-> Bool Bool tptp.assn)) (Xs2 tptp.list_o) (Xsi tptp.list_o) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L7363604446928714179sn_o_o A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_o Xsi) (@ tptp.size_size_list_o Xs2)))))
% 9.16/7.10 (assert (forall ((A2 (-> tptp.nat Bool tptp.assn)) (Xs2 tptp.list_nat) (Xsi tptp.list_o) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L7887682484454631235_nat_o A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_o Xsi) (@ tptp.size_size_list_nat Xs2)))))
% 9.16/7.10 (assert (forall ((A2 (-> tptp.int Bool tptp.assn)) (Xs2 tptp.list_int) (Xsi tptp.list_o) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L6066640139021943271_int_o A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_o Xsi) (@ tptp.size_size_list_int Xs2)))))
% 9.16/7.10 (assert (forall ((A2 (-> tptp.real tptp.nat tptp.assn)) (Xs2 tptp.list_real) (Xsi tptp.list_nat) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L1446010312343316929al_nat A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_real Xs2)))))
% 9.16/7.10 (assert (forall ((A2 (-> Bool tptp.nat tptp.assn)) (Xs2 tptp.list_o) (Xsi tptp.list_nat) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ (@ tptp.vEBT_L4785011123346445925_o_nat A2) Xs2) Xsi)) H2) (= (@ tptp.size_size_list_nat Xsi) (@ tptp.size_size_list_o Xs2)))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X))))
% 9.16/7.10 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X)) tptp.one_one_real)))
% 9.16/7.10 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X)) tptp.one_one_rat)))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X))))
% 9.16/7.10 (assert (forall ((X tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool))) (= (forall ((X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 Xs2)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBTi Xs2) I2)))))))
% 9.16/7.10 (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 ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool))) (= (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs2)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I2)))))))
% 9.16/7.10 (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 ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I2)))))))
% 9.16/7.10 (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 ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I2)))))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool)) (X tptp.vEBT_VEBTi)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBTi Xs2) I3)))) (=> (@ (@ tptp.member_VEBT_VEBTi X) (@ tptp.set_VEBT_VEBTi2 Xs2)) (@ P X)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I3)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (@ P X)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) I3)))) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (@ P X)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X Bool)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I3)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I3)))) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (@ P X)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I3)))) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (@ P X)))))
% 9.16/7.10 (assert (forall ((L tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool))) (= (forall ((X2 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X2) (@ tptp.set_VEBT_VEBTi2 L)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s7982070591426661849_VEBTi L)) (@ P (@ (@ tptp.nth_VEBT_VEBTi L) I2)))))))
% 9.16/7.10 (assert (forall ((L tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 L)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT L)) (@ P (@ (@ tptp.nth_VEBT_VEBT L) I2)))))))
% 9.16/7.10 (assert (forall ((L tptp.list_real) (P (-> tptp.real Bool))) (= (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 L)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real L)) (@ P (@ (@ tptp.nth_real L) I2)))))))
% 9.16/7.10 (assert (forall ((L tptp.list_o) (P (-> Bool Bool))) (= (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 L)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o L)) (@ P (@ (@ tptp.nth_o L) I2)))))))
% 9.16/7.10 (assert (forall ((L tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 L)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat L)) (@ P (@ (@ tptp.nth_nat L) I2)))))))
% 9.16/7.10 (assert (forall ((L tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 L)) (@ P X2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int L)) (@ P (@ (@ tptp.nth_int L) I2)))))))
% 9.16/7.10 (assert (forall ((X tptp.vEBT_VEBTi) (Xs2 tptp.list_VEBT_VEBTi)) (= (@ (@ tptp.member_VEBT_VEBTi X) (@ tptp.set_VEBT_VEBTi2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (= (@ (@ tptp.nth_VEBT_VEBTi Xs2) I2) X))))))
% 9.16/7.10 (assert (forall ((X tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I2) X))))))
% 9.16/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I2) X))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I2) X))))))
% 9.16/7.10 (assert (forall ((X Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I2) X))))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I2) X))))))
% 9.16/7.10 (assert (forall ((X tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I2) X))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (P (-> tptp.vEBT_VEBTi Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (=> (forall ((X3 tptp.vEBT_VEBTi)) (=> (@ (@ tptp.member_VEBT_VEBTi X3) (@ tptp.set_VEBT_VEBTi2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_VEBT_VEBTi Xs2) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_real Xs2) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ P X3))) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ 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) N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (@ (@ tptp.member_VEBT_VEBTi (@ (@ tptp.nth_VEBT_VEBTi Xs2) N)) (@ tptp.set_VEBT_VEBTi2 Xs2)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs2) N)) (@ tptp.set_complex2 Xs2)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) N)) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs2) N)) (@ tptp.set_real2 Xs2)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs2) N)) (@ tptp.set_o2 Xs2)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs2) N)) (@ tptp.set_nat2 Xs2)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs2) N)) (@ tptp.set_int2 Xs2)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) X) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 9.16/7.10 (assert (forall ((X tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) X) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat)))))
% 9.16/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))))
% 9.16/7.10 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X)) (@ tptp.archimedean_frac_rat Y)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat _let_1) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))))
% 9.16/7.10 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)))) (let ((_let_2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X)) (@ tptp.archimedean_frac_rat Y))) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 9.16/7.10 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N 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) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((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))))))))))
% 9.16/7.10 (assert (forall ((Ps tptp.assn) (H2 tptp.produc3658429121746597890et_nat) (P tptp.assn) (R tptp.assn) (F2 tptp.assn)) (=> (@ (@ tptp.rep_assn Ps) H2) (=> (@ (@ tptp.entails P) R) (=> (@ (@ tptp.entails Ps) (@ (@ tptp.times_times_assn P) F2)) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn R) F2)) H2))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B4 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B4))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B2))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A5 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B2)))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 9.16/7.10 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 9.16/7.10 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 9.16/7.10 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N))) _let_1)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 9.16/7.10 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N) M)))))
% 9.16/7.10 (assert (forall ((X tptp.complex)) (not (= (@ tptp.exp_complex X) tptp.zero_zero_complex))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (not (= (@ tptp.exp_real X) tptp.zero_zero_real))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 9.16/7.10 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X3 tptp.real)) (= (@ tptp.exp_real X3) Y)))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N) M)) _let_2) _let_1) A))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se1745604003318907178nteger N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2793503036327961859nteger M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 9.16/7.10 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_cnt (@ (@ tptp.vEBT_Leaf A) B)) tptp.one_one_real)))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_cnt2 (@ (@ tptp.vEBT_Leaf A) B)) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) A)) (@ _let_1 A))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 9.16/7.10 (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)))
% 9.16/7.10 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N))))
% 9.16/7.10 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 9.16/7.10 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 9.16/7.10 (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))))))))))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc N))) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc N))) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) tptp.one_one_nat)))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool) (Va2 tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va2))) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Uu Bool) (B Bool)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat) tptp.one_one_nat)))
% 9.16/7.10 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 9.16/7.10 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 9.16/7.10 (assert (= tptp.times_times_assn (lambda ((A3 tptp.assn) (B4 tptp.assn)) (@ (@ tptp.times_times_assn B4) A3))))
% 9.16/7.10 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (let ((_let_2 (@ tptp.times_times_assn B))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 9.16/7.10 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ (@ tptp.times_times_assn (@ _let_1 C)) B)))))
% 9.16/7.10 (assert (forall ((P tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ (@ tptp.entails P) Q))) (=> _let_1 _let_1))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_space2 (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (assert (forall ((A Bool) (Uw Bool)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool) (Va2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va2))) (@ _let_1 (@ (@ (@ tptp.if_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((Uu Bool) (B Bool)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_space (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X)))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((A Bool) (Uw Bool)) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A))))
% 9.16/7.10 (assert (forall ((L tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat L) N))) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) L) (not (@ _let_1 N)))))))
% 9.16/7.10 (assert (forall ((L tptp.nat) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int L) N))) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) L) (not (@ _let_1 N)))))))
% 9.16/7.10 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.pred_numeral L)) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 K))) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 9.16/7.10 (assert (forall ((P tptp.assn) (R tptp.assn) (Ps tptp.assn) (F2 tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails Ps))) (=> (@ (@ tptp.entails P) R) (=> (@ _let_1 (@ (@ tptp.times_times_assn P) F2)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn R) F2)) Q) (@ _let_1 Q)))))))
% 9.16/7.10 (assert (forall ((A2 tptp.assn) (B3 tptp.assn) (C5 tptp.assn)) (let ((_let_1 (@ tptp.entails A2))) (=> (@ _let_1 (@ (@ tptp.times_times_assn B3) C5)) (@ _let_1 (@ (@ tptp.times_times_assn C5) B3))))))
% 9.16/7.10 (assert (forall ((A2 tptp.assn) (B3 tptp.assn) (C5 tptp.assn)) (=> (@ (@ tptp.entails A2) B3) (@ (@ tptp.entails (@ (@ tptp.times_times_assn A2) C5)) (@ (@ tptp.times_times_assn B3) C5)))))
% 9.16/7.10 (assert (forall ((A2 tptp.assn) (B3 tptp.assn) (C5 tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn A2) B3)) C5) (@ (@ tptp.entails (@ (@ tptp.times_times_assn B3) A2)) C5))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A) A)))
% 9.16/7.10 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn A) tptp.one_one_assn) A)))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer))))))))))
% 9.16/7.10 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))))
% 9.16/7.10 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))))
% 9.16/7.10 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 K))) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.pred_numeral L)) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real X)))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_height (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat)))
% 9.16/7.10 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 9.16/7.10 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 9.16/7.10 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 9.16/7.10 (assert (= tptp.size_size_uint32 (lambda ((P5 tptp.uint32)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))
% 9.16/7.10 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.slice_VEBT_VEBT From) To) Xs2)) I) (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.plus_plus_nat From) I))))))))
% 9.16/7.10 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.slice_VEBT_VEBTi From) To) Xs2)) I) (@ (@ tptp.nth_VEBT_VEBTi Xs2) (@ (@ tptp.plus_plus_nat From) I))))))))
% 9.16/7.10 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs2 tptp.list_real) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_real Xs2)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_real (@ (@ (@ tptp.slice_real From) To) Xs2)) I) (@ (@ tptp.nth_real Xs2) (@ (@ tptp.plus_plus_nat From) I))))))))
% 9.16/7.10 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs2 tptp.list_o) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_o Xs2)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.slice_o From) To) Xs2)) I) (@ (@ tptp.nth_o Xs2) (@ (@ tptp.plus_plus_nat From) I))))))))
% 9.16/7.10 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs2 tptp.list_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_nat Xs2)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.slice_nat From) To) Xs2)) I) (@ (@ tptp.nth_nat Xs2) (@ (@ tptp.plus_plus_nat From) I))))))))
% 9.16/7.10 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs2 tptp.list_int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_int Xs2)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.slice_int From) To) Xs2)) I) (@ (@ tptp.nth_int Xs2) (@ (@ tptp.plus_plus_nat From) I))))))))
% 9.16/7.10 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real)) (= (@ (@ (@ tptp.slice_real tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)) Xs2) Xs2)))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_o)) (= (@ (@ (@ tptp.slice_o tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)) Xs2) Xs2)))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat)) (= (@ (@ (@ tptp.slice_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)) Xs2) Xs2)))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_int)) (= (@ (@ (@ tptp.slice_int tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)) Xs2) Xs2)))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 9.16/7.10 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q3)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q3)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 9.16/7.10 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X3 tptp.num)) (=> (@ P X3) (@ P (@ tptp.inc X3)))) (@ P X)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))))
% 9.16/7.10 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X)) tptp.one_one_complex))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 9.16/7.10 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (M4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.10 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 9.16/7.10 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.10 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 9.16/7.10 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 9.16/7.10 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N3)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 9.16/7.10 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 9.16/7.10 (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)))))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N))) (@ tptp.semiri773545260158071498ct_rat N))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N))) (@ tptp.semiri2265585572941072030t_real N))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N))) (@ tptp.semiri5044797733671781792omplex N))))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_set_encode (@ tptp.nat_set_decode N)) N)))
% 9.16/7.10 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 9.16/7.10 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 9.16/7.10 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 9.16/7.10 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 9.16/7.10 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 9.16/7.10 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 9.16/7.10 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 9.16/7.10 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 9.16/7.10 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A2)) A2))))
% 9.16/7.10 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 9.16/7.10 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 9.16/7.10 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 9.16/7.10 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri3624122377584611663nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger _let_1)) (@ tptp.semiri3624122377584611663nteger N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N))))))
% 9.16/7.10 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 9.16/7.10 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_real _let_1)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_int _let_1)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K))) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 _let_1)) (@ tptp.ring_17405671764205052669omplex _let_1)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_nat)))
% 9.16/7.10 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_real Z)))))
% 9.16/7.10 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_int Z)))))
% 9.16/7.10 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 Z)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 9.16/7.10 (assert (forall ((V tptp.num) (V2 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V2)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V2))))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 9.16/7.10 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int N)) K))))
% 9.16/7.10 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ (@ tptp.dvd_dvd_int K) (@ tptp.semiri1314217659103216013at_int N)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 9.16/7.10 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.10 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 9.16/7.10 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri773545260158071498ct_rat N) tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N) tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N) tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N) tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5044797733671781792omplex N) tptp.zero_zero_complex))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 9.16/7.10 (assert (= tptp.numeral_numeral_nat (lambda ((I2 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I2)))))
% 9.16/7.10 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 9.16/7.10 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 9.16/7.10 (assert (= (lambda ((P6 (-> tptp.nat Bool))) (exists ((X8 tptp.nat)) (@ P6 X8))) (lambda ((P2 (-> tptp.nat Bool))) (exists ((X2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P2 (@ tptp.nat2 X2)))))))
% 9.16/7.10 (assert (= (lambda ((P6 (-> tptp.nat Bool))) (forall ((X8 tptp.nat)) (@ P6 X8))) (lambda ((P2 (-> tptp.nat Bool))) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ P2 (@ tptp.nat2 X2)))))))
% 9.16/7.10 (assert (forall ((Z tptp.int) (Z5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z5) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z5)) (= Z Z5)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real M)))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ tptp.finite_finite_nat B3) (= (= (@ tptp.nat_set_encode A2) (@ tptp.nat_set_encode B3)) (= A2 B3))))))
% 9.16/7.10 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 9.16/7.10 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 9.16/7.10 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 9.16/7.10 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 9.16/7.10 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 9.16/7.10 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M4) (@ tptp.semiri1314217659103216013at_int N3))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N))))))
% 9.16/7.10 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z) (and (= M (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) M)) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 9.16/7.10 (assert (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.nat_set_encode A2) tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N)))))))))
% 9.16/7.10 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R2)))) (@ (@ tptp.power_power_nat N) R2)))))
% 9.16/7.10 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R2)))) R2))))
% 9.16/7.10 (assert (forall ((R2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real R2)))) R2))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.binomial N) K)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat2 W) M) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat2 W)) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 9.16/7.10 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N3 tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N3)) (@ P N3))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((Z tptp.int) (Z5 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z5) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z5)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z5))))))))
% 9.16/7.10 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 9.16/7.10 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 9.16/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))
% 9.16/7.10 (assert (forall ((Z tptp.int) (Z5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z5)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z5))))))
% 9.16/7.10 (assert (forall ((Z5 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z5) (=> (@ (@ tptp.ord_less_eq_int Z5) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z5)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z5)))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1406184849735516958ct_int N)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri3624122377584611663nteger N)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))) (@ tptp.semiri2265585572941072030t_real N)))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((K tptp.num)) (= (@ tptp.semiri3624122377584611663nteger (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger K)) (@ tptp.semiri3624122377584611663nteger (@ tptp.pred_numeral K))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))))
% 9.16/7.10 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K))))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((Z tptp.int) (Z5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z5)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z5)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.10 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K3))))))
% 9.16/7.10 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K3))))))
% 9.16/7.10 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 K3))))))
% 9.16/7.10 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K3))))))
% 9.16/7.10 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 K3))))))
% 9.16/7.10 (assert (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 9.16/7.10 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M4 tptp.nat)) (@ (@ (@ tptp.if_rat (= M4 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M4)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (= tptp.semiri3624122377584611663nteger (lambda ((M4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M4 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M4)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M4 tptp.nat)) (@ (@ (@ tptp.if_int (= M4 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M4 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M4)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M4 tptp.nat)) (@ (@ (@ tptp.if_real (= M4 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M4)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M4 tptp.nat)) (@ (@ (@ tptp.if_complex (= M4 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M4)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri3624122377584611663nteger N) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1406184849735516958ct_int N) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri1408675320244567234ct_nat N) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri2265585572941072030t_real N) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.semiri5044797733671781792omplex N) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N))) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ tptp.semiri3624122377584611663nteger N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N))) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ tptp.semiri773545260158071498ct_rat N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ tptp.semiri1406184849735516958ct_int N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N))) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ tptp.semiri5044797733671781792omplex N)))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K)))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K)))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K)))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N) K))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N) K))))))))
% 9.16/7.10 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N) K))))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (= tptp.binomial (lambda ((N3 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N3) K3))) (let ((_let_2 (@ tptp.ord_less_nat N3))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N3) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N3) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 9.16/7.10 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N3 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 9.16/7.10 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N3 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 9.16/7.10 (assert (= tptp.semiri5044797733671781792omplex (lambda ((N3 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 9.16/7.10 (assert (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L2))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L2) K3))))))))))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ tptp.sgn_sgn_int _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.sgn_sgn_complex A))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1))))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 9.16/7.10 (assert (= (@ tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat))
% 9.16/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))))
% 9.16/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ tptp.sgn_sgn_int A)))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ tptp.sgn_sgn_Code_integer A)))))
% 9.16/7.10 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex A)))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.sgn_sgn_rat A)))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat (@ tptp.sgn_sgn_rat A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.sgn_sgn_real A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.sgn_sgn_int A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.sgn_sgn_Code_integer A)) N))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.sgn_sgn_Code_integer A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.sgn_sgn_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.sgn_sgn_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ tptp.sgn_sgn_Code_integer A)) (@ _let_1 A)))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A)) (@ _let_1 A)))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.sgn_sgn_rat A)) (@ _let_1 A)))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A)) (@ _let_1 A)))))
% 9.16/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (= (@ (@ tptp.divide_divide_real A) _let_1) (@ (@ tptp.times_times_real A) _let_1)))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (= (@ (@ tptp.divide_divide_rat A) _let_1) (@ (@ tptp.times_times_rat A) _let_1)))))
% 9.16/7.10 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 9.16/7.10 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.sgn_sgn_real A) tptp.one_one_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) tptp.one_one_Code_integer))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) tptp.one_one_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) tptp.one_one_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat)))))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real)))))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int)))))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger)))))))
% 9.16/7.10 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.10 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.abs_abs_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.abs_abs_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.abs_abs_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.abs_abs_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.abs_abs_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.zero_n2052037380579107095ol_rat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.zero_n3304061248610475627l_real (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((A tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((X tptp.complex)) (= (= (@ tptp.sgn_sgn_complex X) tptp.zero_zero_complex) (= X tptp.zero_zero_complex))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (= (@ tptp.sgn_sgn_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 9.16/7.10 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))))
% 9.16/7.10 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B)))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.sgn_sgn_Code_integer B)))))
% 9.16/7.10 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))))
% 9.16/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) (@ tptp.sgn_sgn_real Y)))))
% 9.16/7.10 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex X)) (@ tptp.sgn_sgn_complex Y)))))
% 9.16/7.10 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (=> (= (@ tptp.sgn_sgn_Code_integer B) _let_1) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1)))))
% 9.16/7.10 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (=> (= (@ tptp.sgn_sgn_real B) _let_1) (= (@ tptp.sgn_sgn_real (@ (@ tptp.plus_plus_real A) B)) _let_1)))))
% 9.16/7.10 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (=> (= (@ tptp.sgn_sgn_rat B) _let_1) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1)))))
% 9.16/7.10 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B)) _let_1)))))
% 9.16/7.10 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B))) (let ((_let_2 (@ tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 9.16/7.10 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (let ((_let_2 (@ tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 9.16/7.10 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer B))) (let ((_let_2 (@ tptp.sgn_sgn_Code_integer A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 9.16/7.10 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (let ((_let_2 (@ tptp.sgn_sgn_rat A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_rat)) (=> (not (= _let_1 tptp.zero_zero_rat)) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.sgn_sgn_int _let_1) _let_1)))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.sgn_sgn_real _let_1) _let_1)))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1)))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1)))
% 9.16/7.10 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1)))
% 9.16/7.10 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (= (@ tptp.sgn_sgn_Code_integer B) (@ tptp.sgn_sgn_Code_integer A)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))))))
% 9.16/7.10 (assert (forall ((B tptp.real) (A tptp.real)) (=> (= (@ tptp.sgn_sgn_real B) (@ tptp.sgn_sgn_real A)) (= (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 9.16/7.10 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (= (@ tptp.sgn_sgn_rat B) (@ tptp.sgn_sgn_rat A)) (= (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 9.16/7.10 (assert (forall ((B tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B) (@ tptp.sgn_sgn_int A)) (= (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))))))
% 9.16/7.10 (assert (= tptp.abs_abs_rat (lambda ((K3 tptp.rat)) (@ (@ tptp.times_times_rat K3) (@ tptp.sgn_sgn_rat K3)))))
% 9.16/7.10 (assert (= tptp.abs_abs_real (lambda ((K3 tptp.real)) (@ (@ tptp.times_times_real K3) (@ tptp.sgn_sgn_real K3)))))
% 9.16/7.10 (assert (= tptp.abs_abs_int (lambda ((K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ tptp.sgn_sgn_int K3)))))
% 9.16/7.10 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger K3) (@ tptp.sgn_sgn_Code_integer K3)))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.sgn_sgn_Code_integer A)) A)))
% 9.16/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.abs_abs_Code_integer A)) A)))
% 9.16/7.10 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)))
% 9.16/7.10 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X)) (@ tptp.abs_abs_rat X)) X)))
% 9.16/7.10 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) (@ tptp.abs_abs_real X)) X)))
% 9.16/7.10 (assert (forall ((X tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X)) (@ tptp.abs_abs_int X)) X)))
% 9.16/7.10 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer X)) (@ tptp.abs_abs_Code_integer X)) X)))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)))) (let ((_let_2 (= A tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer)))))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)))) (let ((_let_2 (= A tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 9.16/7.10 (assert (= tptp.sgn_sgn_int (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_int (= X2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 9.16/7.10 (assert (= tptp.sgn_sgn_real (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_real (= X2 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 9.16/7.10 (assert (= tptp.sgn_sgn_Code_integer (lambda ((X2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X2 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X2)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 9.16/7.10 (assert (= tptp.sgn_sgn_rat (lambda ((X2 tptp.rat)) (@ (@ (@ tptp.if_rat (= X2 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 9.16/7.10 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 9.16/7.10 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 9.16/7.10 (assert (= tptp.sgn_sgn_int (lambda ((I2 tptp.int)) (@ (@ (@ tptp.if_int (= I2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I2)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 9.16/7.10 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X)))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 9.16/7.10 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X)))) (let ((_let_2 (= X tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A3 tptp.nat) (B4 tptp.nat) (Acc tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B4) A3)) Acc) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) B4) (@ (@ F3 A3) Acc))))))
% 9.16/7.10 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa3 tptp.nat) (Xb3 tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb3) Xa3))) (=> (= (@ (@ (@ _let_1 Xa3) Xb3) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa3) tptp.one_one_nat)) Xb3) (@ (@ X Xa3) Xc))))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (assert (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K3))))) _let_2)))))))))))
% 9.16/7.10 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))))))))))))))))
% 9.16/7.10 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))))
% 9.16/7.10 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (=> (not (= _let_1 tptp.zero_zero_int)) (= (@ tptp.sgn_sgn_int _let_1) (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)))))))
% 9.16/7.10 (assert (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A5) B2))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M2)) (=> (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 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (=> (= M2 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M2)) (=> (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 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat) (Mi tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) 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))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat) (Mi tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M2) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M2)) (=> (= M2 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M2)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M2)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) 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))) M2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2)))))))))))))))))))))))))))))))
% 9.16/7.10 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A3 Bool) (B4 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B4))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) N3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (= A23 (@ (@ tptp.plus_plus_nat N3) N3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N3))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N3) _let_1)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi2 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi2 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 Mi2) Ma3))) A23) TreeList3) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) N3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 N3)) (= A23 (@ (@ tptp.plus_plus_nat N3) N3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi2) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi2 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi2 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 Mi2) Ma3))) A23) TreeList3) Summary3)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 _let_3)) (= A23 (@ (@ tptp.plus_plus_nat N3) _let_3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N3))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (@ (@ tptp.ord_less_eq_nat Mi2) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N3))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))
% 9.16/7.10 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B))) (= (@ (@ tptp.bit_se3949692690581998587nteger _let_1) B) _let_1))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se3949692690581998587nteger A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 9.16/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) A) A)))
% 9.16/7.10 (assert (forall ((Mi3 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 Mi3) Ma))) Deg) TreeList) Summary)) Deg) (=> (= Mi3 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))))))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (Mi3 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 Mi3) Ma))) Deg) TreeList) Summary))) (=> (or (= X Mi3) (= 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))))))
% 9.16/7.10 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.10 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.10 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 9.16/7.10 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.zero_z3403309356797280102nteger) X) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 9.16/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y6 tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y6))))))
% 9.16/7.10 (assert (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y6 tptp.nat)) (= X (@ tptp.some_nat Y6))))))
% 9.16/7.10 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y6 tptp.num)) (= X (@ tptp.some_num Y6))))))
% 9.16/7.10 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y6 tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y6)))) (= X tptp.none_P5556105721700978146at_nat))))
% 9.16/7.10 (assert (forall ((X tptp.option_nat)) (= (forall ((Y6 tptp.nat)) (not (= X (@ tptp.some_nat Y6)))) (= X tptp.none_nat))))
% 9.16/7.10 (assert (forall ((X tptp.option_num)) (= (forall ((Y6 tptp.num)) (not (= X (@ tptp.some_num Y6)))) (= X tptp.none_num))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se1745604003318907178nteger N))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B)) (@ (@ tptp.bit_se3949692690581998587nteger (@ _let_1 A)) (@ _let_1 B))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (Mi3 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) Deg) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Mi3))) Deg) TreeList) Summary)) X)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1))))))))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (Mi3 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Mi3))) Deg) TreeList) Summary)) X)) tptp.one_one_nat))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 9.16/7.10 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) X)))
% 9.16/7.10 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 9.16/7.10 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 9.16/7.10 (assert (forall ((V tptp.option2661157926820139483um_num)) (= (forall ((X2 tptp.num) (Y6 tptp.num)) (not (= V (@ tptp.some_P6201964756284913402um_num (@ (@ tptp.product_Pair_num_num X2) Y6))))) (= V tptp.none_P4394680061957285238um_num))))
% 9.16/7.10 (assert (forall ((V tptp.option4624381673175914239nt_int)) (= (forall ((X2 tptp.int) (Y6 tptp.int)) (not (= V (@ tptp.some_P4184893108420464158nt_int (@ (@ tptp.product_Pair_int_int X2) Y6))))) (= V tptp.none_P2377608414092835994nt_int))))
% 9.16/7.10 (assert (forall ((V tptp.option5190343406534369742et_nat)) (= (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y6 tptp.produc3658429121746597890et_nat)) (not (= V (@ tptp.some_P750831030444334937et_nat (@ (@ tptp.produc5001842942810119800et_nat X2) Y6))))) (= V tptp.none_P4972525538344268765et_nat))))
% 9.16/7.10 (assert (forall ((V tptp.option2860828798490689354et_nat)) (= (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y6 tptp.produc3925858234332021118et_nat)) (not (= V (@ tptp.some_P1630309045189364437et_nat (@ (@ tptp.produc2245416461498447860et_nat X2) Y6))))) (= V tptp.none_P199884684680593241et_nat))))
% 9.16/7.10 (assert (forall ((V tptp.option4927543243414619207at_nat)) (= (forall ((X2 tptp.nat) (Y6 tptp.nat)) (not (= V (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y6))))) (= V tptp.none_P5556105721700978146at_nat))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (Mi3 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 Mi3) 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 Mi3) (= X Ma)))))))
% 9.16/7.10 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_le5914376470875661696on_nat (@ tptp.some_nat X)) tptp.none_nat))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_le6622620407824499402on_num (@ tptp.some_num X)) tptp.none_num))))
% 9.16/7.10 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_option_real (@ tptp.some_real X)) (@ tptp.some_real Y)) (@ (@ tptp.ord_less_real X) Y))))
% 9.16/7.10 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_option_rat (@ tptp.some_rat X)) (@ tptp.some_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 9.16/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_option_num (@ tptp.some_num X)) (@ tptp.some_num Y)) (@ (@ tptp.ord_less_num X) Y))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_option_nat (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat X) Y))))
% 9.16/7.10 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_option_int (@ tptp.some_int X)) (@ tptp.some_int Y)) (@ (@ tptp.ord_less_int X) Y))))
% 9.16/7.10 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_option_nat tptp.none_nat) (@ tptp.some_nat X))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_option_num tptp.none_num) (@ tptp.some_num X))))
% 9.16/7.10 (assert (forall ((Mi3 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 Mi3) Ma))) Deg) TreeList) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi3) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi3) 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)))))))))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi3 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 Mi3) Ma))) Deg) TreeList) Summary)) X))))))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) tptp.one_one_int)))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 9.16/7.10 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 9.16/7.10 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) tptp.one_one_Code_integer)))
% 9.16/7.10 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 9.16/7.10 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 9.16/7.10 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 9.16/7.10 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int)))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)))
% 9.16/7.10 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.zero_zero_int)))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.ring_18347121197199848620nteger K)) (@ tptp.ring_18347121197199848620nteger L)))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (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)))))))
% 9.16/7.10 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se3949692690581998587nteger B))) (let ((_let_2 (@ tptp.bit_se3949692690581998587nteger A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 9.16/7.10 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A3 tptp.int) (B4 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B4) A3))))
% 9.16/7.10 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B4) A3))))
% 9.16/7.10 (assert (= tptp.bit_se3949692690581998587nteger (lambda ((A3 tptp.code_integer) (B4 tptp.code_integer)) (@ (@ tptp.bit_se3949692690581998587nteger B4) A3))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se3949692690581998587nteger A))) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger B) C))))))
% 9.16/7.10 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M2 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K2) M2)))))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 9.16/7.10 (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) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 9.16/7.10 (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) (B2 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 9.16/7.10 (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) (B2 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_num B2)) (@ (@ P X) Y)))) _let_1))))))
% 9.16/7.10 (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) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 9.16/7.10 (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) (B2 tptp.nat)) (=> (= X (@ tptp.some_nat A5)) (=> (= Y (@ tptp.some_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 9.16/7.10 (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) (B2 tptp.num)) (=> (= X (@ tptp.some_nat A5)) (=> (= Y (@ tptp.some_num B2)) (@ (@ P X) Y)))) _let_1))))))
% 9.16/7.10 (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) (B2 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 9.16/7.10 (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) (B2 tptp.nat)) (=> (= X (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_nat B2)) (@ (@ P X) Y)))) _let_1))))))
% 9.16/7.10 (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) (B2 tptp.num)) (=> (= X (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_num B2)) (@ (@ P X) Y)))) _let_1))))))
% 9.16/7.10 (assert (= (lambda ((P6 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X8 tptp.option4927543243414619207at_nat)) (@ P6 X8))) (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P2 tptp.none_P5556105721700978146at_nat) (forall ((X2 tptp.product_prod_nat_nat)) (@ P2 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 9.16/7.10 (assert (= (lambda ((P6 (-> tptp.option_nat Bool))) (forall ((X8 tptp.option_nat)) (@ P6 X8))) (lambda ((P2 (-> tptp.option_nat Bool))) (and (@ P2 tptp.none_nat) (forall ((X2 tptp.nat)) (@ P2 (@ tptp.some_nat X2)))))))
% 9.16/7.10 (assert (= (lambda ((P6 (-> tptp.option_num Bool))) (forall ((X8 tptp.option_num)) (@ P6 X8))) (lambda ((P2 (-> tptp.option_num Bool))) (and (@ P2 tptp.none_num) (forall ((X2 tptp.num)) (@ P2 (@ tptp.some_num X2)))))))
% 9.16/7.10 (assert (= (lambda ((P6 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X8 tptp.option4927543243414619207at_nat)) (@ P6 X8))) (lambda ((P2 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P2 tptp.none_P5556105721700978146at_nat) (exists ((X2 tptp.product_prod_nat_nat)) (@ P2 (@ tptp.some_P7363390416028606310at_nat X2)))))))
% 9.16/7.10 (assert (= (lambda ((P6 (-> tptp.option_nat Bool))) (exists ((X8 tptp.option_nat)) (@ P6 X8))) (lambda ((P2 (-> tptp.option_nat Bool))) (or (@ P2 tptp.none_nat) (exists ((X2 tptp.nat)) (@ P2 (@ tptp.some_nat X2)))))))
% 9.16/7.10 (assert (= (lambda ((P6 (-> tptp.option_num Bool))) (exists ((X8 tptp.option_num)) (@ P6 X8))) (lambda ((P2 (-> tptp.option_num Bool))) (or (@ P2 tptp.none_num) (exists ((X2 tptp.num)) (@ P2 (@ tptp.some_num X2)))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y (@ tptp.some_nat X23))))))))
% 9.16/7.10 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))))
% 9.16/7.10 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 9.16/7.10 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 9.16/7.10 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 9.16/7.10 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 9.16/7.10 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 9.16/7.10 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 9.16/7.10 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A5 Bool) (B2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A5) B2)))) (=> (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 ((Mi 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 Mi) Ma2))) Ux2) Uy2) Uz2)))))))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) tptp.zero_zero_nat) Va2) Vb)) X) (or (= X Mi3) (= X Ma)))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (= tptp.sgn_sgn_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real X2) (@ tptp.abs_abs_real X2)))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) tptp.zero_zero_nat) TreeList) Summary)) X) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) tptp.zero_zero_nat) TreeList) Summary)) X) tptp.one_one_nat)))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) (@ tptp.suc tptp.zero_zero_nat)) TreeList) Summary)) X) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) (@ tptp.suc tptp.zero_zero_nat)) TreeList) Summary)) X) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((X tptp.option_nat)) (=> (@ (@ tptp.ord_less_option_nat tptp.none_nat) X) (exists ((Z3 tptp.nat)) (= X (@ tptp.some_nat Z3))))))
% 9.16/7.10 (assert (forall ((X tptp.option_num)) (=> (@ (@ tptp.ord_less_option_num tptp.none_num) X) (exists ((Z3 tptp.num)) (= X (@ tptp.some_num Z3))))))
% 9.16/7.10 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_option_nat tptp.none_nat) (@ tptp.some_nat X))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_option_num tptp.none_num) (@ tptp.some_num X))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height _let_1))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc)))))))))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 9.16/7.10 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc2 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) Vc2)) X))))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve)) Vf) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve)) Vf) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc2) Vd)) Ve) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc2) Vd)) Ve) tptp.one_one_nat)))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (= (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi) tptp.one_one_nat)))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (= (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi) tptp.one_one_nat)))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc2 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) Vc2)) X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 9.16/7.10 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi3 Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi3) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 9.16/7.10 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi3 Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi3) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (Mi3 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 Mi3) 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 Mi3) Ma))) Deg) TreeList) Summary)) X) tptp.none_nat)))))))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi3 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 Mi3) Ma))) Deg) TreeList) Summary)) X) tptp.none_nat)))))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (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))))))))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_eq_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X) tptp.none_nat))))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (and (= X Mi3) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete T) X)) N))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete T) X)) Y) (and (not (= X Y)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) Y))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_delete T) X)) Y) (and (not (= X Y)) (@ (@ tptp.vEBT_vebt_member T) Y))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Px)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Sx)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ 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))) N))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ 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))) N))))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (Mi3 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 Mi3) Ma))) Deg) TreeList) Summary))) (=> (or (@ (@ tptp.ord_less_nat X) Mi3) (@ (@ tptp.ord_less_nat Ma) X)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Mi3 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) Mi3) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) X) (@ tptp.some_nat Mi3))))))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi3 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 Mi3) Ma))) Deg) TreeList) Summary)) X) (@ tptp.some_nat Ma))))))
% 9.16/7.10 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X2)) (@ tptp.some_nat Y6)))))
% 9.16/7.10 (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)))
% 9.16/7.10 (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)))
% 9.16/7.10 (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)))
% 9.16/7.10 (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)))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (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))))))
% 9.16/7.10 (assert (forall ((B Bool) (A Bool) (Va2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va2))))) (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))))))))
% 9.16/7.10 (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) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) Deg3))))))))
% 9.16/7.10 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.none_nat)))
% 9.16/7.10 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 9.16/7.10 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va2) tptp.none_nat)))
% 9.16/7.10 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va2 tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va2)) Vb) tptp.none_nat)))
% 9.16/7.10 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 9.16/7.10 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N2))))) (=> (forall ((N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N2))))) (=> (forall ((M2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M2)) tptp.one)))) (=> (forall ((M2 tptp.num) (N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M2)) (@ tptp.bit0 N2))))) (=> (forall ((M2 tptp.num) (N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M2)) (@ tptp.bit1 N2))))) (=> (forall ((M2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M2)) tptp.one)))) (=> (forall ((M2 tptp.num) (N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M2)) (@ tptp.bit0 N2))))) (not (forall ((M2 tptp.num) (N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M2)) (@ tptp.bit1 N2))))))))))))))))
% 9.16/7.10 (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)))
% 9.16/7.10 (assert (forall ((V tptp.product_prod_nat_nat) (Vc2 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) Vc2) Vd)) Ve) tptp.none_nat)))
% 9.16/7.10 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B2 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) 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) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList2) S2)) X3)))))))))
% 9.16/7.10 (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)))
% 9.16/7.10 (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)))
% 9.16/7.10 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) tptp.zero_zero_nat)))) (=> (forall ((A5 Bool) (B2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A5 Bool) (B2 Bool) (N2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) (@ tptp.suc (@ tptp.suc N2)))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) Uu2)))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2)) X3)))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2)) X3)))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X3)))))))))))))
% 9.16/7.10 (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) (B2 Bool) (Va tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) (@ tptp.suc (@ tptp.suc Va)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3)) Vb2)))) (=> (forall ((V3 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 V3)) tptp.zero_zero_nat) Vd2) Ve2)) Vf2)))) (=> (forall ((V3 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 V3)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2)))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X3)))))))))))))
% 9.16/7.10 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B2)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N2))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va3)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc) Vd2)) Ve2)))) (=> (forall ((V3 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 V3)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2)))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X3))))))))))))
% 9.16/7.10 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B2 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) 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 ((V3 tptp.nat) (TreeList2 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 V3))) TreeList2) Summary2)) X3)))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X3)))))))))))
% 9.16/7.10 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B2 Bool) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) X3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X3)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz2)) X3)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc)) X3)))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X3)))))))))))
% 9.16/7.10 (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 ((Mi tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X3)))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc V3)) TreeList2) Vc)) X3)))) (not (forall ((V3 tptp.nat) (TreeList2 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 V3)) TreeList2) Vd2)) X3)))))))))))
% 9.16/7.10 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M4 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 M4) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M4) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 9.16/7.10 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M4 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 M4)) (not (@ _let_2 N3))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M4) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete T) X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_d_e_l_e_t_e T) X)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) N) (=> (not (= Mi3 Ma)) (and (@ (@ tptp.ord_less_nat Mi3) Ma) (exists ((M2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M2) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) tptp.zero_zero_nat) TrLst) Smry))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat Mini) X))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete T) X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_V1232361888498592333_e_t_e T) X)) tptp.one_one_nat)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.some_nat M) (@ tptp.vEBT_vebt_mint T)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.10 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc))) Y))))))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t T) L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) (@ tptp.suc (@ tptp.suc N))) _let_1))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B))))
% 9.16/7.10 (assert (forall ((Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) Uu) _let_1))))
% 9.16/7.10 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (= (@ (@ tptp.vEBT_vebt_delete (@ _let_1 B)) (@ tptp.suc tptp.zero_zero_nat)) (@ _let_1 false)))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va2) _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 Mi3) Ma))) Deg) TreeList) Summary)) N) (=> (= N (@ tptp.suc (@ tptp.suc Va2))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi3)) (=> (not (= Ma Mi3)) (@ (@ 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)))))))))))
% 9.16/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (not (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= 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 ((Mi 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 Mi) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Mi)))))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (= tptp.ord_less_nat (lambda ((Y6 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X2)) (@ tptp.some_nat Y6)))))
% 9.16/7.10 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 9.16/7.10 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 9.16/7.10 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 9.16/7.10 (assert (forall ((Uu (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv tptp.option4927543243414619207at_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uu) tptp.none_P5556105721700978146at_nat) Uv) tptp.none_P5556105721700978146at_nat)))
% 9.16/7.10 (assert (forall ((Uu (-> tptp.num tptp.num tptp.num)) (Uv tptp.option_num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uu) tptp.none_num) Uv) tptp.none_num)))
% 9.16/7.10 (assert (forall ((Uu (-> tptp.nat tptp.nat tptp.nat)) (Uv tptp.option_nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uu) tptp.none_nat) Uv) tptp.none_nat)))
% 9.16/7.10 (assert (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_Pr8591224930841456533at_nat Option) (@ tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))))
% 9.16/7.10 (assert (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_nat Option) (@ tptp.the_nat Option2)))) (= Option Option2)))))))
% 9.16/7.10 (assert (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_num Option) (@ tptp.the_num Option2)))) (= Option Option2)))))))
% 9.16/7.10 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 9.16/7.10 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 9.16/7.10 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 9.16/7.10 (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)))
% 9.16/7.10 (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)))
% 9.16/7.10 (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)))
% 9.16/7.10 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa3 tptp.option4927543243414619207at_nat) (Xb3 tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa3) Xb3) Y) (=> (=> (= Xa3 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat)) (= Xa3 (@ tptp.some_P7363390416028606310at_nat V3))) (=> (= Xb3 tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A5 tptp.product_prod_nat_nat)) (=> (= Xa3 (@ tptp.some_P7363390416028606310at_nat A5)) (forall ((B2 tptp.product_prod_nat_nat)) (=> (= Xb3 (@ tptp.some_P7363390416028606310at_nat B2)) (not (= Y (@ tptp.some_P7363390416028606310at_nat (@ (@ X A5) B2)))))))))))))))
% 9.16/7.10 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa3 tptp.option_num) (Xb3 tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa3) Xb3) Y) (=> (=> (= Xa3 tptp.none_num) _let_1) (=> (=> (exists ((V3 tptp.num)) (= Xa3 (@ tptp.some_num V3))) (=> (= Xb3 tptp.none_num) _let_1)) (not (forall ((A5 tptp.num)) (=> (= Xa3 (@ tptp.some_num A5)) (forall ((B2 tptp.num)) (=> (= Xb3 (@ tptp.some_num B2)) (not (= Y (@ tptp.some_num (@ (@ X A5) B2)))))))))))))))
% 9.16/7.10 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa3 tptp.option_nat) (Xb3 tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa3) Xb3) Y) (=> (=> (= Xa3 tptp.none_nat) _let_1) (=> (=> (exists ((V3 tptp.nat)) (= Xa3 (@ tptp.some_nat V3))) (=> (= Xb3 tptp.none_nat) _let_1)) (not (forall ((A5 tptp.nat)) (=> (= Xa3 (@ tptp.some_nat A5)) (forall ((B2 tptp.nat)) (=> (= Xb3 (@ tptp.some_nat B2)) (not (= Y (@ tptp.some_nat (@ (@ X A5) B2)))))))))))))))
% 9.16/7.10 (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)) (V3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V3)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F4 (-> 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 F4) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X3)) (@ tptp.some_P7363390416028606310at_nat Y3)))))))))))
% 9.16/7.10 (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)) (V3 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V3)) tptp.none_nat))))) (not (forall ((F4 (-> tptp.nat tptp.nat Bool)) (X3 tptp.nat) (Y3 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat F4) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X3)) (@ tptp.some_nat Y3)))))))))))
% 9.16/7.10 (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)) (V3 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V3)) tptp.none_num))))) (not (forall ((F4 (-> tptp.num tptp.num Bool)) (X3 tptp.num) (Y3 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num F4) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X3)) (@ tptp.some_num Y3)))))))))))
% 9.16/7.10 (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)) (V3 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V3)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F4 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A5 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat F4) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A5)) (@ tptp.some_P7363390416028606310at_nat B2)))))))))))
% 9.16/7.10 (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)) (V3 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V3)) tptp.none_nat))))) (not (forall ((F4 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B2 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat F4) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A5)) (@ tptp.some_nat B2)))))))))))
% 9.16/7.10 (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)) (V3 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V3)) tptp.none_num))))) (not (forall ((F4 (-> tptp.num tptp.num tptp.num)) (A5 tptp.num) (B2 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num F4) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A5)) (@ tptp.some_num B2)))))))))))
% 9.16/7.10 (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)))
% 9.16/7.10 (assert (forall ((Mi3 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 Mi3) Ma))) Deg) TreeList) Summary)) Deg) (=> (not (= Mi3 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)))))))))
% 9.16/7.10 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 9.16/7.10 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (I tptp.nat) (X tptp.vEBT_VEBTi) (Y tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I))) (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ _let_1 X)) I) Y) (@ _let_1 Y)))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat X) Maxi))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X))))))
% 9.16/7.10 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (I tptp.nat) (X tptp.vEBT_VEBTi)) (= (@ tptp.size_s7982070591426661849_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) X)) (@ tptp.size_s7982070591426661849_VEBTi Xs2))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real) (I tptp.nat) (X tptp.real)) (= (@ tptp.size_size_list_real (@ (@ (@ tptp.list_update_real Xs2) I) X)) (@ tptp.size_size_list_real Xs2))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X)) (@ tptp.size_size_list_nat Xs2))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I) (@ (@ tptp.nth_nat Xs2) I)) Xs2)))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs2) I) (@ (@ tptp.nth_int Xs2) I)) Xs2)))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) (@ (@ tptp.nth_VEBT_VEBT Xs2) I)) Xs2)))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (I tptp.nat)) (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) (@ (@ tptp.nth_VEBT_VEBTi Xs2) I)) Xs2)))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (X tptp.vEBT_VEBTi)) (=> (not (= I J)) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) X)) J) (@ (@ tptp.nth_VEBT_VEBTi Xs2) J)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (I tptp.nat) (X tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s7982070591426661849_VEBTi Xs2)) I) (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) X) Xs2))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_real) (I tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_real Xs2)) I) (= (@ (@ (@ tptp.list_update_real Xs2) I) X) Xs2))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) I) (= (@ (@ (@ tptp.list_update_nat Xs2) I) X) Xs2))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) J) X)) I) (@ (@ tptp.nth_VEBT_VEBT L) I)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBTi) (J tptp.nat) (X tptp.vEBT_VEBTi)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L))) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) J) X)) I) (@ (@ tptp.nth_VEBT_VEBTi L) I)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_real) (J tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L))) (= (@ (@ tptp.nth_real (@ (@ (@ tptp.list_update_real L) J) X)) I) (@ (@ tptp.nth_real L) I)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_o) (J tptp.nat) (X Bool)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L))) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o L) J) X)) I) (@ (@ tptp.nth_o L) I)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_nat) (J tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L))) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat L) J) X)) I) (@ (@ tptp.nth_nat L) I)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_int) (J tptp.nat) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L))) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int L) J) X)) I) (@ (@ tptp.nth_int L) I)))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (X tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) X)) I) X))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real (@ (@ (@ tptp.list_update_real Xs2) I) X)) I) X))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBTi Xs2))) (let ((_let_2 (@ tptp.size_s7982070591426661849_VEBTi Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_VEBT_VEBTi2 Xs2))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (Xs2 tptp.list_real) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_real Xs2))) (let ((_let_2 (@ tptp.size_size_list_real Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real (@ (@ (@ tptp.list_update_real Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_real2 Xs2))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((Mi3 tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Newlist 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.product_Pair_nat_nat Mi3))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_4 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_2) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) (@ (@ tptp.power_power_nat _let_1) _let_2))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_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.power_power_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xn) _let_2))) (let ((_let_6 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi3) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_5 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_4 _let_6))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_2) L) (=> (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 H2)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (I5 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (X6 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs2))) (=> (not (= I I5)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I) X)) I5) X6) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I5) X6)) I) X))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (I5 tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (X tptp.vEBT_VEBTi) (X6 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.list_u6098035379799741383_VEBTi Xs2))) (=> (not (= I I5)) (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ (@ _let_1 I) X)) I5) X6) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ (@ _let_1 I5) X6)) I) X))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (A2 tptp.set_VEBT_VEBTi) (X tptp.vEBT_VEBTi) (I tptp.nat)) (=> (@ (@ tptp.ord_le6592769550269828683_VEBTi (@ tptp.set_VEBT_VEBTi2 Xs2)) A2) (=> (@ (@ tptp.member_VEBT_VEBTi X) A2) (@ (@ tptp.ord_le6592769550269828683_VEBTi (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) X))) A2)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s3451745648224563538omplex L)) (= (@ _let_1 (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_complex2 L)) (forall ((Y6 tptp.complex)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex L) I) Y6)))))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L)) (= (@ _let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_VEBT_VEBT2 L)) (forall ((Y6 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y6)))))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBTi) (X tptp.vEBT_VEBTi) (Y tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.member_VEBT_VEBTi X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L)) (= (@ _let_1 (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_VEBT_VEBTi2 L)) (forall ((Y6 tptp.vEBT_VEBTi)) (@ (@ tptp.member_VEBT_VEBTi X) (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y6)))))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L)) (= (@ _let_1 (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_real2 L)) (forall ((Y6 tptp.real)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y6)))))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_o) (X Bool) (Y Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L)) (= (@ _let_1 (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_o2 L)) (forall ((Y6 Bool)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y6)))))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ _let_1 (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_nat2 L)) (forall ((Y6 tptp.nat)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y6)))))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ _let_1 (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y))) (or (= X Y) (and (@ _let_1 (@ tptp.set_int2 L)) (forall ((Y6 tptp.int)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y6)))))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N) X))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N) X))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (X tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (@ (@ tptp.member_VEBT_VEBTi X) (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) N) X))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N) X))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N) X))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N) X))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N) X))))))
% 9.16/7.10 (assert (forall ((X tptp.complex) (L tptp.list_complex) (I tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s3451745648224563538omplex L)) (not (= X Y))) (@ _let_1 (@ tptp.set_complex2 L)))))))
% 9.16/7.10 (assert (forall ((X tptp.vEBT_VEBT) (L tptp.list_VEBT_VEBT) (I tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L)) (not (= X Y))) (@ _let_1 (@ tptp.set_VEBT_VEBT2 L)))))))
% 9.16/7.10 (assert (forall ((X tptp.vEBT_VEBTi) (L tptp.list_VEBT_VEBTi) (I tptp.nat) (Y tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.member_VEBT_VEBTi X))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L)) (not (= X Y))) (@ _let_1 (@ tptp.set_VEBT_VEBTi2 L)))))))
% 9.16/7.10 (assert (forall ((X tptp.real) (L tptp.list_real) (I tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L)) (not (= X Y))) (@ _let_1 (@ tptp.set_real2 L)))))))
% 9.16/7.10 (assert (forall ((X Bool) (L tptp.list_o) (I tptp.nat) (Y Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ _let_1 (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L)) (= X (not Y))) (@ _let_1 (@ tptp.set_o2 L)))))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (L tptp.list_nat) (I tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (not (= X Y))) (@ _let_1 (@ tptp.set_nat2 L)))))))
% 9.16/7.10 (assert (forall ((X tptp.int) (L tptp.list_int) (I tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (not (= X Y))) (@ _let_1 (@ tptp.set_int2 L)))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_complex) (X tptp.complex) (Y tptp.complex)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s3451745648224563538omplex L)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex L) I) Y))) (or (= X Y) (forall ((Y6 tptp.complex)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex L) I) Y6)))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y))) (or (= X Y) (forall ((Y6 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) Y6)))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBTi) (X tptp.vEBT_VEBTi) (Y tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L)) (= (@ (@ tptp.member_VEBT_VEBTi X) (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y))) (or (= X Y) (forall ((Y6 tptp.vEBT_VEBTi)) (@ (@ tptp.member_VEBT_VEBTi X) (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) Y6)))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y))) (or (= X Y) (forall ((Y6 tptp.real)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) Y6)))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_o) (X Bool) (Y Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y))) (or (= X Y) (forall ((Y6 Bool)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) Y6)))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y))) (or (= X Y) (forall ((Y6 tptp.nat)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) Y6)))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (L tptp.list_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y))) (or (= X Y) (forall ((Y6 tptp.int)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) Y6)))))))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (X tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (= (= (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) X) Xs2) (= (@ (@ tptp.nth_VEBT_VEBTi Xs2) I) X)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (Xs2 tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs2)) (= (= (@ (@ (@ tptp.list_update_real Xs2) I) X) Xs2) (= (@ (@ tptp.nth_real Xs2) I) X)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) X)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L))))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT L) J))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_VEBT_VEBTi) (X tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) X)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L))))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBTi L) J))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.nth_real (@ (@ (@ tptp.list_update_real L) I) X)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L))))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_real L) J))))))))
% 9.16/7.10 (assert (forall ((L tptp.list_o) (I tptp.nat) (X Bool) (J tptp.nat)) (let ((_let_1 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L))))) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o L) I) X)) J) (and (=> _let_1 X) (=> (not _let_1) (@ (@ tptp.nth_o L) J)))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat L) I) X)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L))))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat L) J))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (J tptp.nat) (L tptp.list_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int L) I) X)) J))) (let ((_let_2 (and (= I J) (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L))))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int L) J))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (J tptp.nat) (X tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBTi (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBTi Xs2) J)))))))))
% 9.16/7.10 (assert (forall ((I tptp.nat) (Xs2 tptp.list_real) (J tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.nth_real (@ (@ (@ tptp.list_update_real Xs2) I) X)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real Xs2)) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_real Xs2) J)))))))))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))
% 9.16/7.10 (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))))))))
% 9.16/7.10 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (not (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (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 ((Mi 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 Mi) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Ma2)))))))))))
% 9.16/7.10 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi3 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 Mi3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi3) 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))))))))))))))
% 9.16/7.10 (assert (forall ((Mi3 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 Mi3) _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) Mi3) (=> (@ (@ 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 Mi3) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi3) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi3) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 9.16/7.10 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X2)) (@ tptp.some_nat Y6)))))
% 9.16/7.10 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 9.16/7.10 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (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)))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 9.16/7.10 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 9.16/7.10 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (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)))))))))
% 9.16/7.10 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K))))))
% 9.16/7.10 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q3))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q3)) (@ (@ tptp.times_times_nat N) Q3)))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q3)) (@ (@ tptp.plus_plus_nat N) Q3)))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q3))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M)) M) (@ (@ tptp.ord_max_nat N) M))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 9.16/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 9.16/7.11 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 9.16/7.11 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 9.16/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 9.16/7.11 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 9.16/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 9.16/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 9.16/7.11 (assert (forall ((Deg tptp.nat) (Mi3 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 Mi3) X) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) 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)))))))))))))))
% 9.16/7.11 (assert (forall ((Deg tptp.nat) (Mi3 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 Mi3) 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 Mi3) 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)))))))))))))))))))))
% 9.16/7.11 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 9.16/7.11 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q3) tptp.zero_z5237406670263579293d_enat) Q3)))
% 9.16/7.11 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q3) Q3)))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_int A) I2) (@ (@ tptp.ord_less_int I2) B)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) C)))))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_int A) I2) (@ (@ tptp.ord_less_eq_int I2) B)))))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I2) (@ (@ tptp.ord_less_int I2) B)))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= X Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Mi3))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 Ma))) Deg) TreeList) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (=> (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_3) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT) (Summary tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi3))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high X) _let_4))) (=> (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_6 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_4) L) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Mi3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat _let_3) _let_4)) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn))))))))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) _let_1))) (let ((_let_3 (@ tptp.nth_VEBT_VEBT _let_2))) (let ((_let_4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_5 (@ (@ tptp.divide_divide_nat Deg) _let_4))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_4) _let_5))) (let ((_let_7 (@ tptp.if_nat (= X Ma)))) (let ((_let_8 (@ tptp.product_Pair_nat_nat Mi3))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_5))) (=> (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_4) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_5) L) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_1)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 _let_11)))))) Ma)))) Deg) _let_2) _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 H2))))) Ma)))) Deg) _let_2) Summary)))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Mi3 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 Mi3) Ma))) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_high _let_7) _let_3))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_8)) (@ (@ tptp.vEBT_VEBT_low _let_7) _let_3)))) (let ((_let_10 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_8) _let_9))) (let ((_let_11 (@ tptp.nth_VEBT_VEBT _let_10))) (let ((_let_12 (@ tptp.if_nat (= _let_7 Ma)))) (let ((_let_13 (@ tptp.product_Pair_nat_nat _let_7))) (let ((_let_14 (@ (@ tptp.vEBT_vebt_delete Summary) _let_8))) (let ((_let_15 (@ tptp.vEBT_vebt_maxt _let_14))) (let ((_let_16 (@ tptp.the_nat _let_15))) (=> (and (= X Mi3) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_8) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ (@ tptp.if_nat (= _let_15 tptp.none_nat)) _let_7) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_16)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_16)))))) Ma)))) Deg) _let_10) _let_14)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_8))))) Ma)))) Deg) _let_10) Summary))) _let_1)))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_high Xn) _let_4))) (let ((_let_8 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi3) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_7 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_5)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_8))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_4) L) (=> (@ (@ tptp.ord_less_nat _let_7) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_6 H2)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn)))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_3))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi3) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_12 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_3) L) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_12 H2)) L)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Newnode)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ _let_1 H2)) L))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT _let_3))) (let ((_let_5 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_6 (@ (@ tptp.divide_divide_nat Deg) _let_5))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_5) _let_6))) (let ((_let_8 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_9 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_10 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ tptp.the_nat _let_11))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_6))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi3) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_5) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_1 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_6) L) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) Deg) TreeList) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_2)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ (@ tptp.if_nat (= _let_11 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_12)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 _let_12)))))) Ma)))) Deg) _let_3) _let_10)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 H2))))) Ma)))) Deg) _let_3) Summary))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (X 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 Mi3) Ma))) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (= X Mi3))) (let ((_let_9 (@ tptp.if_nat _let_8))) (let ((_let_10 (@ (@ _let_9 _let_7) X))) (let ((_let_11 (@ (@ tptp.vEBT_VEBT_high _let_10) _let_3))) (let ((_let_12 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_11)) (@ (@ tptp.vEBT_VEBT_low _let_10) _let_3)))) (let ((_let_13 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_11) _let_12))) (let ((_let_14 (@ tptp.nth_VEBT_VEBT _let_13))) (let ((_let_15 (@ tptp.if_nat (and (=> _let_8 (= _let_7 Ma)) (=> (not _let_8) (= X Ma)))))) (let ((_let_16 (@ (@ _let_9 _let_10) Mi3))) (let ((_let_17 (@ tptp.product_Pair_nat_nat _let_16))) (let ((_let_18 (@ (@ tptp.vEBT_vebt_delete Summary) _let_11))) (let ((_let_19 (@ tptp.vEBT_vebt_maxt _let_18))) (let ((_let_20 (@ tptp.the_nat _let_19))) (=> (and (@ (@ tptp.ord_less_eq_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi3 Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_11) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_12)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ (@ tptp.if_nat (= _let_19 tptp.none_nat)) _let_16) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_20)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_20)))))) Ma)))) Deg) _let_13) _let_18)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_11) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_11))))) Ma)))) Deg) _let_13) Summary))) _let_1)))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi3 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 Mi3) 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 Mi3) X)) (@ tptp.some_nat Mi3)) 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)))))))))))))))
% 9.16/7.11 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi3 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 Mi3) 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 Mi3) X)) (@ tptp.some_nat Mi3)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 9.16/7.11 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B4 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B4)) B4) A3))))
% 9.16/7.11 (assert (= tptp.ord_max_set_nat (lambda ((A3 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B4)) B4) A3))))
% 9.16/7.11 (assert (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B4 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B4)) B4) A3))))
% 9.16/7.11 (assert (= tptp.ord_max_num (lambda ((A3 tptp.num) (B4 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B4)) B4) A3))))
% 9.16/7.11 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B4)) B4) A3))))
% 9.16/7.11 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B4)) B4) A3))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 9.16/7.11 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 9.16/7.11 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) A)))) (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) B)))) (and (@ (@ tptp.dvd_dvd_complex A) B) (not (@ (@ tptp.dvd_dvd_complex B) A))))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) A)))) (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) A)))) (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 9.16/7.11 (assert (= (lambda ((X2 tptp.rat)) X2) (@ tptp.times_times_rat tptp.one_one_rat)))
% 9.16/7.11 (assert (= (lambda ((X2 tptp.assn)) X2) (@ tptp.times_times_assn tptp.one_one_assn)))
% 9.16/7.11 (assert (= (lambda ((X2 tptp.real)) X2) (@ tptp.times_times_real tptp.one_one_real)))
% 9.16/7.11 (assert (= (lambda ((X2 tptp.nat)) X2) (@ tptp.times_times_nat tptp.one_one_nat)))
% 9.16/7.11 (assert (= (lambda ((X2 tptp.int)) X2) (@ tptp.times_times_int tptp.one_one_int)))
% 9.16/7.11 (assert (= (lambda ((X2 tptp.code_integer)) X2) (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer)))
% 9.16/7.11 (assert (= (lambda ((X2 tptp.complex)) X2) (@ tptp.times_times_complex tptp.one_one_complex)))
% 9.16/7.11 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 9.16/7.11 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 9.16/7.11 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 9.16/7.11 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 9.16/7.11 (assert (= (lambda ((H tptp.code_integer)) tptp.zero_z3403309356797280102nteger) (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger)))
% 9.16/7.11 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 9.16/7.11 (assert (forall ((C tptp.assn)) (= (lambda ((X2 tptp.assn)) (@ (@ tptp.times_times_assn X2) C)) (@ tptp.times_times_assn C))))
% 9.16/7.11 (assert (forall ((C tptp.real)) (= (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C)) (@ tptp.times_times_real C))))
% 9.16/7.11 (assert (forall ((C tptp.nat)) (= (lambda ((X2 tptp.nat)) (@ (@ tptp.times_times_nat X2) C)) (@ tptp.times_times_nat C))))
% 9.16/7.11 (assert (forall ((C tptp.int)) (= (lambda ((X2 tptp.int)) (@ (@ tptp.times_times_int X2) C)) (@ tptp.times_times_int C))))
% 9.16/7.11 (assert (forall ((C tptp.code_integer)) (= (lambda ((X2 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger X2) C)) (@ tptp.times_3573771949741848930nteger C))))
% 9.16/7.11 (assert (forall ((C tptp.complex)) (= (lambda ((X2 tptp.complex)) (@ (@ tptp.times_times_complex X2) C)) (@ tptp.times_times_complex C))))
% 9.16/7.11 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) A)))) (@ tptp.collect_complex (lambda ((C4 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C4) B)))) (@ (@ tptp.dvd_dvd_complex A) B))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) A)))) (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) A)))) (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 9.16/7.11 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A6))) (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) B7))))))
% 9.16/7.11 (assert (= tptp.ord_less_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) A6))) (lambda ((X2 tptp.real)) (@ (@ tptp.member_real X2) B7))))))
% 9.16/7.11 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A6))) (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) B7))))))
% 9.16/7.11 (assert (= tptp.ord_le3480810397992357184T_VEBT (lambda ((A6 tptp.set_VEBT_VEBT) (B7 tptp.set_VEBT_VEBT)) (@ (@ tptp.ord_less_VEBT_VEBT_o (lambda ((X2 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X2) A6))) (lambda ((X2 tptp.vEBT_VEBT)) (@ (@ tptp.member_VEBT_VEBT X2) B7))))))
% 9.16/7.11 (assert (= tptp.ord_less_set_complex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ (@ tptp.ord_less_complex_o (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) A6))) (lambda ((X2 tptp.complex)) (@ (@ tptp.member_complex X2) B7))))))
% 9.16/7.11 (assert (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D tptp.int)) (@ (@ tptp.dvd_dvd_int D) I)))))))
% 9.16/7.11 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I)))))))
% 9.16/7.11 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 9.16/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B4)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 9.16/7.11 (assert (forall ((Z tptp.assn) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_assn Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_assn _let_2) _let_2))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((Z tptp.code_integer) (W tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_2))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((Z tptp.assn) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_assn Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn Z) _let_2)) _let_2))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((Z tptp.code_integer) (W tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger Z) _let_2)) _let_2))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 9.16/7.11 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D tptp.nat)) (@ (@ tptp.dvd_dvd_nat D) M)))))))
% 9.16/7.11 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 9.16/7.11 (assert (= tptp.minus_minus_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 9.16/7.11 (assert (= tptp.divide_divide_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 9.16/7.11 (assert (= tptp.modulo_modulo_nat (lambda ((A3 tptp.nat) (B4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B4))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z6 tptp.real)) (= (@ (@ tptp.power_power_real Z6) N) tptp.one_one_real)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) tptp.one_one_complex)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (N tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger A2) (@ tptp.finite1283093830868386564nteger (@ tptp.collec3483841146883906114nteger (lambda ((Xs tptp.list_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.set_Code_integer2 Xs)) A2) (= (@ tptp.size_s3445333598471063425nteger Xs) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (N tptp.nat)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite306553202115118035t_real (@ tptp.collect_list_real (lambda ((Xs tptp.list_real)) (and (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (= (@ tptp.size_size_list_real Xs) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (= (@ tptp.size_size_list_o Xs) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (= (@ tptp.size_size_list_int Xs) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (= (@ tptp.size_size_list_nat Xs) N))))))))
% 9.16/7.11 (assert (forall ((Z5 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z5))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z5)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z5) 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)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (N tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger A2) (@ tptp.finite1283093830868386564nteger (@ tptp.collec3483841146883906114nteger (lambda ((Xs tptp.list_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.set_Code_integer2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3445333598471063425nteger Xs)) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (N tptp.nat)) (=> (@ tptp.finite_finite_real A2) (@ tptp.finite306553202115118035t_real (@ tptp.collect_list_real (lambda ((Xs tptp.list_real)) (and (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_real Xs)) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A3 tptp.code_integer) (N3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N3 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((O tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.semiri4939895301339042750nteger O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_Code_integer)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 9.16/7.11 (assert (forall ((Va2 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 Va2)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ tptp.vEBT_V8346862874174094_d_u_p _let_4))) (let ((_let_6 (@ (@ tptp.plus_plus_nat _let_5) tptp.one_one_nat))) (let ((_let_7 (@ tptp.suc _let_4))) (let ((_let_8 (@ tptp.power_power_nat _let_2))) (let ((_let_9 (@ tptp.vEBT_V8346862874174094_d_u_p _let_3))) (let ((_let_10 (@ (@ tptp.dvd_dvd_nat _let_2) _let_3))) (and (=> _let_10 (= _let_9 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_8 _let_4)) _let_6))))) (=> (not _let_10) (= _let_9 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 _let_1)))) (@ tptp.vEBT_V8346862874174094_d_u_p _let_7))) (@ (@ tptp.times_times_nat (@ _let_8 _let_7)) _let_6)))))))))))))))))
% 9.16/7.11 (assert (forall ((Va2 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 Va2)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ tptp.vEBT_V8646137997579335489_i_l_d _let_4))) (let ((_let_6 (@ tptp.suc _let_4))) (let ((_let_7 (@ tptp.power_power_nat _let_2))) (let ((_let_8 (@ tptp.vEBT_V8646137997579335489_i_l_d _let_3))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_2) _let_3))) (and (=> _let_9 (= _let_8 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_7 _let_4)) _let_5))))) (=> (not _let_9) (= _let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ tptp.vEBT_V8646137997579335489_i_l_d _let_6))) (@ (@ tptp.times_times_nat (@ _let_7 _let_6)) _let_5))))))))))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))) (=> (= (@ tptp.vEBT_V8346862874174094_d_u_p X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.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_V8346862874174094_d_u_p _let_4))) (let ((_let_6 (@ (@ tptp.plus_plus_nat _let_5) tptp.one_one_nat))) (let ((_let_7 (@ tptp.suc _let_4))) (let ((_let_8 (@ tptp.power_power_nat _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_2) _let_3))) (=> (= X _let_3) (not (and (=> _let_9 (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_8 _let_4)) _let_6))))) (=> (not _let_9) (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 _let_1)))) (@ tptp.vEBT_V8346862874174094_d_u_p _let_7))) (@ (@ tptp.times_times_nat (@ _let_8 _let_7)) _let_6))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))) (=> (= (@ tptp.vEBT_V8646137997579335489_i_l_d X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.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_V8646137997579335489_i_l_d _let_4))) (let ((_let_6 (@ tptp.suc _let_4))) (let ((_let_7 (@ tptp.power_power_nat _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_3))) (=> (= X _let_3) (not (and (=> _let_8 (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_7 _let_4)) _let_5))))) (=> (not _let_8) (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ tptp.vEBT_V8646137997579335489_i_l_d _let_6))) (@ (@ tptp.times_times_nat (@ _let_7 _let_6)) _let_5)))))))))))))))))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi3)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) _let_1) TreeList) Summary)) X) (=> (not (= X Mi3)) (=> (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))))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 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 Mi3) Ma))) _let_1) TreeList) Vc2)) X) (or (= X Mi3) (= 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)))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _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) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList2) S2))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa3) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList2) S2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa3) Y) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _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) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList2) S2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B4 tptp.extended_enat) (A3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B4)) (not (= A3 B4))))))
% 9.16/7.11 (assert (= tptp.ord_less_real (lambda ((B4 tptp.real) (A3 tptp.real)) (and (= A3 (@ (@ tptp.ord_max_real A3) B4)) (not (= A3 B4))))))
% 9.16/7.11 (assert (= tptp.ord_less_rat (lambda ((B4 tptp.rat) (A3 tptp.rat)) (and (= A3 (@ (@ tptp.ord_max_rat A3) B4)) (not (= A3 B4))))))
% 9.16/7.11 (assert (= tptp.ord_less_num (lambda ((B4 tptp.num) (A3 tptp.num)) (and (= A3 (@ (@ tptp.ord_max_num A3) B4)) (not (= A3 B4))))))
% 9.16/7.11 (assert (= tptp.ord_less_nat (lambda ((B4 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_max_nat A3) B4)) (not (= A3 B4))))))
% 9.16/7.11 (assert (= tptp.ord_less_int (lambda ((B4 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.ord_max_int A3) B4)) (not (= A3 B4))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa3) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa3 Mi) (= Xa3 Ma2))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc V3)) TreeList2) Vc))) (not (or (= Xa3 Mi) (= Xa3 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3)))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3)))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa3) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa3) Mi)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (not (=> (not (= Xa3 Mi)) (=> (not (= Xa3 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa3) 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 ((Mi tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa3 Mi) (= Xa3 Ma2)))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc V3)) TreeList2) Vc))) (= Y (not (or (= Xa3 Mi) (= Xa3 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa3)) (=> (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 ((Mi tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa3 Mi) (= Xa3 Ma2)))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc V3)) TreeList2) Vc))) (or (= Xa3 Mi) (= Xa3 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 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 Va2)))) (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 Mi3) Ma))) _let_3) TreeList) Summary)) X) (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= X Mi3)) 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) Mi3)) 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)))))))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) 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) Mi3)))) (let ((_let_5 (@ (@ _let_4 Mi3) 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 Mi3) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi3)) (@ (@ 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)))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa3) Y) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc))) Y) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa3) Mi)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (= Y (not (=> (not (= Xa3 Mi)) (=> (not (= Xa3 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc)))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa3) Mi)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (=> (not (= Xa3 Mi)) (=> (not (= Xa3 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) _let_3))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 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) Xa3) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (not (= Y (@ (@ tptp.plus_plus_nat _let_1) (@ (@ (@ tptp.if_nat (= Xa3 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 ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz2))) _let_2) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc))) _let_2) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa3) _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 Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (not (= Y (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= Xa3 Mi)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (= Xa3 Ma2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa3) Mi)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa3)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ _let_5 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_3)))) tptp.one_one_nat)))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa3) Y) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (= Xa3 tptp.one_one_nat))) (let ((_let_4 (= Xa3 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B2))) (=> (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 ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V3)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa3) Xa3))) _let_1) TreeList2) Summary2)))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa3) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) Xa3))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa3 Mi) (= Xa3 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa3) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 9.16/7.11 (assert (forall ((Ma tptp.nat) (X tptp.nat) (Mi3 tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_6 (@ tptp.vEBT_vebt_mint _let_5))) (let ((_let_7 (@ (@ tptp.vEBT_T_p_r_e_d2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) _let_1) TreeList) Summary)) X))) (let ((_let_8 (@ (@ tptp.ord_less_nat Ma) X))) (and (=> _let_8 (= _let_7 tptp.one_one_nat)) (=> (not _let_8) (= _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_nat (and (not (= _let_6 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_4)) _let_6))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_p_r_e_d2 _let_5) _let_4))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_p_r_e_d2 Summary) _let_3)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_6 (@ tptp.vEBT_vebt_maxt _let_5))) (let ((_let_7 (@ (@ tptp.vEBT_T_s_u_c_c2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) _let_1) TreeList) Summary)) X))) (let ((_let_8 (@ (@ tptp.ord_less_nat X) Mi3))) (and (=> _let_8 (= _let_7 tptp.one_one_nat)) (=> (not _let_8) (= _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_nat (and (not (= _let_6 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_4)) _let_6))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_s_u_c_c2 _let_5) _let_4))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_s_u_c_c2 Summary) _let_3)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat) (Va2 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 Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_6 (= X Mi3))) (let ((_let_7 (@ (@ (@ tptp.if_nat _let_6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) (@ (@ tptp.power_power_nat _let_1) _let_3))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4))))) X))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_high _let_7) _let_3))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low _let_7) _let_3))) (let ((_let_10 (@ _let_5 _let_8))) (let ((_let_11 (@ (@ tptp.vEBT_V1232361888498592333_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) _let_2) TreeList) Summary)) X))) (let ((_let_12 (and _let_6 (= X Ma)))) (let ((_let_13 (= _let_11 tptp.one_one_nat))) (let ((_let_14 (or (@ (@ tptp.ord_less_nat X) Mi3) (@ (@ tptp.ord_less_nat Ma) X)))) (and (=> _let_14 _let_13) (=> (not _let_14) (and (=> _let_12 _let_13) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_8) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_V1232361888498592333_e_t_e _let_10) _let_9)) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete _let_10) _let_9))) (@ (@ tptp.vEBT_V1232361888498592333_e_t_e Summary) _let_8)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((Ma tptp.nat) (X tptp.nat) (Mi3 tptp.nat) (Va2 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 Va2)))) (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 Mi3) 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 Mi3) X)) (@ tptp.some_nat Mi3)) 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))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat) (Va2 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 Va2)))) (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 Mi3) Ma))) _let_2) TreeList) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat X) Mi3))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi3))) (=> (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))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (Mi3 tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) _let_1) TreeList) Summary))) (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.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= X Mi3))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) X))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= X Ma))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi3))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (@ (@ tptp.vEBT_vebt_delete _let_2) X))) (let ((_let_24 (and _let_9 _let_16))) (let ((_let_25 (or (@ (@ tptp.ord_less_nat X) Mi3) (@ (@ tptp.ord_less_nat Ma) X)))) (and (=> _let_25 (= _let_23 _let_2)) (=> (not _let_25) (and (=> _let_24 (= _let_23 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary))) (=> (not _let_24) (= _let_23 (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma)))) _let_1) _let_14) Summary))) _let_2)))))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_p_r_e_d2 X) Xa3) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa3 tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((A5 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= Xa3 (@ tptp.suc tptp.zero_zero_nat)) _let_1)) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (exists ((Va tptp.nat)) (= Xa3 (@ tptp.suc (@ tptp.suc Va)))) _let_1)) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_6 (@ tptp.vEBT_vebt_mint _let_5))) (let ((_let_7 (@ (@ tptp.ord_less_nat Ma2) Xa3))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2)) (not (and (=> _let_7 (= Y tptp.one_one_nat)) (=> (not _let_7) (= Y (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_nat (and (not (= _let_6 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_4)) _let_6))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_p_r_e_d2 _let_5) _let_4))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_p_r_e_d2 Summary2) _let_3)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c2 X) Xa3) Y) (=> (=> (exists ((Uu2 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= Xa3 tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N2 tptp.nat)) (= Xa3 (@ tptp.suc N2))) _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 ((V3 tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc) Vd2))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_6 (@ tptp.vEBT_vebt_maxt _let_5))) (let ((_let_7 (@ (@ tptp.ord_less_nat Xa3) Mi))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2)) (not (and (=> _let_7 (= Y tptp.one_one_nat)) (=> (not _let_7) (= Y (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_nat (and (not (= _let_6 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_4)) _let_6))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_s_u_c_c2 _let_5) _let_4))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_s_u_c_c2 Summary2) _let_3)) tptp.one_one_nat))) tptp.one_one_nat))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa3) Y) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (=> (= Xa3 tptp.zero_zero_nat) (not (= Y (@ (@ tptp.vEBT_Leaf false) B2)))))) (=> (forall ((A5 Bool)) (=> (exists ((B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= Xa3 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y (@ (@ tptp.vEBT_Leaf A5) false)))))) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (exists ((N2 tptp.nat)) (= Xa3 (@ tptp.suc (@ tptp.suc N2)))) (not (= Y _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) TrLst2) Smry2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (=> (= X _let_1) (not (= Y _let_1))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa3 Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa3))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa3 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa3) Mi) (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (=> (= X _let_2) (not (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))))))))))))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e X) Xa3) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= Xa3 tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= Xa3 (@ tptp.suc tptp.zero_zero_nat)) _let_1)) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (exists ((N2 tptp.nat)) (= Xa3 (@ tptp.suc (@ tptp.suc N2)))) _let_1)) (=> (=> (exists ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) _let_1) (=> (=> (exists ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2))) _let_1) (=> (=> (exists ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.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.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (= Xa3 Mi))) (let ((_let_7 (@ (@ (@ tptp.if_nat _let_6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) (@ (@ tptp.power_power_nat _let_1) _let_3))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4))))) Xa3))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_high _let_7) _let_3))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low _let_7) _let_3))) (let ((_let_10 (@ _let_5 _let_8))) (let ((_let_11 (and _let_6 (= Xa3 Ma2)))) (let ((_let_12 (= Y tptp.one_one_nat))) (let ((_let_13 (or (@ (@ tptp.ord_less_nat Xa3) Mi) (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_13 _let_12) (=> (not _let_13) (and (=> _let_11 _let_12) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_8) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_V1232361888498592333_e_t_e _let_10) _let_9)) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete _let_10) _let_9))) (@ (@ tptp.vEBT_V1232361888498592333_e_t_e Summary2) _let_8)) tptp.one_one_nat))) tptp.one_one_nat)))))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa3) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa3 tptp.zero_zero_nat) _let_1)) (=> (forall ((A5 Bool)) (=> (exists ((Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= Xa3 (@ 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) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (=> (exists ((Va tptp.nat)) (= Xa3 (@ tptp.suc (@ tptp.suc Va)))) (not (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (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) (Va3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.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 Xa3) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa3) _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) Xa3))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_2) TreeList2) 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 TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) Xa3)) (@ 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)))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa3) Y) (=> (forall ((Uu2 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uu2) B2)) (=> (= Xa3 tptp.zero_zero_nat) (not (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= Y tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N2 tptp.nat)) (= Xa3 (@ tptp.suc N2))) _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 ((V3 tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc) Vd2))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.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 Xa3) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa3) _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 Xa3) Mi))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Mi))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))))))))))))
% 9.16/7.11 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K3) _let_1))))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K3) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 9.16/7.11 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 9.16/7.11 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 9.16/7.11 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 9.16/7.11 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (N tptp.nat)) (@ (@ (@ (@ tptp.time_htt_nat tptp.one_one_assn) (@ (@ tptp.vEBT_VEBT_lowi X) N)) (lambda ((R5 tptp.nat)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_VEBT_low X) N))))) tptp.one_one_nat)))
% 9.16/7.11 (assert (forall ((X tptp.nat) (N tptp.nat)) (@ (@ (@ (@ tptp.time_htt_nat tptp.one_one_assn) (@ (@ tptp.vEBT_VEBT_highi X) N)) (lambda ((R5 tptp.nat)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_VEBT_high X) N))))) tptp.one_one_nat)))
% 9.16/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.divide_divide_nat X))) (let ((_let_3 (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat (@ _let_2 _let_1)) Y)))) (let ((_let_4 (@ (@ tptp.minus_minus_nat X) (@ (@ tptp.times_times_nat _let_3) Y)))) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.product_Pair_nat_nat (@ _let_2 Y)) (@ (@ tptp.modulo_modulo_nat X) Y)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat Y) _let_4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_3) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat _let_4) Y))) (@ (@ tptp.product_Pair_nat_nat _let_3) _let_4))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 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) Xa3) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (not (= Y (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa3 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 ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V3))) TreeList2) Summary2))) (not (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc 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 Xa3) Mi)) Mi) Xa3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_5))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_2) TreeList2) 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 TreeList2)) (not (or (= Xa3 Mi) (= Xa3 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))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X) Xa3) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) _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 ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz2))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_1))) (let ((_let_3 (@ tptp.ord_less_nat Xa3))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (not (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa3 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa3 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_3 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi) Xa3) (@ _let_3 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_1))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 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 Va2)))) (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) Mi3)) Mi3) 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 Mi3) 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 Mi3) (= 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)))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X) Xa3) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) _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 ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V3))) TreeList2) Summary2))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa3) Mi)) Mi) Xa3))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2)) (not (= Y (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa3 Mi) (= Xa3 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)))))))))))))))))))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))
% 9.16/7.11 (assert (forall ((Uu Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf Uu) true)) tptp.one_one_nat)))
% 9.16/7.11 (assert (forall ((Uv Bool)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf true) Uv)) tptp.one_one_nat)))
% 9.16/7.11 (assert (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ tptp.vEBT_Leaf false) false)) tptp.one_one_nat))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))
% 9.16/7.11 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va2 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_T_m_i_n_N_u_l_l (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va2) Vb) Vc2)) tptp.one_one_nat)))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) Y)) tptp.one_one_nat)))))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ tptp.vEBT_VEBT_minNull T) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) L)) tptp.one_one_nat)))))
% 9.16/7.11 (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)))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 T) X)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))))))
% 9.16/7.11 (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) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc))) _let_1))))))))))
% 9.16/7.11 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc2 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) Vc2)) X) tptp.one_one_nat)))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ 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))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi3)) Mi3) 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 Mi3) Ma))) _let_1) TreeList) Summary)) X) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X Mi3) (= 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)))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ tptp.ord_less_nat X))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) _let_1) TreeList) Summary)) X) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= X Mi3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X Ma)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_4 Mi3)) 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 Mi3) 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)))))))))))))
% 9.16/7.11 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat N3) K))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e X) Xa3) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= Xa3 tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= Xa3 (@ tptp.suc tptp.zero_zero_nat)) _let_1)) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (exists ((N2 tptp.nat)) (= Xa3 (@ tptp.suc (@ tptp.suc N2)))) _let_1)) (=> (=> (exists ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) _let_1) (=> (=> (exists ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2))) _let_1) (=> (=> (exists ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.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.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ _let_6 _let_5))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) (@ (@ tptp.power_power_nat _let_2) _let_4))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint _let_7))))) (let ((_let_9 (= Xa3 Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa3))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4))) (let ((_let_14 (@ _let_6 _let_12))) (let ((_let_15 (@ (@ tptp.vEBT_vebt_delete _let_14) _let_13))) (let ((_let_16 (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_12) _let_15)))) (let ((_let_17 (@ tptp.bit1 tptp.one))) (let ((_let_18 (@ tptp.bit0 _let_17))) (let ((_let_19 (= Xa3 Ma2))) (let ((_let_20 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_19))))) (let ((_let_21 (@ tptp.plus_plus_nat _let_2))) (let ((_let_22 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_23 (@ tptp.vEBT_vebt_maxt _let_22))) (let ((_let_24 (@ tptp.bit0 _let_1))) (let ((_let_25 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_26 (@ tptp.numeral_numeral_nat _let_17))) (let ((_let_27 (@ tptp.plus_plus_nat _let_26))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_3) TreeList2) Summary2)) (not (= Y (@ _let_27 (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat Xa3) Mi) (@ (@ tptp.ord_less_nat Ma2) Xa3))) tptp.one_one_nat) (@ _let_27 (@ (@ (@ tptp.if_nat (and _let_9 _let_19)) _let_26) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_18))) (@ (@ _let_10 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.vEBT_T_m_i_n_t Summary2)) (@ tptp.vEBT_T_m_i_n_t _let_7))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_17)))) tptp.one_one_nat))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat _let_24)) (@ (@ tptp.vEBT_T_d_e_l_e_t_e _let_14) _let_13))) (@ (@ tptp.plus_plus_nat (@ _let_25 (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_15))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_15)) (@ (@ tptp.plus_plus_nat (@ _let_25 (@ (@ tptp.vEBT_T_d_e_l_e_t_e Summary2) _let_12))) (@ _let_21 (@ (@ _let_20 (@ (@ tptp.plus_plus_nat (@ _let_25 (@ tptp.vEBT_T_m_a_x_t _let_22))) (@ _let_25 (@ (@ (@ tptp.if_nat (= _let_23 tptp.none_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_24))) (@ tptp.vEBT_T_m_a_x_t (@ _let_16 (@ tptp.the_nat _let_23)))))))) tptp.one_one_nat)))) (@ _let_21 (@ (@ _let_20 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat _let_18)) (@ tptp.vEBT_T_m_a_x_t (@ _let_16 _let_12)))) tptp.one_one_nat)))))) tptp.one_one_nat))))))))))))))))))))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 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 Va2)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_7 (@ _let_6 _let_5))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) (@ (@ tptp.power_power_nat _let_2) _let_4))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint _let_7))))) (let ((_let_9 (= X Mi3))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) X))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4))) (let ((_let_14 (@ _let_6 _let_12))) (let ((_let_15 (@ (@ tptp.vEBT_vebt_delete _let_14) _let_13))) (let ((_let_16 (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_12) _let_15)))) (let ((_let_17 (@ tptp.bit1 tptp.one))) (let ((_let_18 (@ tptp.bit0 _let_17))) (let ((_let_19 (= X Ma))) (let ((_let_20 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma)) (=> (not _let_9) _let_19))))) (let ((_let_21 (@ tptp.plus_plus_nat _let_2))) (let ((_let_22 (@ (@ tptp.vEBT_vebt_delete Summary) _let_12))) (let ((_let_23 (@ tptp.vEBT_vebt_maxt _let_22))) (let ((_let_24 (@ tptp.bit0 _let_1))) (let ((_let_25 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_26 (@ tptp.numeral_numeral_nat _let_17))) (let ((_let_27 (@ tptp.plus_plus_nat _let_26))) (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) _let_3) TreeList) Summary)) X) (@ _let_27 (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat X) Mi3) (@ (@ tptp.ord_less_nat Ma) X))) tptp.one_one_nat) (@ _let_27 (@ (@ (@ tptp.if_nat (and _let_9 _let_19)) _let_26) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_18))) (@ (@ _let_10 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.vEBT_T_m_i_n_t Summary)) (@ tptp.vEBT_T_m_i_n_t _let_7))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_17)))) tptp.one_one_nat))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat _let_24)) (@ (@ tptp.vEBT_T_d_e_l_e_t_e _let_14) _let_13))) (@ (@ tptp.plus_plus_nat (@ _let_25 (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_15))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_15)) (@ (@ tptp.plus_plus_nat (@ _let_25 (@ (@ tptp.vEBT_T_d_e_l_e_t_e Summary) _let_12))) (@ _let_21 (@ (@ _let_20 (@ (@ tptp.plus_plus_nat (@ _let_25 (@ tptp.vEBT_T_m_a_x_t _let_22))) (@ _let_25 (@ (@ (@ tptp.if_nat (= _let_23 tptp.none_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_24))) (@ tptp.vEBT_T_m_a_x_t (@ _let_16 (@ tptp.the_nat _let_23)))))))) tptp.one_one_nat)))) (@ _let_21 (@ (@ _let_20 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat _let_18)) (@ tptp.vEBT_T_m_a_x_t (@ _let_16 _let_12)))) tptp.one_one_nat)))))) tptp.one_one_nat))))))))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c X) Xa3) Y) (=> (=> (exists ((Uu2 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= Xa3 tptp.zero_zero_nat) (not (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N2 tptp.nat)) (= Xa3 (@ tptp.suc N2))) _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 ((V3 tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc) Vd2))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _let_1)))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (let ((_let_8 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa3) _let_3))) (let ((_let_10 (@ _let_6 _let_4))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_2) TreeList2) Summary2)) (not (= Y (@ _let_8 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa3) Mi)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ _let_8 (@ tptp.vEBT_T_m_a_x_t _let_10))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ (@ tptp.if_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ _let_7 (@ (@ tptp.vEBT_T_s_u_c_c _let_10) _let_9))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_8 (@ (@ tptp.vEBT_T_s_u_c_c Summary2) _let_4))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_5 tptp.none_nat)) tptp.one_one_nat) (@ _let_7 (@ tptp.vEBT_T_m_i_n_t (@ _let_6 (@ tptp.the_nat _let_5)))))))))) tptp.one_one_nat)))))))))))))))))))))))))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((Mi3 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 Mi3) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((Mi3 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 Mi3) Ma))) Ux) Uy) Uz)) tptp.one_one_nat)))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((A8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A8) (=> (forall ((B8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B8) A8) (@ P B8))) (@ P A8)))) (@ P A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((A8 tptp.set_int)) (=> (@ tptp.finite_finite_int A8) (=> (forall ((B8 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B8) A8) (@ P B8))) (@ P A8)))) (@ P A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((A8 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A8) (=> (forall ((B8 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex B8) A8) (@ P B8))) (@ P A8)))) (@ P A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (forall ((A8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A8) (=> (forall ((B8 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le1307284697595431911nteger B8) A8) (@ P B8))) (@ P A8)))) (@ P A2)))))
% 9.16/7.11 (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) (B2 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (not (= Y (@ _let_1 (@ (@ (@ tptp.if_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) _let_1) (not (=> (exists ((Mi 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 Mi) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 9.16/7.11 (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 ((B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (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 ((Mi 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 Mi) Ma2))) Ux2) Uy2) Uz2))) _let_1))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 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 Va2)))) (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.vEBT_vebt_pred Summary) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList))) (let ((_let_8 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (let ((_let_9 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_10 (@ (@ tptp.vEBT_VEBT_low X) _let_4))) (let ((_let_11 (@ _let_7 _let_5))) (let ((_let_12 (@ tptp.vEBT_vebt_mint _let_11))) (= (@ (@ tptp.vEBT_T_p_r_e_d (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) _let_3) TreeList) Summary)) X) (@ _let_9 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_2) (@ tptp.vEBT_T_m_i_n_t _let_11))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))) (@ (@ (@ tptp.if_nat (and (not (= _let_12 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_10)) _let_12))) (@ _let_8 (@ (@ tptp.vEBT_T_p_r_e_d _let_11) _let_10))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_9 (@ (@ tptp.vEBT_T_p_r_e_d Summary) _let_5))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_6 tptp.none_nat)) (@ _let_9 tptp.one_one_nat)) (@ _let_8 (@ tptp.vEBT_T_m_a_x_t (@ _let_7 (@ tptp.the_nat _let_6))))))))) tptp.one_one_nat)))))))))))))))))))
% 9.16/7.11 (assert (forall ((Mi3 tptp.nat) (Ma tptp.nat) (Va2 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 Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) (@ tptp.numeral_numeral_nat _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.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (let ((_let_8 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_10 (@ _let_6 _let_4))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (= (@ (@ tptp.vEBT_T_s_u_c_c (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma))) _let_2) TreeList) Summary)) X) (@ _let_8 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi3)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.plus_plus_nat (@ _let_8 (@ tptp.vEBT_T_m_a_x_t _let_10))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ (@ tptp.if_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ _let_7 (@ (@ tptp.vEBT_T_s_u_c_c _let_10) _let_9))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_8 (@ (@ tptp.vEBT_T_s_u_c_c Summary) _let_4))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_5 tptp.none_nat)) tptp.one_one_nat) (@ _let_7 (@ tptp.vEBT_T_m_i_n_t (@ _let_6 (@ tptp.the_nat _let_5)))))))))) tptp.one_one_nat))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (let ((_let_1 (not (= Y tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_p_r_e_d X) Xa3) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa3 tptp.zero_zero_nat) _let_1)) (=> (=> (exists ((A5 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= Xa3 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (=> (exists ((Va tptp.nat)) (= Xa3 (@ tptp.suc (@ tptp.suc Va)))) (not (= Y (@ _let_1 (@ (@ (@ tptp.if_nat B2) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V3 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) _let_1) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.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 Xa3) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (let ((_let_9 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_10 (@ (@ tptp.vEBT_VEBT_low Xa3) _let_4))) (let ((_let_11 (@ _let_7 _let_5))) (let ((_let_12 (@ tptp.vEBT_vebt_mint _let_11))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_3) TreeList2) Summary2)) (not (= Y (@ _let_9 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa3)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_2) (@ tptp.vEBT_T_m_i_n_t _let_11))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))) (@ (@ (@ tptp.if_nat (and (not (= _let_12 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_10)) _let_12))) (@ _let_8 (@ (@ tptp.vEBT_T_p_r_e_d _let_11) _let_10))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_9 (@ (@ tptp.vEBT_T_p_r_e_d Summary2) _let_5))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_6 tptp.none_nat)) (@ _let_9 tptp.one_one_nat)) (@ _let_8 (@ tptp.vEBT_T_m_a_x_t (@ _let_7 (@ tptp.the_nat _let_6))))))))) tptp.one_one_nat)))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_d_e_l_e_t_e X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Xa3 tptp.zero_zero_nat) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_2) (=> (= Xa3 _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N2)))) (=> (= Xa3 _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) _let_1))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.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.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ _let_7 _let_6))) (let ((_let_9 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) (@ (@ tptp.power_power_nat _let_4) _let_5))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint _let_8))))) (let ((_let_10 (= Xa3 Mi))) (let ((_let_11 (@ tptp.if_nat _let_10))) (let ((_let_12 (@ (@ _let_11 _let_9) Xa3))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high _let_12) _let_5))) (let ((_let_14 (@ (@ tptp.vEBT_VEBT_low _let_12) _let_5))) (let ((_let_15 (@ _let_7 _let_13))) (let ((_let_16 (@ (@ tptp.vEBT_vebt_delete _let_15) _let_14))) (let ((_let_17 (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_13) _let_16)))) (let ((_let_18 (@ tptp.bit1 tptp.one))) (let ((_let_19 (@ tptp.bit0 _let_18))) (let ((_let_20 (= Xa3 Ma2))) (let ((_let_21 (@ tptp.if_nat (and (=> _let_10 (= _let_9 Ma2)) (=> (not _let_10) _let_20))))) (let ((_let_22 (@ tptp.plus_plus_nat _let_4))) (let ((_let_23 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_13))) (let ((_let_24 (@ tptp.vEBT_vebt_maxt _let_23))) (let ((_let_25 (@ tptp.bit0 _let_3))) (let ((_let_26 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_27 (@ tptp.numeral_numeral_nat _let_18))) (let ((_let_28 (@ tptp.plus_plus_nat _let_27))) (=> (= X _let_2) (=> (= Y (@ _let_28 (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat Xa3) Mi) (@ (@ tptp.ord_less_nat Ma2) Xa3))) tptp.one_one_nat) (@ _let_28 (@ (@ (@ tptp.if_nat (and _let_10 _let_20)) _let_27) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_19))) (@ (@ _let_11 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.vEBT_T_m_i_n_t Summary2)) (@ tptp.vEBT_T_m_i_n_t _let_8))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 _let_18)))) tptp.one_one_nat))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat _let_25)) (@ (@ tptp.vEBT_T_d_e_l_e_t_e _let_15) _let_14))) (@ (@ tptp.plus_plus_nat (@ _let_26 (@ tptp.vEBT_T_m_i_n_N_u_l_l _let_16))) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull _let_16)) (@ (@ tptp.plus_plus_nat (@ _let_26 (@ (@ tptp.vEBT_T_d_e_l_e_t_e Summary2) _let_13))) (@ _let_22 (@ (@ _let_21 (@ (@ tptp.plus_plus_nat (@ _let_26 (@ tptp.vEBT_T_m_a_x_t _let_23))) (@ _let_26 (@ (@ (@ tptp.if_nat (= _let_24 tptp.none_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_25))) (@ tptp.vEBT_T_m_a_x_t (@ _let_17 (@ tptp.the_nat _let_24)))))))) tptp.one_one_nat)))) (@ _let_22 (@ (@ _let_21 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat _let_19)) (@ tptp.vEBT_T_m_a_x_t (@ _let_17 _let_13)))) tptp.one_one_nat)))))) tptp.one_one_nat))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8441311223069195367_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3)))))))))))))))))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((Uu2 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= X _let_1) (=> (= Xa3 tptp.zero_zero_nat) (=> (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (= Xa3 _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc) Vd2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat _let_3)))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_3))))) (let ((_let_9 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_10 (@ (@ tptp.vEBT_VEBT_low Xa3) _let_4))) (let ((_let_11 (@ _let_7 _let_5))) (let ((_let_12 (@ tptp.vEBT_vebt_maxt _let_11))) (=> (= X _let_2) (=> (= Y (@ _let_9 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa3) Mi)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_3)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ _let_9 (@ tptp.vEBT_T_m_a_x_t _let_11))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ (@ tptp.if_nat (and (not (= _let_12 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_10)) _let_12))) (@ _let_8 (@ (@ tptp.vEBT_T_s_u_c_c _let_11) _let_10))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_9 (@ (@ tptp.vEBT_T_s_u_c_c Summary2) _let_5))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_6 tptp.none_nat)) tptp.one_one_nat) (@ _let_8 (@ tptp.vEBT_T_m_i_n_t (@ _let_7 (@ tptp.the_nat _let_6)))))))))) tptp.one_one_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_p_r_e_d X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa3 tptp.zero_zero_nat) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ 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) (=> (= Xa3 _let_1) (=> (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= Xa3 _let_1) (=> (= Y (@ _let_2 (@ (@ (@ tptp.if_nat B2) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) _let_1)))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.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 Xa3) _let_5))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_6))) (let ((_let_8 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_9 (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_3))))) (let ((_let_10 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_11 (@ (@ tptp.vEBT_VEBT_low Xa3) _let_5))) (let ((_let_12 (@ _let_8 _let_6))) (let ((_let_13 (@ tptp.vEBT_vebt_mint _let_12))) (=> (= X _let_2) (=> (= Y (@ _let_10 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa3)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_3)))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_4) (@ tptp.vEBT_T_m_i_n_t _let_12))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))) (@ (@ (@ tptp.if_nat (and (not (= _let_13 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_11)) _let_13))) (@ _let_9 (@ (@ tptp.vEBT_T_p_r_e_d _let_12) _let_11))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_10 (@ (@ tptp.vEBT_T_p_r_e_d Summary2) _let_6))) tptp.one_one_nat)) (@ (@ (@ tptp.if_nat (= _let_7 tptp.none_nat)) (@ _let_10 tptp.one_one_nat)) (@ _let_9 (@ tptp.vEBT_T_m_a_x_t (@ _let_8 (@ tptp.the_nat _let_7))))))))) tptp.one_one_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel2) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y6 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y6) (@ (@ tptp.ord_less_nat Y6) X)))) tptp.bot_bot_set_nat)))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y6 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y6) (@ (@ tptp.ord_less_nat X) Y6)))) tptp.bot_bot_set_nat)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (= (@ (@ tptp.set_or189985376899183464nteger A) B) tptp.bot_bo3990330152332043303nteger))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((P tptp.assn) (Q tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) Q)) _let_1) (and (@ (@ tptp.rep_assn P) _let_1) (@ (@ tptp.rep_assn Q) _let_1))))))
% 9.16/7.11 (assert (forall ((B Bool) (H2 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.rep_assn (@ tptp.pure_assn B)) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)) B)))
% 9.16/7.11 (assert (forall ((Q3 tptp.array_VEBT_VEBTi) (Y tptp.list_VEBT_VEBTi) (H2 tptp.heap_e7401611519738050253t_unit)) (not (@ (@ tptp.rep_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Q3) Y)) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)))))
% 9.16/7.11 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 9.16/7.11 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 9.16/7.11 (assert (forall ((P tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit) (H4 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.rep_assn P))) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) tptp.bot_bot_set_nat))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A2) tptp.bot_bot_set_real))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S3) (=> (not (= S3 tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) S3) (not (exists ((Xa tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa) S3) (@ (@ tptp.ord_le6747313008572928689nteger Xa) X3))))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (assert (forall ((X9 tptp.set_Code_integer)) (=> (not (= X9 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) X9) (exists ((Xa tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa) X9) (@ (@ tptp.ord_le6747313008572928689nteger X3) Xa))))) (not (@ tptp.finite6017078050557962740nteger X9))))))
% 9.16/7.11 (assert (forall ((X9 tptp.set_real)) (=> (not (= X9 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) X9) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X9) (@ (@ tptp.ord_less_real X3) Xa))))) (not (@ tptp.finite_finite_real X9))))))
% 9.16/7.11 (assert (forall ((X9 tptp.set_rat)) (=> (not (= X9 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) X9) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X9) (@ (@ tptp.ord_less_rat X3) Xa))))) (not (@ tptp.finite_finite_rat X9))))))
% 9.16/7.11 (assert (forall ((X9 tptp.set_num)) (=> (not (= X9 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) X9) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X9) (@ (@ tptp.ord_less_num X3) Xa))))) (not (@ tptp.finite_finite_num X9))))))
% 9.16/7.11 (assert (forall ((X9 tptp.set_nat)) (=> (not (= X9 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X9) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X9) (@ (@ tptp.ord_less_nat X3) Xa))))) (not (@ tptp.finite_finite_nat X9))))))
% 9.16/7.11 (assert (forall ((X9 tptp.set_int)) (=> (not (= X9 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X9) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X9) (@ (@ tptp.ord_less_int X3) Xa))))) (not (@ tptp.finite_finite_int X9))))))
% 9.16/7.11 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.one_one_assn) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((Uu2 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= X _let_1) (=> (= Xa3 tptp.zero_zero_nat) (=> (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= 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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (= Xa3 _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) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc) Vd2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ 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) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.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 Xa3) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa3) _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 Xa3) Mi))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Mi))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa3 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) (=> (= Xa3 _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) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (=> (= Xa3 _let_1) (=> (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (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) B2)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) 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) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ 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) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.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 Xa3) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa3) _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) Xa3))) (=> (= 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 TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) Xa3)) (@ tptp.some_nat Mi)) 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) Xa3)))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_V1232361888498592333_e_t_e X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Xa3 tptp.zero_zero_nat) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_2) (=> (= Xa3 _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N2)))) (=> (= Xa3 _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) _let_1))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (= Xa3 Mi))) (let ((_let_8 (@ (@ (@ tptp.if_nat _let_7) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5))))) Xa3))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_high _let_8) _let_4))) (let ((_let_10 (@ (@ tptp.vEBT_VEBT_low _let_8) _let_4))) (let ((_let_11 (@ _let_6 _let_9))) (let ((_let_12 (and _let_7 (= Xa3 Ma2)))) (let ((_let_13 (= Y tptp.one_one_nat))) (let ((_let_14 (or (@ (@ tptp.ord_less_nat Xa3) Mi) (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (=> (= X _let_2) (=> (and (=> _let_14 _let_13) (=> (not _let_14) (and (=> _let_12 _let_13) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_9) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_V1232361888498592333_e_t_e _let_11) _let_10)) (@ (@ (@ tptp.if_nat (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete _let_11) _let_10))) (@ (@ tptp.vEBT_V1232361888498592333_e_t_e Summary2) _let_9)) tptp.one_one_nat))) tptp.one_one_nat)))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V6368547301243506412_e_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3)))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Xa3 tptp.zero_zero_nat) (=> (= Y (@ (@ tptp.vEBT_Leaf false) B2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A5))) (let ((_let_3 (@ _let_2 B2))) (=> (= X _let_3) (=> (= Xa3 _let_1) (=> (= Y (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N2)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= Xa3 _let_1) (=> (= Y _let_2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1)))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) TrLst2) Smry2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa3 Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa3))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa3 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa3) Mi) (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (=> (= X _let_2) (=> (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3)))))))))))))))))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (not (forall ((H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (not (= X (@ (@ tptp.produc7507926704131184380et_nat H3) As)))))))
% 9.16/7.11 (assert (forall ((X tptp.produc2732055786443039994et_nat)) (not (forall ((P7 (-> tptp.produc3658429121746597890et_nat Bool)) (Q8 (-> tptp.produc3658429121746597890et_nat Bool)) (H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (not (= X (@ (@ tptp.produc2245416461498447860et_nat P7) (@ (@ tptp.produc5001842942810119800et_nat Q8) (@ (@ tptp.produc7507926704131184380et_nat H3) As)))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_s_u_c_c2 X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((Uu2 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B2))) (=> (= X _let_1) (=> (= Xa3 tptp.zero_zero_nat) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (= Xa3 _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vc) Vd2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_low Xa3) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4))) (let ((_let_7 (@ tptp.vEBT_vebt_maxt _let_6))) (let ((_let_8 (@ (@ tptp.ord_less_nat Xa3) Mi))) (=> (= X _let_2) (=> (and (=> _let_8 (= Y tptp.one_one_nat)) (=> (not _let_8) (= Y (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_nat (and (not (= _let_7 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_5)) _let_7))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_s_u_c_c2 _let_6) _let_5))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_s_u_c_c2 Summary2) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_s_u_c_c_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T9217963907923527482_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X _let_1) (=> (= Y (@ _let_2 (@ (@ (@ tptp.if_nat (= Xa3 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) Xa3)))))))) (=> (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) Xa3))))))) (=> (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) Xa3))))))) (=> (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V3))) TreeList2) 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) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.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 Xa3) Mi)) Mi) Xa3))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_4))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _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 TreeList2)) (not (or (= Xa3 Mi) (= Xa3 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) Xa3))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_p_r_e_d2 X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa3 tptp.zero_zero_nat) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_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) (=> (= Xa3 _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (=> (= Xa3 _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B2)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_low Xa3) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4))) (let ((_let_7 (@ tptp.vEBT_vebt_mint _let_6))) (let ((_let_8 (@ (@ tptp.ord_less_nat Ma2) Xa3))) (=> (= X _let_2) (=> (and (=> _let_8 (= Y tptp.one_one_nat)) (=> (not _let_8) (= Y (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_nat (and (not (= _let_7 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_5)) _let_7))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.vEBT_T_p_r_e_d2 _let_6) _let_5))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.vEBT_T_p_r_e_d2 Summary2) _let_4)) tptp.one_one_nat))) tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T_p_r_e_d_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3)))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B2))) (let ((_let_3 (= Xa3 tptp.one_one_nat))) (let ((_let_4 (= Xa3 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B2))) (=> (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) Xa3)))))))))) (=> (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) Xa3))))))) (=> (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) Xa3))))))) (=> (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V3)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (= X _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa3) Xa3))) _let_1) TreeList2) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3)))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa3) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) Xa3))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa3 Mi) (= Xa3 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa3) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_i_n_s_e_r_t2 X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (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) Xa3))))))) (=> (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) Xa3))))))) (=> (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V3))) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5076183648494686801_t_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa3) Mi)) Mi) Xa3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high _let_4) _let_3))) (let ((_let_6 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_5))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa3 Mi) (= Xa3 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) Xa3)))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= Xa3 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) Xa3))))))) (=> (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) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) 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) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc))) (=> (= 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) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.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 Xa3) _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 (= Xa3 Mi)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (= Xa3 Ma2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa3) Mi)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa3)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_3)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ _let_7 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_5)))) tptp.one_one_nat))))))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (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) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) 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) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_3))) (let ((_let_5 (@ tptp.ord_less_nat Xa3))) (=> (= X _let_2) (=> (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa3 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa3 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_5 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi) Xa3) (@ _let_5 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa3) _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) Xa3))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa3)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa3)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3)))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3)))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3)))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa3) Mi)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa3)) (=> (not (= Xa3 Mi)) (=> (not (= Xa3 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) _let_4))))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa3)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa3) Mi)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa3)) (not (=> (not (= Xa3 Mi)) (=> (not (= Xa3 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) _let_4))))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (let ((_let_2 (= Xa3 tptp.one_one_nat))) (let ((_let_3 (= Xa3 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B2) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))))) (=> (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) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) 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) Xa3))))))) (=> (forall ((V3 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V3)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa3)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa3) Mi)))) (=> (= X _let_2) (=> (= Y (=> (not (= Xa3 Mi)) (=> (not (= Xa3 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa3)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa3)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa3)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) _let_4))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (= Xa3 tptp.one_one_nat))) (let ((_let_2 (= Xa3 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa3)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B2) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa3)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) _let_4))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (let ((_let_2 (= Xa3 tptp.one_one_nat))) (let ((_let_3 (= Xa3 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B2) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))))) (=> (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) Xa3))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa3)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (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) Xa3)))))) (=> (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) Xa3)))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3)) (or (= Xa3 Mi) (= Xa3 Ma2)))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Vc))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa3)) (or (= Xa3 Mi) (= Xa3 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) _let_4)))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa3)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) _let_4))))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3)) (not (or (= Xa3 Mi) (= Xa3 Ma2))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Vc))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa3)) (not (or (= Xa3 Mi) (= Xa3 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) _let_4))))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa3)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_2))) _let_4)))))))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (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) Xa3))))))) (=> (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) Xa3))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (= Y (or (= Xa3 Mi) (= Xa3 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (=> (forall ((Mi tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma2))) _let_1) TreeList2) Vc))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X _let_2) (=> (= Y (or (= Xa3 Mi) (= Xa3 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa3) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa3) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa3))))))))))))))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_delete T) X)) (@ (@ tptp.minus_minus_set_nat (@ tptp.vEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (D2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.nth_nat Xs2) I3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.minus_minus_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) Xs2) D2)) D2)))))
% 9.16/7.11 (assert (forall ((D2 tptp.nat) (Ys tptp.list_nat)) (@ (@ tptp.ord_less_eq_nat D2) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) Ys) D2))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 Xs2))) (=> (@ (@ tptp.member_nat X3) _let_1) (=> (@ (@ tptp.member_nat Y3) _let_1) (= X3 Y3))))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (= X3 Y))) (= (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) Xs2) tptp.zero_zero_nat) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) Y))))))
% 9.16/7.11 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_VEBT_set_vebt (@ (@ tptp.vEBT_vebt_delete T) X)) (@ (@ tptp.minus_minus_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.foldr_nat_nat tptp.plus_plus_nat))) (let ((_let_2 (@ tptp.size_size_list_nat Ys))) (=> (= (@ tptp.size_size_list_nat Xs2) _let_2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.nth_nat Xs2) I3)) (@ (@ tptp.nth_nat Ys) I3)))) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ _let_1 Xs2) C)) _let_2)) (@ (@ _let_1 Ys) D2)))))))))
% 9.16/7.11 (assert (forall ((L tptp.list_real)) (= (@ (@ (@ tptp.foldr_real_nat (lambda ((X2 tptp.real) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) tptp.zero_zero_nat) (@ tptp.size_size_list_real L))))
% 9.16/7.11 (assert (forall ((L tptp.list_o)) (= (@ (@ (@ tptp.foldr_o_nat (lambda ((X2 Bool) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) tptp.zero_zero_nat) (@ tptp.size_size_list_o L))))
% 9.16/7.11 (assert (forall ((L tptp.list_nat)) (= (@ (@ (@ tptp.foldr_nat_nat (lambda ((X2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) tptp.zero_zero_nat) (@ tptp.size_size_list_nat L))))
% 9.16/7.11 (assert (forall ((L tptp.list_int)) (= (@ (@ (@ tptp.foldr_int_nat (lambda ((X2 tptp.int) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) tptp.zero_zero_nat) (@ tptp.size_size_list_int L))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.int)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A2)))))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (L tptp.list_o) (K tptp.list_o) (F (-> Bool tptp.nat tptp.nat)) (G (-> Bool tptp.nat tptp.nat))) (=> (= A B) (=> (= L K) (=> (forall ((A5 tptp.nat) (X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 L)) (= (@ (@ F X3) A5) (@ (@ G X3) A5)))) (= (@ (@ (@ tptp.foldr_o_nat F) L) A) (@ (@ (@ tptp.foldr_o_nat G) K) B)))))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (L tptp.list_nat) (K tptp.list_nat) (F (-> tptp.nat tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat tptp.nat))) (=> (= A B) (=> (= L K) (=> (forall ((A5 tptp.nat) (X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 L)) (= (@ (@ F X3) A5) (@ (@ G X3) A5)))) (= (@ (@ (@ tptp.foldr_nat_nat F) L) A) (@ (@ (@ tptp.foldr_nat_nat G) K) B)))))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real) (L tptp.list_real) (K tptp.list_real) (F (-> tptp.real tptp.real tptp.real)) (G (-> tptp.real tptp.real tptp.real))) (=> (= A B) (=> (= L K) (=> (forall ((A5 tptp.real) (X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 L)) (= (@ (@ F X3) A5) (@ (@ G X3) A5)))) (= (@ (@ (@ tptp.foldr_real_real F) L) A) (@ (@ (@ tptp.foldr_real_real G) K) B)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((B2 tptp.code_integer) (A8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A8) (=> (forall ((X5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X5) A8) (@ (@ tptp.ord_le6747313008572928689nteger B2) X5))) (=> (@ P A8) (@ P (@ (@ tptp.insert_Code_integer B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B2 tptp.real) (A8 tptp.set_real)) (=> (@ tptp.finite_finite_real A8) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A8) (@ (@ tptp.ord_less_real B2) X5))) (=> (@ P A8) (@ P (@ (@ tptp.insert_real B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B2 tptp.rat) (A8 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A8) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.member_rat X5) A8) (@ (@ tptp.ord_less_rat B2) X5))) (=> (@ P A8) (@ P (@ (@ tptp.insert_rat B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B2 tptp.num) (A8 tptp.set_num)) (=> (@ tptp.finite_finite_num A8) (=> (forall ((X5 tptp.num)) (=> (@ (@ tptp.member_num X5) A8) (@ (@ tptp.ord_less_num B2) X5))) (=> (@ P A8) (@ P (@ (@ tptp.insert_num B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B2 tptp.nat) (A8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A8) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A8) (@ (@ tptp.ord_less_nat B2) X5))) (=> (@ P A8) (@ P (@ (@ tptp.insert_nat B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B2 tptp.int) (A8 tptp.set_int)) (=> (@ tptp.finite_finite_int A8) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A8) (@ (@ tptp.ord_less_int B2) X5))) (=> (@ P A8) (@ P (@ (@ tptp.insert_int B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((B2 tptp.code_integer) (A8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A8) (=> (forall ((X5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X5) A8) (@ (@ tptp.ord_le6747313008572928689nteger X5) B2))) (=> (@ P A8) (@ P (@ (@ tptp.insert_Code_integer B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B2 tptp.real) (A8 tptp.set_real)) (=> (@ tptp.finite_finite_real A8) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A8) (@ (@ tptp.ord_less_real X5) B2))) (=> (@ P A8) (@ P (@ (@ tptp.insert_real B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B2 tptp.rat) (A8 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A8) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.member_rat X5) A8) (@ (@ tptp.ord_less_rat X5) B2))) (=> (@ P A8) (@ P (@ (@ tptp.insert_rat B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B2 tptp.num) (A8 tptp.set_num)) (=> (@ tptp.finite_finite_num A8) (=> (forall ((X5 tptp.num)) (=> (@ (@ tptp.member_num X5) A8) (@ (@ tptp.ord_less_num X5) B2))) (=> (@ P A8) (@ P (@ (@ tptp.insert_num B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B2 tptp.nat) (A8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A8) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A8) (@ (@ tptp.ord_less_nat X5) B2))) (=> (@ P A8) (@ P (@ (@ tptp.insert_nat B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B2 tptp.int) (A8 tptp.set_int)) (=> (@ tptp.finite_finite_int A8) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A8) (@ (@ tptp.ord_less_int X5) B2))) (=> (@ P A8) (@ P (@ (@ tptp.insert_int B2) A8)))))) (@ P A2))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N)))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (S3 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) S3) (@ (@ tptp.ord_le3480810397992357184T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))) S3))))
% 9.16/7.11 (assert (forall ((X tptp.complex) (S3 tptp.set_complex)) (=> (@ (@ tptp.member_complex X) S3) (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))) S3))))
% 9.16/7.11 (assert (forall ((X tptp.real) (S3 tptp.set_real)) (=> (@ (@ tptp.member_real X) S3) (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) S3))))
% 9.16/7.11 (assert (forall ((X tptp.int) (S3 tptp.set_int)) (=> (@ (@ tptp.member_int X) S3) (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) S3))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (S3 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) S3) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) S3))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBTi) (I tptp.nat) (X tptp.vEBT_VEBTi)) (@ (@ tptp.ord_le6592769550269828683_VEBTi (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) I) X))) (@ (@ tptp.insert_VEBT_VEBTi X) (@ tptp.set_VEBT_VEBTi2 Xs2)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((L tptp.list_real) (A tptp.nat)) (= (@ (@ (@ tptp.foldr_real_nat (lambda ((X2 tptp.real) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.size_size_list_real L)))))
% 9.16/7.11 (assert (forall ((L tptp.list_o) (A tptp.nat)) (= (@ (@ (@ tptp.foldr_o_nat (lambda ((X2 Bool) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.size_size_list_o L)))))
% 9.16/7.11 (assert (forall ((L tptp.list_nat) (A tptp.nat)) (= (@ (@ (@ tptp.foldr_nat_nat (lambda ((X2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.size_size_list_nat L)))))
% 9.16/7.11 (assert (forall ((L tptp.list_int) (A tptp.nat)) (= (@ (@ (@ tptp.foldr_int_nat (lambda ((X2 tptp.int) (__flatten_var_0 tptp.nat)) (@ tptp.suc __flatten_var_0))) L) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.size_size_list_int L)))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((T3 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le3480810397992357184T_VEBT T3) S3) (=> (@ P T3) (exists ((X5 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) T3)) (@ P (@ (@ tptp.insert_VEBT_VEBT X5) T3))))))) (@ P S3))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((T3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex T3) S3) (=> (@ P T3) (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) (@ (@ tptp.minus_811609699411566653omplex S3) T3)) (@ P (@ (@ tptp.insert_complex X5) T3))))))) (@ P S3))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger S3) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((T3 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le1307284697595431911nteger T3) S3) (=> (@ P T3) (exists ((X5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X5) (@ (@ tptp.minus_2355218937544613996nteger S3) T3)) (@ P (@ (@ tptp.insert_Code_integer X5) T3))))))) (@ P S3))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real S3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((T3 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real T3) S3) (=> (@ P T3) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) (@ (@ tptp.minus_minus_set_real S3) T3)) (@ P (@ (@ tptp.insert_real X5) T3))))))) (@ P S3))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T3) S3) (=> (@ P T3) (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) (@ (@ tptp.minus_minus_set_int S3) T3)) (@ P (@ (@ tptp.insert_int X5) T3))))))) (@ P S3))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T3) S3) (=> (@ P T3) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) (@ (@ tptp.minus_minus_set_nat S3) T3)) (@ P (@ (@ tptp.insert_nat X5) T3))))))) (@ P S3))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N)) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N)) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N)) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_VEBT_VEBT X))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_le3480810397992357184T_VEBT A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le3480810397992357184T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_3 tptp.bot_bo8194388402131092736T_VEBT))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) B3)))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_complex X))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_complex A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A2) B3)))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_real X))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B3)))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_int X))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B3)))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_nat X))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B3)))))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X)))) (let ((_let_2 (= N 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))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L)) (= (@ (@ tptp.insert_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT L) I)) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) X))) (@ (@ tptp.insert_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 L))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBTi) (X tptp.vEBT_VEBTi)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s7982070591426661849_VEBTi L)) (= (@ (@ tptp.insert_VEBT_VEBTi (@ (@ tptp.nth_VEBT_VEBTi L) I)) (@ tptp.set_VEBT_VEBTi2 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi L) I) X))) (@ (@ tptp.insert_VEBT_VEBTi X) (@ tptp.set_VEBT_VEBTi2 L))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_real L)) (= (@ (@ tptp.insert_real (@ (@ tptp.nth_real L) I)) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real L) I) X))) (@ (@ tptp.insert_real X) (@ tptp.set_real2 L))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o L)) (= (@ (@ tptp.insert_o (@ (@ tptp.nth_o L) I)) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o L) I) X))) (@ (@ tptp.insert_o X) (@ tptp.set_o2 L))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ (@ tptp.insert_nat (@ (@ tptp.nth_nat L) I)) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat L) I) X))) (@ (@ tptp.insert_nat X) (@ tptp.set_nat2 L))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int L)) (= (@ (@ tptp.insert_int (@ (@ tptp.nth_int L) I)) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int L) I) X))) (@ (@ tptp.insert_int X) (@ tptp.set_int2 L))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat N) _let_1))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_real) (Y tptp.real)) (=> (forall ((X3 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ tptp.set_real2 Xs2))) (=> (@ (@ tptp.member_real X3) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (= X3 Y3))))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (= X3 Y))) (= (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) Xs2) tptp.zero_zero_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_real Xs2))) Y))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.set_nat tptp.nat)) (N4 (-> tptp.set_nat tptp.nat))) (=> (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M7 X2)) (@ N4 X2)))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.nat tptp.nat)) (N4 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M7 X2)) (@ N4 X2)))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.int tptp.nat)) (N4 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M7 X2)) (@ N4 X2)))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.complex tptp.nat)) (N4 (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M7 X2)) (@ N4 X2)))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.code_integer tptp.nat)) (N4 (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M7 X2)) (@ N4 X2)))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.set_nat tptp.nat)) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (let ((_let_1 (@ M7 X2))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X2 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.nat tptp.nat)) (A tptp.nat)) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (let ((_let_1 (@ M7 X2))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X2 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.int tptp.nat)) (A tptp.int)) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (let ((_let_1 (@ M7 X2))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X2 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.complex tptp.nat)) (A tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (let ((_let_1 (@ M7 X2))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X2 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.code_integer tptp.nat)) (A tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (let ((_let_1 (@ M7 X2))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X2 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 9.16/7.11 (assert (forall ((Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 9.16/7.11 (assert (forall ((Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 9.16/7.11 (assert (forall ((Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) tptp.one_one_nat))))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ (@ tptp.foldr_real_real tptp.plus_plus_real) Xs2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real C) D2)) (@ (@ tptp.plus_plus_real (@ _let_1 D2)) C)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6906906614972039071t_assn 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_assn)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_assn (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3455450783089532116nteger 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_Code_integer)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_3573771949741848930nteger (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I2)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) A))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I2)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A2)) A))))
% 9.16/7.11 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I2 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I2)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) A))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I2) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I2) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I2)))) _let_1)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I2)))) _let_1)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.assn)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6906906614972039071t_assn G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_assn (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3455450783089532116nteger G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_assn (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_3573771949741848930nteger (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_complex (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_assn (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_3573771949741848930nteger (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_complex (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_assn (@ (@ tptp.groups6906906614972039071t_assn G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_assn (@ G M)) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G M)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.groups3455450783089532116nteger G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_3573771949741848930nteger (@ G M)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups6464643781859351333omplex G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_complex (@ G M)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) _let_1)))))))
% 9.16/7.11 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 9.16/7.11 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N3 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 9.16/7.11 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N3 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 9.16/7.11 (assert (= tptp.semiri5044797733671781792omplex (lambda ((N3 tptp.nat)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 9.16/7.11 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))))
% 9.16/7.11 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I2 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J2) I2)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I2) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.assn)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6906906614972039071t_assn F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1959793692361082170t_assn (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.assn)) (@ (@ tptp.times_times_assn (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_assn))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3455450783089532116nteger F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_Code_integer))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3190895334310489300er_nat F) A2)) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups858564598930262913ex_int F) A2)) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3188404863801439024er_int F) A2)) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups705719431365010083at_int F) A2)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.assn)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_assn (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.code_integer)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3455450783089532116nteger G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.complex)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_complex (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P4 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P4))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N3 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N3) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 9.16/7.11 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N3 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N3) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 9.16/7.11 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A3 tptp.complex) (N3 tptp.nat)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N3) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 9.16/7.11 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N3) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 9.16/7.11 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N3) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.assn)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_assn (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3455450783089532116nteger G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_3573771949741848930nteger (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.complex)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_complex (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.set_nat tptp.nat)) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X2)) (@ M7 X2)) tptp.zero_zero_nat))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.nat tptp.nat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X2)) (@ M7 X2)) tptp.zero_zero_nat))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.int tptp.nat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X2)) (@ M7 X2)) tptp.zero_zero_nat))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.complex tptp.nat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X2)) (@ M7 X2)) tptp.zero_zero_nat))))))))
% 9.16/7.11 (assert (forall ((M7 (-> tptp.code_integer tptp.nat)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M7 X2))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X2)) (@ M7 X2)) tptp.zero_zero_nat))))))))
% 9.16/7.11 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K3) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.int) (Xa3 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 Xa3)))))) (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 Xa3) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa3) 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 Xa3) _let_1)))))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.assn))) (let ((_let_1 (@ tptp.groups1155561341820557179l_assn G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ tptp.groups569574905686396791T_assn G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (@ (@ tptp.member_VEBT_VEBT X) A2)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X) A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (not (@ (@ tptp.member_Code_integer X) A2)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X) A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A2))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.assn))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_1 (= (@ (@ tptp.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.assn))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.assn))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S3))) (=> (@ tptp.finite6017078050557962740nteger S3) (and (=> _let_1 (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (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 ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_1 (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 9.16/7.11 (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 ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 9.16/7.11 (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 ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.assn))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_1 (= (@ (@ tptp.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.assn))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.assn))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S3))) (=> (@ tptp.finite6017078050557962740nteger S3) (and (=> _let_1 (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S3) tptp.one_one_assn)))))))
% 9.16/7.11 (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 ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_1 (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 9.16/7.11 (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 ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 9.16/7.11 (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 ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (= A K3)) (@ B K3)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups4696554848551431203al_nat F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups6361806394783013919BT_nat F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups1707563613775114915nt_nat F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups861055069439313189ex_nat F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (A tptp.code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (@ (@ tptp.member_Code_integer A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups3190895334310489300er_nat F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups4694064378042380927al_int F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups6359315924273963643BT_int F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups858564598930262913ex_int F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (A tptp.code_integer) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (@ (@ tptp.member_Code_integer A) A2) (@ (@ tptp.dvd_dvd_int (@ F A)) (@ (@ tptp.groups3188404863801439024er_int F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (@ (@ tptp.dvd_dvd_nat (@ F A)) (@ (@ tptp.groups708209901874060359at_nat F) A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups6464643781859351333omplex F) A2) tptp.zero_zero_complex) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_complex)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups7440179247065528705omplex F) A2) tptp.zero_zero_complex) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_complex)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups3708469109370488835omplex F) A2) tptp.zero_zero_complex) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_complex)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.complex))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (= (@ (@ tptp.groups862514429393162674omplex F) A2) tptp.zero_zero_complex) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A2) (= (@ F X2) tptp.zero_zero_complex)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups129246275422532515t_real F) A2) tptp.zero_zero_real) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_real)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups2316167850115554303t_real F) A2) tptp.zero_zero_real) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_real)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups766887009212190081x_real F) A2) tptp.zero_zero_real) (exists ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.zero_zero_real)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (= (@ (@ tptp.groups9004974159866482096r_real F) A2) tptp.zero_zero_real) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A2) (= (@ F X2) tptp.zero_zero_real)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups73079841787564623at_rat F) A2) tptp.zero_zero_rat) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.zero_zero_rat)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1072433553688619179nt_rat F) A2) tptp.zero_zero_rat) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.zero_zero_rat)))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.real tptp.assn))) (= (@ (@ tptp.groups1155561341820557179l_assn G) tptp.bot_bot_set_real) tptp.one_one_assn)))
% 9.16/7.11 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 9.16/7.11 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G) tptp.bot_bot_set_real) tptp.one_one_rat)))
% 9.16/7.11 (assert (forall ((G (-> tptp.real tptp.nat))) (= (@ (@ tptp.groups4696554848551431203al_nat G) tptp.bot_bot_set_real) tptp.one_one_nat)))
% 9.16/7.11 (assert (forall ((G (-> tptp.real tptp.int))) (= (@ (@ tptp.groups4694064378042380927al_int G) tptp.bot_bot_set_real) tptp.one_one_int)))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.assn))) (= (@ (@ tptp.groups6906906614972039071t_assn G) tptp.bot_bot_set_nat) tptp.one_one_assn)))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 9.16/7.11 (assert (forall ((G (-> tptp.int tptp.assn))) (= (@ (@ tptp.groups7882442080178216443t_assn G) tptp.bot_bot_set_int) tptp.one_one_assn)))
% 9.16/7.11 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups6906906614972039071t_assn G) A2) tptp.one_one_assn))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.assn))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups7882442080178216443t_assn G) A2) tptp.one_one_assn))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.assn))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups4150731942483176573x_assn G) A2) tptp.one_one_assn))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (=> (not (@ tptp.finite6017078050557962740nteger A2)) (= (@ (@ tptp.groups1304777262505850412r_assn G) A2) tptp.one_one_assn))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (=> (not (@ tptp.finite6017078050557962740nteger A2)) (= (@ (@ tptp.groups9004974159866482096r_real G) A2) tptp.one_one_real))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B tptp.nat) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.groups4696554848551431203al_nat F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B tptp.nat) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.groups6361806394783013919BT_nat F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B tptp.nat) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (B tptp.nat) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.groups861055069439313189ex_nat F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (A tptp.code_integer) (B tptp.nat) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (@ (@ tptp.member_Code_integer A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.groups3190895334310489300er_nat F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B tptp.int) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.groups4694064378042380927al_int F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B tptp.int) (F (-> tptp.vEBT_VEBT tptp.int))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.groups6359315924273963643BT_int F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (B tptp.int) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.groups858564598930262913ex_int F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (A tptp.code_integer) (B tptp.int) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (@ (@ tptp.member_Code_integer A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.groups3188404863801439024er_int F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (=> (= B (@ F A)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.groups708209901874060359at_nat F) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (= (@ (@ tptp.groups1707563613775114915nt_nat F) A2) tptp.one_one_nat) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (= (@ F X2) tptp.one_one_nat)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups861055069439313189ex_nat F) A2) tptp.one_one_nat) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (= (@ F X2) tptp.one_one_nat)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (= (@ (@ tptp.groups3190895334310489300er_nat F) A2) tptp.one_one_nat) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A2) (= (@ F X2) tptp.one_one_nat)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (= (@ (@ tptp.groups708209901874060359at_nat F) A2) tptp.one_one_nat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (= (@ F X2) tptp.one_one_nat)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (forall ((X2 tptp.complex)) (=> (@ (@ tptp.member_complex X2) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups3190895334310489300er_nat F) A2)) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X2))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A2)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X2))))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.assn)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6906906614972039071t_assn G) A2) tptp.one_one_assn)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.real tptp.assn)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1155561341820557179l_assn G) A2) tptp.one_one_assn)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.int tptp.assn)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7882442080178216443t_assn G) A2) tptp.one_one_assn)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.vEBT_VEBT tptp.assn)) (A2 tptp.set_VEBT_VEBT)) (=> (not (= (@ (@ tptp.groups569574905686396791T_assn G) A2) tptp.one_one_assn)) (not (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) A2) (= (@ G A5) tptp.one_one_assn)))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.complex tptp.assn)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups4150731942483176573x_assn G) A2) tptp.one_one_assn)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_assn)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((G (-> tptp.vEBT_VEBT tptp.real)) (A2 tptp.set_VEBT_VEBT)) (=> (not (= (@ (@ tptp.groups2703838992350267259T_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups6361806394783013919BT_nat F) A2)) (@ (@ tptp.groups6361806394783013919BT_nat G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (@ (@ tptp.dvd_dvd_int (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int)) (G (-> tptp.vEBT_VEBT tptp.int))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) A2) (@ (@ tptp.dvd_dvd_int (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups6359315924273963643BT_int F) A2)) (@ (@ tptp.groups6359315924273963643BT_int G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (@ (@ tptp.dvd_dvd_int (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (@ (@ tptp.dvd_dvd_int (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups705719431365010083at_int F) A2)) (@ (@ tptp.groups705719431365010083at_int G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (@ (@ tptp.dvd_dvd_int (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int G) A2)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_nat (@ F X2)) N))) A2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N) (@ (@ tptp.groups705719431365010083at_int (lambda ((X2 tptp.nat)) (@ (@ tptp.power_power_int (@ F X2)) N))) A2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X2 tptp.int)) (@ (@ tptp.power_power_int (@ F X2)) N))) A2))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((I3 tptp.vEBT_VEBT)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_VEBT_VEBT I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2703838992350267259T_real F) A2)) (@ (@ tptp.groups2703838992350267259T_real G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A2)) (@ (@ tptp.groups73079841787564623at_rat G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A2)) (@ (@ tptp.groups1072433553688619179nt_rat G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat)) (G (-> tptp.vEBT_VEBT tptp.rat))) (=> (forall ((I3 tptp.vEBT_VEBT)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_VEBT_VEBT I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5726676334696518183BT_rat F) A2)) (@ (@ tptp.groups5726676334696518183BT_rat G) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2703838992350267259T_real F) A2)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) A2) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups5726676334696518183BT_rat F) A2)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat A2) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (= (@ F X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups6464643781859351333omplex F) A2) tptp.zero_zero_complex)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (= (@ F X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7440179247065528705omplex F) A2) tptp.zero_zero_complex)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (= (@ F X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups3708469109370488835omplex F) A2) tptp.zero_zero_complex)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.complex))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (exists ((X5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X5) A2) (= (@ F X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups862514429393162674omplex F) A2) tptp.zero_zero_complex)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (= (@ F X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups129246275422532515t_real F) A2) tptp.zero_zero_real)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (= (@ F X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups2316167850115554303t_real F) A2) tptp.zero_zero_real)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (exists ((X5 tptp.complex)) (and (@ (@ tptp.member_complex X5) A2) (= (@ F X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups766887009212190081x_real F) A2) tptp.zero_zero_real)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (exists ((X5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X5) A2) (= (@ F X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups9004974159866482096r_real F) A2) tptp.zero_zero_real)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (= (@ F X5) tptp.zero_zero_rat))) (= (@ (@ tptp.groups73079841787564623at_rat F) A2) tptp.zero_zero_rat)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (exists ((X5 tptp.int)) (and (@ (@ tptp.member_int X5) A2) (= (@ F X5) tptp.zero_zero_rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat F) A2) tptp.zero_zero_rat)))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ X I2) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ Y I2) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I2)) (@ Y I2)) tptp.zero_zero_complex))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_VEBT_VEBT) (X (-> tptp.vEBT_VEBT tptp.complex)) (Y (-> tptp.vEBT_VEBT tptp.complex))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ X I2) tptp.zero_zero_complex)))))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ Y I2) tptp.zero_zero_complex)))))) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I2)) (@ Y I2)) tptp.zero_zero_complex))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ X I2) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ Y I2) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I2)) (@ Y I2)) tptp.zero_zero_complex))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ X I2) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ Y I2) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I2)) (@ Y I2)) tptp.zero_zero_complex))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I2 tptp.complex)) (and (@ (@ tptp.member_complex I2) I6) (not (= (@ X I2) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I2 tptp.complex)) (and (@ (@ tptp.member_complex I2) I6) (not (= (@ Y I2) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I2 tptp.complex)) (and (@ (@ tptp.member_complex I2) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I2)) (@ Y I2)) tptp.zero_zero_complex))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_Code_integer) (X (-> tptp.code_integer tptp.complex)) (Y (-> tptp.code_integer tptp.complex))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I2) I6) (not (= (@ X I2) tptp.zero_zero_complex)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I2) I6) (not (= (@ Y I2) tptp.zero_zero_complex)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I2) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I2)) (@ Y I2)) tptp.zero_zero_complex))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ X I2) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ Y I2) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I2)) (@ Y I2)) tptp.zero_zero_real))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_VEBT_VEBT) (X (-> tptp.vEBT_VEBT tptp.real)) (Y (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ X I2) tptp.zero_zero_real)))))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ Y I2) tptp.zero_zero_real)))))) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I2)) (@ Y I2)) tptp.zero_zero_real))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ X I2) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ Y I2) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I2)) (@ Y I2)) tptp.zero_zero_real))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ X I2) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ Y I2) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I2)) (@ Y I2)) tptp.zero_zero_real))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ X I2) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ Y I2) tptp.one_one_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ (@ tptp.times_times_rat (@ X I2)) (@ Y I2)) tptp.one_one_rat))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_VEBT_VEBT) (X (-> tptp.vEBT_VEBT tptp.rat)) (Y (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ X I2) tptp.one_one_rat)))))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ Y I2) tptp.one_one_rat)))))) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ (@ tptp.times_times_rat (@ X I2)) (@ Y I2)) tptp.one_one_rat))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ X I2) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ Y I2) tptp.one_one_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ (@ tptp.times_times_rat (@ X I2)) (@ Y I2)) tptp.one_one_rat))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.rat)) (Y (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ X I2) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ Y I2) tptp.one_one_rat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ (@ tptp.times_times_rat (@ X I2)) (@ Y I2)) tptp.one_one_rat))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.rat)) (Y (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I2 tptp.complex)) (and (@ (@ tptp.member_complex I2) I6) (not (= (@ X I2) tptp.one_one_rat)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I2 tptp.complex)) (and (@ (@ tptp.member_complex I2) I6) (not (= (@ Y I2) tptp.one_one_rat)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I2 tptp.complex)) (and (@ (@ tptp.member_complex I2) I6) (not (= (@ (@ tptp.times_times_rat (@ X I2)) (@ Y I2)) tptp.one_one_rat))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_Code_integer) (X (-> tptp.code_integer tptp.rat)) (Y (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I2) I6) (not (= (@ X I2) tptp.one_one_rat)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I2) I6) (not (= (@ Y I2) tptp.one_one_rat)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I2) I6) (not (= (@ (@ tptp.times_times_rat (@ X I2)) (@ Y I2)) tptp.one_one_rat))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.assn)) (Y (-> tptp.real tptp.assn))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ X I2) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ Y I2) tptp.one_one_assn)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I2 tptp.real)) (and (@ (@ tptp.member_real I2) I6) (not (= (@ (@ tptp.times_times_assn (@ X I2)) (@ Y I2)) tptp.one_one_assn))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_VEBT_VEBT) (X (-> tptp.vEBT_VEBT tptp.assn)) (Y (-> tptp.vEBT_VEBT tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ X I2) tptp.one_one_assn)))))) (=> (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ Y I2) tptp.one_one_assn)))))) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.collect_VEBT_VEBT (lambda ((I2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT I2) I6) (not (= (@ (@ tptp.times_times_assn (@ X I2)) (@ Y I2)) tptp.one_one_assn))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.assn)) (Y (-> tptp.nat tptp.assn))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ X I2) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ Y I2) tptp.one_one_assn)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (and (@ (@ tptp.member_nat I2) I6) (not (= (@ (@ tptp.times_times_assn (@ X I2)) (@ Y I2)) tptp.one_one_assn))))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.assn)) (Y (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ X I2) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ Y I2) tptp.one_one_assn)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.member_int I2) I6) (not (= (@ (@ tptp.times_times_assn (@ X I2)) (@ Y I2)) tptp.one_one_assn))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.assn)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1155561341820557179l_assn G) (@ tptp.collect_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.member_real X2) A2) (@ P X2))))) (@ (@ tptp.groups1155561341820557179l_assn (lambda ((X2 tptp.real)) (@ (@ (@ tptp.if_assn (@ P X2)) (@ G X2)) tptp.one_one_assn))) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn)) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ (@ tptp.groups569574905686396791T_assn G) (@ tptp.collect_VEBT_VEBT (lambda ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) A2) (@ P X2))))) (@ (@ tptp.groups569574905686396791T_assn (lambda ((X2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (@ P X2)) (@ G X2)) tptp.one_one_assn))) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.assn)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A2) (@ P X2))))) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((X2 tptp.nat)) (@ (@ (@ tptp.if_assn (@ P X2)) (@ G X2)) tptp.one_one_assn))) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.assn)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups7882442080178216443t_assn G) (@ tptp.collect_int (lambda ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A2) (@ P X2))))) (@ (@ tptp.groups7882442080178216443t_assn (lambda ((X2 tptp.int)) (@ (@ (@ tptp.if_assn (@ P X2)) (@ G X2)) tptp.one_one_assn))) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.assn)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups4150731942483176573x_assn G) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (and (@ (@ tptp.member_complex X2) A2) (@ P X2))))) (@ (@ tptp.groups4150731942483176573x_assn (lambda ((X2 tptp.complex)) (@ (@ (@ tptp.if_assn (@ P X2)) (@ G X2)) tptp.one_one_assn))) A2)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ (@ tptp.groups1304777262505850412r_assn G) (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A2) (@ P X2))))) (@ (@ tptp.groups1304777262505850412r_assn (lambda ((X2 tptp.code_integer)) (@ (@ (@ tptp.if_assn (@ P X2)) (@ G X2)) tptp.one_one_assn))) A2)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ (@ tptp.groups2703838992350267259T_real G) (@ tptp.collect_VEBT_VEBT (lambda ((X2 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X2) A2) (@ P X2))))) (@ (@ tptp.groups2703838992350267259T_real (lambda ((X2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (@ P X2)) (@ G X2)) tptp.one_one_real))) A2)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_VEBT_VEBT 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.groups2703838992350267259T_real F) A2)) tptp.one_one_real))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_VEBT_VEBT 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.groups5726676334696518183BT_rat F) A2)) tptp.one_one_rat))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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 ((X1 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X1) Y1)) (@ (@ 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))))))))
% 9.16/7.11 (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 ((X1 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X1) Y1)) (@ (@ 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))))))))
% 9.16/7.11 (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 ((X1 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X1) Y1)) (@ (@ 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))))))))
% 9.16/7.11 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X1 tptp.rat) (Y1 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X1) Y1)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite6017078050557962740nteger S3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2555765274223993564er_rat H2) S3)) (@ (@ tptp.groups2555765274223993564er_rat G) S3))))))))
% 9.16/7.11 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.assn)) (G (-> tptp.nat tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X1 tptp.assn) (Y1 tptp.assn) (X23 tptp.assn) (Y23 tptp.assn)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_assn X1) Y1)) (@ (@ tptp.times_times_assn X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups6906906614972039071t_assn H2) S3)) (@ (@ tptp.groups6906906614972039071t_assn G) S3))))))))
% 9.16/7.11 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.assn)) (G (-> tptp.int tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X1 tptp.assn) (Y1 tptp.assn) (X23 tptp.assn) (Y23 tptp.assn)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_assn X1) Y1)) (@ (@ tptp.times_times_assn X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups7882442080178216443t_assn H2) S3)) (@ (@ tptp.groups7882442080178216443t_assn G) S3))))))))
% 9.16/7.11 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.assn)) (G (-> tptp.complex tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X1 tptp.assn) (Y1 tptp.assn) (X23 tptp.assn) (Y23 tptp.assn)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_assn X1) Y1)) (@ (@ tptp.times_times_assn X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups4150731942483176573x_assn H2) S3)) (@ (@ tptp.groups4150731942483176573x_assn G) S3))))))))
% 9.16/7.11 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S3 tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X1 tptp.assn) (Y1 tptp.assn) (X23 tptp.assn) (Y23 tptp.assn)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_assn X1) Y1)) (@ (@ tptp.times_times_assn X23) Y23)))) (=> (@ tptp.finite6017078050557962740nteger S3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups1304777262505850412r_assn H2) S3)) (@ (@ tptp.groups1304777262505850412r_assn G) S3))))))))
% 9.16/7.11 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S3) (@ (@ R (@ H2 X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups129246275422532515t_real H2) S3)) (@ (@ tptp.groups129246275422532515t_real G) S3))))))))
% 9.16/7.11 (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 ((X1 tptp.real) (Y1 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X1) X23) (@ (@ R Y1) Y23)) (@ (@ R (@ (@ tptp.times_times_real X1) Y1)) (@ (@ 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))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.assn))) (let ((_let_1 (@ tptp.groups1155561341820557179l_assn 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.times_times_assn (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ tptp.groups569574905686396791T_assn 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.times_times_assn (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn 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.times_times_assn (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn 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.times_times_assn (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn 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.times_times_assn (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X) A2)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X) A2))) (=> (@ tptp.finite6017078050557962740nteger A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_assn (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real 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.times_times_real (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT 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.times_times_real (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat 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.times_times_real (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int 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.times_times_real (@ G X)) _let_2)))))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups4696554848551431203al_nat F) A2)) (@ (@ tptp.groups4696554848551431203al_nat G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ tptp.finite5795047828879050333T_VEBT B3) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) B3) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups6361806394783013919BT_nat F) A2)) (@ (@ tptp.groups6361806394783013919BT_nat G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A2)) (@ (@ tptp.groups1707563613775114915nt_nat G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups861055069439313189ex_nat F) A2)) (@ (@ tptp.groups861055069439313189ex_nat G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) B3) (=> (forall ((A5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups3190895334310489300er_nat F) A2)) (@ (@ tptp.groups3190895334310489300er_nat G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (@ (@ tptp.dvd_dvd_int (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups4694064378042380927al_int F) A2)) (@ (@ tptp.groups4694064378042380927al_int G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int)) (G (-> tptp.vEBT_VEBT tptp.int))) (=> (@ tptp.finite5795047828879050333T_VEBT B3) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) B3) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) A2) (@ (@ tptp.dvd_dvd_int (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups6359315924273963643BT_int F) A2)) (@ (@ tptp.groups6359315924273963643BT_int G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (@ (@ tptp.dvd_dvd_int (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups858564598930262913ex_int F) A2)) (@ (@ tptp.groups858564598930262913ex_int G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) B3) (=> (forall ((A5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A5) A2) (@ (@ tptp.dvd_dvd_int (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups3188404863801439024er_int F) A2)) (@ (@ tptp.groups3188404863801439024er_int G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (@ (@ tptp.dvd_dvd_nat (@ F A5)) (@ G A5)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) (@ (@ tptp.groups708209901874060359at_nat G) B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) B3) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) B3) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A2)) (@ _let_1 B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B3)))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_real) (S3 tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T5 tptp.set_real) (G (-> tptp.real tptp.assn)) (H2 (-> tptp.real tptp.assn))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S3) (@ (@ tptp.groups1155561341820557179l_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_VEBT_VEBT) (S3 tptp.set_real) (I (-> tptp.vEBT_VEBT tptp.real)) (J (-> tptp.real tptp.vEBT_VEBT)) (T5 tptp.set_VEBT_VEBT) (G (-> tptp.real tptp.assn)) (H2 (-> tptp.vEBT_VEBT tptp.assn))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite5795047828879050333T_VEBT T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_VEBT_VEBT (@ J A5)) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T4)))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T4)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S3) (@ (@ tptp.groups569574905686396791T_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_VEBT_VEBT) (T4 tptp.set_real) (S3 tptp.set_VEBT_VEBT) (I (-> tptp.real tptp.vEBT_VEBT)) (J (-> tptp.vEBT_VEBT tptp.real)) (T5 tptp.set_real) (G (-> tptp.vEBT_VEBT tptp.assn)) (H2 (-> tptp.real tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T5) T4)))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real T5) T4)) (@ (@ tptp.member_VEBT_VEBT (@ I B2)) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S3) (@ (@ tptp.groups1155561341820557179l_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_VEBT_VEBT) (T4 tptp.set_VEBT_VEBT) (S3 tptp.set_VEBT_VEBT) (I (-> tptp.vEBT_VEBT tptp.vEBT_VEBT)) (J (-> tptp.vEBT_VEBT tptp.vEBT_VEBT)) (T5 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn)) (H2 (-> tptp.vEBT_VEBT tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (@ tptp.finite5795047828879050333T_VEBT T4) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (@ (@ tptp.member_VEBT_VEBT (@ J A5)) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T4)))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) T4)) (@ (@ tptp.member_VEBT_VEBT (@ I B2)) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S3) (@ (@ tptp.groups569574905686396791T_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_int) (S3 tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T5 tptp.set_int) (G (-> tptp.real tptp.assn)) (H2 (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S3) (@ (@ tptp.groups7882442080178216443t_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_VEBT_VEBT) (T4 tptp.set_int) (S3 tptp.set_VEBT_VEBT) (I (-> tptp.int tptp.vEBT_VEBT)) (J (-> tptp.vEBT_VEBT tptp.int)) (T5 tptp.set_int) (G (-> tptp.vEBT_VEBT tptp.assn)) (H2 (-> tptp.int tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T5) T4)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T5) T4)) (@ (@ tptp.member_VEBT_VEBT (@ I B2)) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S3) (@ (@ tptp.groups7882442080178216443t_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_complex) (S3 tptp.set_real) (I (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T5 tptp.set_complex) (G (-> tptp.real tptp.assn)) (H2 (-> tptp.complex tptp.assn))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S3) (@ (@ tptp.groups4150731942483176573x_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_VEBT_VEBT) (T4 tptp.set_complex) (S3 tptp.set_VEBT_VEBT) (I (-> tptp.complex tptp.vEBT_VEBT)) (J (-> tptp.vEBT_VEBT tptp.complex)) (T5 tptp.set_complex) (G (-> tptp.vEBT_VEBT tptp.assn)) (H2 (-> tptp.complex tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T5) T4)))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex T5) T4)) (@ (@ tptp.member_VEBT_VEBT (@ I B2)) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S3) (@ (@ tptp.groups4150731942483176573x_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_real) (T4 tptp.set_Code_integer) (S3 tptp.set_real) (I (-> tptp.code_integer tptp.real)) (J (-> tptp.real tptp.code_integer)) (T5 tptp.set_Code_integer) (G (-> tptp.real tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite6017078050557962740nteger T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S4)) (@ (@ tptp.member_Code_integer (@ J A5)) (@ (@ tptp.minus_2355218937544613996nteger T5) T4)))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger T5) T4)) (@ (@ tptp.member_real (@ I B2)) (@ (@ tptp.minus_minus_set_real S3) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S3) (@ (@ tptp.groups1304777262505850412r_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((S4 tptp.set_VEBT_VEBT) (T4 tptp.set_Code_integer) (S3 tptp.set_VEBT_VEBT) (I (-> tptp.code_integer tptp.vEBT_VEBT)) (J (-> tptp.vEBT_VEBT tptp.code_integer)) (T5 tptp.set_Code_integer) (G (-> tptp.vEBT_VEBT tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (@ tptp.finite6017078050557962740nteger T4) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)) (@ (@ tptp.member_Code_integer (@ J A5)) (@ (@ tptp.minus_2355218937544613996nteger T5) T4)))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger T5) T4)) (= (@ J (@ I B2)) B2))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger T5) T4)) (@ (@ tptp.member_VEBT_VEBT (@ I B2)) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) S4)))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S4) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) T4) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S3) (@ (@ tptp.groups1304777262505850412r_assn H2) T5)))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X2 tptp.int)) (= (@ G X2) tptp.one_one_assn))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_assn))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (= (@ G X2) tptp.one_one_assn))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X2 tptp.int)) (= (@ G X2) tptp.one_one_real))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_real))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (= (@ G X2) tptp.one_one_real))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X2 tptp.int)) (= (@ G X2) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X2 tptp.complex)) (= (@ G X2) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) (@ tptp.collect_Code_integer (lambda ((X2 tptp.code_integer)) (= (@ G X2) tptp.one_one_rat))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_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.one_one_nat))))) (@ _let_1 A2))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_VEBT_VEBT) (I tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (@ (@ tptp.member_VEBT_VEBT I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I3) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2703838992350267259T_real F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (@ (@ tptp.member_complex I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_Code_integer) (I tptp.code_integer) (F (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite6017078050557962740nteger I6) (=> (@ (@ tptp.member_Code_integer I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I6) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups9004974159866482096r_real F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4061424788464935467al_rat F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_VEBT_VEBT) (I tptp.vEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (@ (@ tptp.member_VEBT_VEBT I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5726676334696518183BT_rat F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1072433553688619179nt_rat F) I6)))))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (not (= I6 tptp.bot_bo8194388402131092736T_VEBT)) (=> (forall ((I3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I3) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2703838992350267259T_real F) I6)))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I6)))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger I6) (=> (not (= I6 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups9004974159866482096r_real F) I6)))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I6)))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I6)))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I6) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I6)))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT I6) (=> (not (= I6 tptp.bot_bo8194388402131092736T_VEBT)) (=> (forall ((I3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT I3) I6) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups5726676334696518183BT_rat F) I6)))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I6) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) I6)))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger I6) (=> (not (= I6 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I6) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups2555765274223993564er_rat F) I6)))))))
% 9.16/7.11 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I6) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) I6)))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.assn)) (H2 (-> tptp.real tptp.assn))) (let ((_let_1 (@ tptp.groups1155561341820557179l_assn H2))) (let ((_let_2 (@ tptp.groups1155561341820557179l_assn G))) (=> (@ tptp.finite_finite_real C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B3) C5) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn)) (H2 (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ tptp.groups569574905686396791T_assn H2))) (let ((_let_2 (@ tptp.groups569574905686396791T_assn G))) (=> (@ tptp.finite5795047828879050333T_VEBT C5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) C5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B3) C5) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.assn)) (H2 (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn H2))) (let ((_let_2 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.assn)) (H2 (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn H2))) (let ((_let_2 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn H2))) (let ((_let_2 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C5) (=> (forall ((A5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A5) (@ (@ tptp.minus_2355218937544613996nteger C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B3) C5) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (H2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real H2))) (let ((_let_2 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT C5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) C5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B3) C5) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real H2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (H2 (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real H2))) (let ((_let_2 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C5) (=> (forall ((A5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A5) (@ (@ tptp.minus_2355218937544613996nteger C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.assn)) (H2 (-> tptp.real tptp.assn))) (let ((_let_1 (@ tptp.groups1155561341820557179l_assn H2))) (let ((_let_2 (@ tptp.groups1155561341820557179l_assn G))) (=> (@ tptp.finite_finite_real C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B3) C5) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn)) (H2 (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ tptp.groups569574905686396791T_assn H2))) (let ((_let_2 (@ tptp.groups569574905686396791T_assn G))) (=> (@ tptp.finite5795047828879050333T_VEBT C5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) C5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B3) C5) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.assn)) (H2 (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn H2))) (let ((_let_2 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.assn)) (H2 (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn H2))) (let ((_let_2 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn H2))) (let ((_let_2 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C5) (=> (forall ((A5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A5) (@ (@ tptp.minus_2355218937544613996nteger C5) A2)) (= (@ G A5) tptp.one_one_assn))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger C5) B3)) (= (@ H2 B2) tptp.one_one_assn))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real H2))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real C5) (=> (@ (@ tptp.ord_less_eq_set_real A2) C5) (=> (@ (@ tptp.ord_less_eq_set_real B3) C5) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (H2 (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real H2))) (let ((_let_2 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT C5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) C5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT B3) C5) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) (@ (@ tptp.minus_5127226145743854075T_VEBT C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_int) (A2 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real H2))) (let ((_let_2 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A2) C5) (=> (@ (@ tptp.ord_less_eq_set_int B3) C5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real H2))) (let ((_let_2 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex C5) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C5) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((C5 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (H2 (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real H2))) (let ((_let_2 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C5) (=> (forall ((A5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A5) (@ (@ tptp.minus_2355218937544613996nteger C5) A2)) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger C5) B3)) (= (@ H2 B2) tptp.one_one_real))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 S3) (@ _let_1 T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ G X3) tptp.one_one_real))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 T5) (@ _let_1 S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.assn)) (G (-> tptp.real tptp.assn))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H2 X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) S3) (@ (@ tptp.groups1155561341820557179l_assn H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S3 tptp.set_VEBT_VEBT) (H2 (-> tptp.vEBT_VEBT tptp.assn)) (G (-> tptp.vEBT_VEBT tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S3) T5) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S3)) (= (@ H2 X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups569574905686396791T_assn G) S3) (@ (@ tptp.groups569574905686396791T_assn H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.assn)) (G (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H2 X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) S3) (@ (@ tptp.groups7882442080178216443t_assn H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.assn)) (G (-> tptp.complex tptp.assn))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H2 X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4150731942483176573x_assn G) S3) (@ (@ tptp.groups4150731942483176573x_assn H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ H2 X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) S3) (@ (@ tptp.groups1304777262505850412r_assn H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ H2 X3) tptp.one_one_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1681761925125756287l_real G) S3) (@ (@ tptp.groups1681761925125756287l_real H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S3 tptp.set_VEBT_VEBT) (H2 (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S3) T5) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S3)) (= (@ H2 X3) tptp.one_one_real))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2703838992350267259T_real G) S3) (@ (@ tptp.groups2703838992350267259T_real H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ H2 X3) tptp.one_one_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2316167850115554303t_real G) S3) (@ (@ tptp.groups2316167850115554303t_real H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ H2 X3) tptp.one_one_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups766887009212190081x_real G) S3) (@ (@ tptp.groups766887009212190081x_real H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.real)) (G (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ H2 X3) tptp.one_one_real))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups9004974159866482096r_real G) S3) (@ (@ tptp.groups9004974159866482096r_real H2) T5))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.assn)) (H2 (-> tptp.real tptp.assn))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1155561341820557179l_assn G) T5) (@ (@ tptp.groups1155561341820557179l_assn H2) S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S3 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn)) (H2 (-> tptp.vEBT_VEBT tptp.assn))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S3) T5) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S3)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups569574905686396791T_assn G) T5) (@ (@ tptp.groups569574905686396791T_assn H2) S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.assn)) (H2 (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) T5) (@ (@ tptp.groups7882442080178216443t_assn H2) S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.assn)) (H2 (-> tptp.complex tptp.assn))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups4150731942483176573x_assn G) T5) (@ (@ tptp.groups4150731942483176573x_assn H2) S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) T5) (@ (@ tptp.groups1304777262505850412r_assn H2) S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T5) (=> (@ (@ tptp.ord_less_eq_set_real S3) T5) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real T5) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1681761925125756287l_real G) T5) (@ (@ tptp.groups1681761925125756287l_real H2) S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_VEBT_VEBT) (S3 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (H2 (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT T5) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT S3) T5) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT T5) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2703838992350267259T_real G) T5) (@ (@ tptp.groups2703838992350267259T_real H2) S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T5) (=> (@ (@ tptp.ord_less_eq_set_int S3) T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T5) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups2316167850115554303t_real G) T5) (@ (@ tptp.groups2316167850115554303t_real H2) S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T5) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex T5) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups766887009212190081x_real G) T5) (@ (@ tptp.groups766887009212190081x_real H2) S3))))))))
% 9.16/7.11 (assert (forall ((T5 tptp.set_Code_integer) (S3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (H2 (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (@ (@ tptp.ord_le7084787975880047091nteger S3) T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T5) S3)) (= (@ G X3) tptp.one_one_real))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S3) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups9004974159866482096r_real G) T5) (@ (@ tptp.groups9004974159866482096r_real H2) S3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A2) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A2) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A2) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (forall ((I3 tptp.vEBT_VEBT)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_VEBT_VEBT I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bo8194388402131092736T_VEBT)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2703838992350267259T_real F) A2)) (@ (@ tptp.groups2703838992350267259T_real G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups766887009212190081x_real F) A2)) (@ (@ tptp.groups766887009212190081x_real G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real)) (G (-> tptp.code_integer tptp.real))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups9004974159866482096r_real F) A2)) (@ (@ tptp.groups9004974159866482096r_real G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups1681761925125756287l_real F) A2)) (@ (@ tptp.groups1681761925125756287l_real G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups129246275422532515t_real F) A2)) (@ (@ tptp.groups129246275422532515t_real G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A2) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups2316167850115554303t_real F) A2)) (@ (@ tptp.groups2316167850115554303t_real G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat)) (G (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (forall ((I3 tptp.vEBT_VEBT)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_VEBT_VEBT I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bo8194388402131092736T_VEBT)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5726676334696518183BT_rat F) A2)) (@ (@ tptp.groups5726676334696518183BT_rat G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_complex)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups225925009352817453ex_rat F) A2)) (@ (@ tptp.groups225925009352817453ex_rat G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2555765274223993564er_rat F) A2)) (@ (@ tptp.groups2555765274223993564er_rat G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A2) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A2 tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups4061424788464935467al_rat F) A2)) (@ (@ tptp.groups4061424788464935467al_rat G) A2)))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ tptp.groups569574905686396791T_assn G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.assn))) (let ((_let_1 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (@ (@ tptp.member_Code_integer X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.assn))) (let ((_let_1 (@ tptp.groups1155561341820557179l_assn G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 9.16/7.11 (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) (=> (@ (@ tptp.member_VEBT_VEBT X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (@ (@ tptp.member_Code_integer X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 9.16/7.11 (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) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.times_times_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.assn)) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X))) (let ((_let_2 (@ tptp.groups569574905686396791T_assn G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.assn)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups4150731942483176573x_assn G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A2) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.assn)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1155561341820557179l_assn G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.assn)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.assn)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A2) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 9.16/7.11 (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.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 9.16/7.11 (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.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.real)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups9004974159866482096r_real G))) (=> (@ tptp.finite6017078050557962740nteger A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A2) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.times_times_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.assn)) (C (-> tptp.vEBT_VEBT tptp.assn))) (let ((_let_1 (@ (@ tptp.groups569574905686396791T_assn 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.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups569574905686396791T_assn (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.assn)) (C (-> tptp.complex tptp.assn))) (let ((_let_1 (@ (@ tptp.groups4150731942483176573x_assn 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.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4150731942483176573x_assn (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.assn)) (C (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ (@ tptp.groups1304777262505850412r_assn C) (@ (@ tptp.minus_2355218937544613996nteger S3) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A) S3))) (=> (@ tptp.finite6017078050557962740nteger S3) (and (=> _let_2 (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.assn)) (C (-> tptp.real tptp.assn))) (let ((_let_1 (@ (@ tptp.groups1155561341820557179l_assn C) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1155561341820557179l_assn (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.assn)) (C (-> tptp.int tptp.assn))) (let ((_let_1 (@ (@ tptp.groups7882442080178216443t_assn 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.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.assn)) (C (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.groups6906906614972039071t_assn C) (@ (@ tptp.minus_minus_set_nat S3) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_2 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_2 (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_assn (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.real)) (C (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.groups2703838992350267259T_real C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2703838992350267259T_real (lambda ((K3 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups766887009212190081x_real C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K3 tptp.complex)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.real)) (C (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ (@ tptp.groups9004974159866482096r_real C) (@ (@ tptp.minus_2355218937544613996nteger S3) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_2 (@ (@ tptp.member_Code_integer A) S3))) (=> (@ tptp.finite6017078050557962740nteger S3) (and (=> _let_2 (= (@ (@ tptp.groups9004974159866482096r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups9004974159866482096r_real (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups1681761925125756287l_real C) (@ (@ tptp.minus_minus_set_real S3) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_2 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_2 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S3) (@ (@ tptp.times_times_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K3 tptp.real)) (@ (@ (@ tptp.if_real (= K3 A)) (@ B K3)) (@ C K3)))) S3) _let_1))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real F))) (=> (@ tptp.finite5795047828879050333T_VEBT B3) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) B3) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real))) (let ((_let_1 (@ tptp.groups9004974159866482096r_real F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) B3) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F B2)))) (=> (forall ((A5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A5) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F A5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B2 tptp.real)) (=> (@ (@ tptp.member_real B2) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat F))) (=> (@ tptp.finite5795047828879050333T_VEBT B3) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT A2) B3) (=> (forall ((B2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT B2) (@ (@ tptp.minus_5127226145743854075T_VEBT B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT A5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B2 tptp.complex)) (=> (@ (@ tptp.member_complex B2) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((B3 tptp.set_Code_integer) (A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A2) B3) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A5) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3)))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.complex)) (A tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.groups127312072573709053omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups3708469109370488835omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.complex)) (A tptp.code_integer)) (let ((_let_1 (@ tptp.groups862514429393162674omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.complex)) (A tptp.real)) (let ((_let_1 (@ tptp.groups713298508707869441omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.complex)) (A tptp.int)) (let ((_let_1 (@ tptp.groups7440179247065528705omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_int A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (A tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= _let_5 tptp.zero_zero_complex)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide1717551699836669952omplex _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (A tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.groups2703838992350267259T_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A2) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (A tptp.complex)) (let ((_let_1 (@ tptp.groups766887009212190081x_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_4 (@ (@ tptp.member_complex A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.real)) (A tptp.code_integer)) (let ((_let_1 (@ tptp.groups9004974159866482096r_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A2) (@ (@ tptp.insert_Code_integer A) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (A tptp.real)) (let ((_let_1 (@ tptp.groups1681761925125756287l_real F))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))) (let ((_let_4 (@ (@ tptp.member_real A) A2))) (let ((_let_5 (@ F A))) (=> (@ tptp.finite_finite_real A2) (=> (not (= _let_5 tptp.zero_zero_real)) (and (=> _let_4 (= _let_3 (@ (@ tptp.divide_divide_real _let_2) _let_5))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_eq_real (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real F) Xs2)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_s6755466524823107622T_VEBT Xs2))) Bound)) I)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_real) (F (-> tptp.real tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_eq_real (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_real_real F) Xs2)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_real Xs2))) Bound)) I)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_o) (F (-> Bool tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_eq_real (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_o_real F) Xs2)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_o Xs2))) Bound)) I)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (F (-> tptp.nat tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_eq_real (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_nat_real F) Xs2)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_nat Xs2))) Bound)) I)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_int) (F (-> tptp.int tptp.real)) (Bound tptp.real) (I tptp.real)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_eq_real (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_real (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_int_real F) Xs2)) I)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_int Xs2))) Bound)) I)))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (C tptp.real) (G (-> tptp.vEBT_VEBT tptp.real)) (D2 tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ (@ tptp.times_times_real C) (@ G X3))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_VEBT_VEBT_real F) Xs2)) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) (@ (@ _let_1 (@ (@ tptp.map_VEBT_VEBT_real G) Xs2)) tptp.zero_zero_real))) D2))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (F (-> tptp.nat tptp.real)) (C tptp.real) (G (-> tptp.nat tptp.real)) (D2 tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ (@ tptp.times_times_real C) (@ G X3))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_nat_real F) Xs2)) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) (@ (@ _let_1 (@ (@ tptp.map_nat_real G) Xs2)) tptp.zero_zero_real))) D2))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_real) (F (-> tptp.real tptp.real)) (C tptp.real) (G (-> tptp.real tptp.real)) (D2 tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ (@ tptp.times_times_real C) (@ G X3))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_real_real F) Xs2)) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) (@ (@ _let_1 (@ (@ tptp.map_real_real G) Xs2)) tptp.zero_zero_real))) D2))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_int) (F (-> tptp.int tptp.real)) (C tptp.real) (G (-> tptp.int tptp.real)) (D2 tptp.real)) (let ((_let_1 (@ tptp.foldr_real_real tptp.plus_plus_real))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_eq_real (@ F X3)) (@ (@ tptp.times_times_real C) (@ G X3))))) (@ (@ tptp.ord_less_eq_real (@ (@ _let_1 (@ (@ tptp.map_int_real F) Xs2)) D2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) (@ (@ _let_1 (@ (@ tptp.map_int_real G) Xs2)) tptp.zero_zero_real))) D2))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_eq_nat (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) Bound)) I)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_real) (F (-> tptp.real tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_eq_nat (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_real_nat F) Xs2)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_real Xs2)) Bound)) I)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_o) (F (-> Bool tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_eq_nat (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_o_nat F) Xs2)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) Bound)) I)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (F (-> tptp.nat tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_eq_nat (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_nat_nat F) Xs2)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) Bound)) I)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_int) (F (-> tptp.int tptp.nat)) (Bound tptp.nat) (I tptp.nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_eq_nat (@ F X3)) Bound))) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_int_nat F) Xs2)) I)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs2)) Bound)) I)))))
% 9.16/7.11 (assert (= (@ tptp.map_nat_nat (lambda ((X2 tptp.nat)) X2)) (lambda ((Xs tptp.list_nat)) Xs)))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_complex) (F (-> tptp.complex tptp.real)) (Y tptp.real)) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real Y) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_complex_real F) Xs2)) Y)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (Y tptp.real)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real Y) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real F) Xs2)) Y)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real Y) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_nat_real F) Xs2)) Y)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_real) (F (-> tptp.real tptp.real)) (Y tptp.real)) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real Y) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_real_real F) Xs2)) Y)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_int) (F (-> tptp.int tptp.real)) (Y tptp.real)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X3)))) (@ (@ tptp.ord_less_eq_real Y) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_int_real F) Xs2)) Y)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_VEBT_VEBT_real F) Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.real tptp.real)) (Xs2 tptp.list_real)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_real_real F) Xs2)) (@ tptp.size_size_list_real Xs2))))
% 9.16/7.11 (assert (forall ((F (-> Bool tptp.real)) (Xs2 tptp.list_o)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_o_real F) Xs2)) (@ tptp.size_size_list_o Xs2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.real)) (Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_nat_real F) Xs2)) (@ tptp.size_size_list_nat Xs2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.int tptp.real)) (Xs2 tptp.list_int)) (= (@ tptp.size_size_list_real (@ (@ tptp.map_int_real F) Xs2)) (@ tptp.size_size_list_int Xs2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.real Bool)) (Xs2 tptp.list_real)) (= (@ tptp.size_size_list_o (@ (@ tptp.map_real_o F) Xs2)) (@ tptp.size_size_list_real Xs2))))
% 9.16/7.11 (assert (forall ((F (-> Bool Bool)) (Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o (@ (@ tptp.map_o_o F) Xs2)) (@ tptp.size_size_list_o Xs2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat Bool)) (Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_o (@ (@ tptp.map_nat_o F) Xs2)) (@ tptp.size_size_list_nat Xs2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.int Bool)) (Xs2 tptp.list_int)) (= (@ tptp.size_size_list_o (@ (@ tptp.map_int_o F) Xs2)) (@ tptp.size_size_list_int Xs2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_size_list_nat (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (= (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2) (@ (@ tptp.map_VEBT_VEBT_nat G) Xs2)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (= (@ F X2) (@ G X2)))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (= (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs2) (@ (@ tptp.map_VEBT_VEBT_real G) Xs2)) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (= (@ F X2) (@ G X2)))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs2 tptp.list_nat) (G (-> tptp.nat tptp.nat))) (= (= (@ (@ tptp.map_nat_nat F) Xs2) (@ (@ tptp.map_nat_nat G) Xs2)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (= (@ F X2) (@ G X2)))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat Bool)) (Xs2 tptp.list_nat) (G (-> tptp.nat Bool))) (= (= (@ (@ tptp.map_nat_o F) Xs2) (@ (@ tptp.map_nat_o G) Xs2)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (= (@ F X2) (@ G X2)))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.replicate_nat N))) (= (@ (@ tptp.map_nat_nat F) (@ _let_1 X)) (@ _let_1 (@ F X))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat Bool)) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.map_nat_o F) (@ (@ tptp.replicate_nat N) X)) (@ (@ tptp.replicate_o N) (@ F X)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_nat F) (@ (@ tptp.replicate_VEBT_VEBT N) X)) (@ (@ tptp.replicate_nat N) (@ F X)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_real F) (@ (@ tptp.replicate_VEBT_VEBT N) X)) (@ (@ tptp.replicate_real N) (@ F X)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT)) (N tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.replicate_VEBT_VEBT N))) (= (@ (@ tptp.map_VE8901447254227204932T_VEBT F) (@ _let_1 X)) (@ _let_1 (@ F X))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs2 tptp.list_VEBT_VEBT) (C tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2)) C)) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real (lambda ((X2 tptp.vEBT_VEBT)) (@ tptp.semiri5074537144036343181t_real (@ F X2)))) Xs2)) (@ tptp.semiri5074537144036343181t_real C)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs2 tptp.list_nat) (C tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_nat_nat F) Xs2)) C)) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_nat_real (lambda ((X2 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X2)))) Xs2)) (@ tptp.semiri5074537144036343181t_real C)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.map_VE8901447254227204932T_VEBT F) Xs2)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (F (-> tptp.vEBT_VEBTi tptp.vEBT_VEBT))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.map_VE7998069337340375161T_VEBT F) Xs2)) N) (@ F (@ (@ tptp.nth_VEBT_VEBTi Xs2) N))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (F (-> tptp.vEBT_VEBTi tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (= (@ (@ tptp.nth_nat (@ (@ tptp.map_VEBT_VEBTi_nat F) Xs2)) N) (@ F (@ (@ tptp.nth_VEBT_VEBTi Xs2) N))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ tptp.map_VE7029150624388687525_VEBTi F) Xs2)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (F (-> tptp.vEBT_VEBTi tptp.vEBT_VEBTi))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (= (@ (@ tptp.nth_VEBT_VEBTi (@ (@ tptp.map_VE483055756984248624_VEBTi F) Xs2)) N) (@ F (@ (@ tptp.nth_VEBT_VEBTi Xs2) N))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_int (@ (@ tptp.map_VEBT_VEBT_int F) Xs2)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBTi) (F (-> tptp.vEBT_VEBTi tptp.int))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s7982070591426661849_VEBTi Xs2)) (= (@ (@ tptp.nth_int (@ (@ tptp.map_VEBT_VEBTi_int F) Xs2)) N) (@ F (@ (@ tptp.nth_VEBT_VEBTi Xs2) N))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_nat (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_real (@ (@ tptp.map_VEBT_VEBT_real F) Xs2)) N) (@ F (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real) (F (-> tptp.real tptp.vEBT_VEBT))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.map_real_VEBT_VEBT F) Xs2)) N) (@ F (@ (@ tptp.nth_real Xs2) N))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2) (@ (@ tptp.map_VEBT_VEBT_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs2) (@ (@ tptp.map_VEBT_VEBT_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.real tptp.nat)) (Ys tptp.list_real)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2) (@ (@ tptp.map_real_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_real Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.real tptp.real)) (Ys tptp.list_real)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs2) (@ (@ tptp.map_real_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_real Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs2 tptp.list_VEBT_VEBT) (G (-> Bool tptp.nat)) (Ys tptp.list_o)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2) (@ (@ tptp.map_o_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_o Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs2 tptp.list_VEBT_VEBT) (G (-> Bool tptp.real)) (Ys tptp.list_o)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs2) (@ (@ tptp.map_o_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_o Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.nat tptp.nat)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2) (@ (@ tptp.map_nat_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_nat Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.nat tptp.real)) (Ys tptp.list_nat)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs2) (@ (@ tptp.map_nat_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_nat Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.int tptp.nat)) (Ys tptp.list_int)) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2) (@ (@ tptp.map_int_nat G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_int Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs2 tptp.list_VEBT_VEBT) (G (-> tptp.int tptp.real)) (Ys tptp.list_int)) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs2) (@ (@ tptp.map_int_real G) Ys)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_size_list_int Ys)))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs2 tptp.list_nat) (K tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.map_nat_nat F))) (= (@ _let_1 (@ (@ (@ tptp.list_update_nat Xs2) K) Y)) (@ (@ (@ tptp.list_update_nat (@ _let_1 Xs2)) K) (@ F Y))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat Bool)) (Xs2 tptp.list_nat) (K tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.map_nat_o F))) (= (@ _let_1 (@ (@ (@ tptp.list_update_nat Xs2) K) Y)) (@ (@ (@ tptp.list_update_o (@ _let_1 Xs2)) K) (@ F Y))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.nat)) (Xs2 tptp.list_VEBT_VEBT) (K tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_nat F))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) K) Y)) (@ (@ (@ tptp.list_update_nat (@ _let_1 Xs2)) K) (@ F Y))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.real)) (Xs2 tptp.list_VEBT_VEBT) (K tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_real F))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) K) Y)) (@ (@ (@ tptp.list_update_real (@ _let_1 Xs2)) K) (@ F Y))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT)) (Xs2 tptp.list_VEBT_VEBT) (K tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VE8901447254227204932T_VEBT F))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) K) Y)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 Xs2)) K) (@ F Y))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi)) (Xs2 tptp.list_VEBT_VEBT) (K tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VE7029150624388687525_VEBTi F))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) K) Y)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ _let_1 Xs2)) K) (@ F Y))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBTi tptp.vEBT_VEBT)) (Xs2 tptp.list_VEBT_VEBTi) (K tptp.nat) (Y tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.map_VE7998069337340375161T_VEBT F))) (= (@ _let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) K) Y)) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 Xs2)) K) (@ F Y))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.vEBT_VEBTi tptp.vEBT_VEBTi)) (Xs2 tptp.list_VEBT_VEBTi) (K tptp.nat) (Y tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.map_VE483055756984248624_VEBTi F))) (= (@ _let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Xs2) K) Y)) (@ (@ (@ tptp.list_u6098035379799741383_VEBTi (@ _let_1 Xs2)) K) (@ F Y))))))
% 9.16/7.11 (assert (forall ((T tptp.list_nat)) (= (@ (@ tptp.map_nat_nat (lambda ((X2 tptp.nat)) X2)) T) T)))
% 9.16/7.11 (assert (forall ((X tptp.list_VEBT_VEBT) (Ya tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (= X Ya) (=> (forall ((Z3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 Ya)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) X) (@ (@ tptp.map_VEBT_VEBT_nat G) Ya))))))
% 9.16/7.11 (assert (forall ((X tptp.list_VEBT_VEBT) (Ya tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (= X Ya) (=> (forall ((Z3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 Ya)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) X) (@ (@ tptp.map_VEBT_VEBT_real G) Ya))))))
% 9.16/7.11 (assert (forall ((X tptp.list_nat) (Ya tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (= X Ya) (=> (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) (@ tptp.set_nat2 Ya)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_nat_nat F) X) (@ (@ tptp.map_nat_nat G) Ya))))))
% 9.16/7.11 (assert (forall ((X tptp.list_nat) (Ya tptp.list_nat) (F (-> tptp.nat Bool)) (G (-> tptp.nat Bool))) (=> (= X Ya) (=> (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) (@ tptp.set_nat2 Ya)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_nat_o F) X) (@ (@ tptp.map_nat_o G) Ya))))))
% 9.16/7.11 (assert (forall ((X tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((Z3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 X)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) X) (@ (@ tptp.map_VEBT_VEBT_nat G) X)))))
% 9.16/7.11 (assert (forall ((X tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((Z3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 X)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) X) (@ (@ tptp.map_VEBT_VEBT_real G) X)))))
% 9.16/7.11 (assert (forall ((X tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) (@ tptp.set_nat2 X)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_nat_nat F) X) (@ (@ tptp.map_nat_nat G) X)))))
% 9.16/7.11 (assert (forall ((X tptp.list_nat) (F (-> tptp.nat Bool)) (G (-> tptp.nat Bool))) (=> (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) (@ tptp.set_nat2 X)) (= (@ F Z3) (@ G Z3)))) (= (@ (@ tptp.map_nat_o F) X) (@ (@ tptp.map_nat_o G) X)))))
% 9.16/7.11 (assert (forall ((X tptp.list_VEBT_VEBT) (Xa3 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (Fa (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((Z3 tptp.vEBT_VEBT) (Za tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 X)) (=> (@ (@ tptp.member_VEBT_VEBT Za) (@ tptp.set_VEBT_VEBT2 Xa3)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ tptp.map_VEBT_VEBT_nat F) X) (@ (@ tptp.map_VEBT_VEBT_nat Fa) Xa3)) (= X Xa3)))))
% 9.16/7.11 (assert (forall ((X tptp.list_VEBT_VEBT) (Xa3 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (Fa (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((Z3 tptp.vEBT_VEBT) (Za tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Z3) (@ tptp.set_VEBT_VEBT2 X)) (=> (@ (@ tptp.member_VEBT_VEBT Za) (@ tptp.set_VEBT_VEBT2 Xa3)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ tptp.map_VEBT_VEBT_real F) X) (@ (@ tptp.map_VEBT_VEBT_real Fa) Xa3)) (= X Xa3)))))
% 9.16/7.11 (assert (forall ((X tptp.list_nat) (Xa3 tptp.list_nat) (F (-> tptp.nat tptp.nat)) (Fa (-> tptp.nat tptp.nat))) (=> (forall ((Z3 tptp.nat) (Za tptp.nat)) (=> (@ (@ tptp.member_nat Z3) (@ tptp.set_nat2 X)) (=> (@ (@ tptp.member_nat Za) (@ tptp.set_nat2 Xa3)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ tptp.map_nat_nat F) X) (@ (@ tptp.map_nat_nat Fa) Xa3)) (= X Xa3)))))
% 9.16/7.11 (assert (forall ((X tptp.list_nat) (Xa3 tptp.list_nat) (F (-> tptp.nat Bool)) (Fa (-> tptp.nat Bool))) (=> (forall ((Z3 tptp.nat) (Za tptp.nat)) (=> (@ (@ tptp.member_nat Z3) (@ tptp.set_nat2 X)) (=> (@ (@ tptp.member_nat Za) (@ tptp.set_nat2 Xa3)) (=> (= (@ F Z3) (@ Fa Za)) (= Z3 Za))))) (=> (= (@ (@ tptp.map_nat_o F) X) (@ (@ tptp.map_nat_o Fa) Xa3)) (= X Xa3)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2) (@ (@ tptp.map_VEBT_VEBT_nat G) Xs2)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs2) (@ (@ tptp.map_VEBT_VEBT_real G) Xs2)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.map_nat_nat F) Xs2) (@ (@ tptp.map_nat_nat G) Xs2)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (F (-> tptp.nat Bool)) (G (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.map_nat_o F) Xs2) (@ (@ tptp.map_nat_o G) Xs2)))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_complex) (F (-> tptp.complex tptp.complex))) (=> (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) (@ tptp.set_complex2 Xs2)) (= (@ F X3) X3))) (= (@ (@ tptp.map_complex_complex F) Xs2) Xs2))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.vEBT_VEBT))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= (@ F X3) X3))) (= (@ (@ tptp.map_VE8901447254227204932T_VEBT F) Xs2) Xs2))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs2)) (= (@ F X3) X3))) (= (@ (@ tptp.map_nat_nat F) Xs2) Xs2))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_real) (F (-> tptp.real tptp.real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 Xs2)) (= (@ F X3) X3))) (= (@ (@ tptp.map_real_real F) Xs2) Xs2))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs2)) (= (@ F X3) X3))) (= (@ (@ tptp.map_int_int F) Xs2) Xs2))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (G (-> tptp.vEBT_VEBT tptp.nat))) (=> (= Xs2 Ys) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Ys)) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.map_VEBT_VEBT_nat F) Xs2) (@ (@ tptp.map_VEBT_VEBT_nat G) Ys))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (G (-> tptp.vEBT_VEBT tptp.real))) (=> (= Xs2 Ys) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Ys)) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.map_VEBT_VEBT_real F) Xs2) (@ (@ tptp.map_VEBT_VEBT_real G) Ys))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (= Xs2 Ys) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Ys)) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.map_nat_nat F) Xs2) (@ (@ tptp.map_nat_nat G) Ys))))))
% 9.16/7.11 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat) (F (-> tptp.nat Bool)) (G (-> tptp.nat Bool))) (=> (= Xs2 Ys) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Ys)) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.map_nat_o F) Xs2) (@ (@ tptp.map_nat_o G) Ys))))))
% 9.16/7.11 (assert (forall ((Ys tptp.list_o) (F (-> tptp.nat Bool))) (= (exists ((Xs tptp.list_nat)) (= Ys (@ (@ tptp.map_nat_o F) Xs))) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Ys)) (exists ((Y6 tptp.nat)) (= X2 (@ F Y6))))))))
% 9.16/7.11 (assert (forall ((Ys tptp.list_nat) (F (-> tptp.vEBT_VEBT tptp.nat))) (= (exists ((Xs tptp.list_VEBT_VEBT)) (= Ys (@ (@ tptp.map_VEBT_VEBT_nat F) Xs))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Ys)) (exists ((Y6 tptp.vEBT_VEBT)) (= X2 (@ F Y6))))))))
% 9.16/7.11 (assert (forall ((Ys tptp.list_nat) (F (-> tptp.nat tptp.nat))) (= (exists ((Xs tptp.list_nat)) (= Ys (@ (@ tptp.map_nat_nat F) Xs))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Ys)) (exists ((Y6 tptp.nat)) (= X2 (@ F Y6))))))))
% 9.16/7.11 (assert (forall ((Ys tptp.list_real) (F (-> tptp.vEBT_VEBT tptp.real))) (= (exists ((Xs tptp.list_VEBT_VEBT)) (= Ys (@ (@ tptp.map_VEBT_VEBT_real F) Xs))) (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Ys)) (exists ((Y6 tptp.vEBT_VEBT)) (= X2 (@ F Y6))))))))
% 9.16/7.11 (assert (forall ((K tptp.nat) (Lst tptp.list_VEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_nat (lambda ((X2 tptp.vEBT_VEBT)) K)) Lst) (@ (@ tptp.replicate_nat (@ tptp.size_s6755466524823107622T_VEBT Lst)) K))))
% 9.16/7.11 (assert (forall ((K tptp.real) (Lst tptp.list_VEBT_VEBT)) (= (@ (@ tptp.map_VEBT_VEBT_real (lambda ((X2 tptp.vEBT_VEBT)) K)) Lst) (@ (@ tptp.replicate_real (@ tptp.size_s6755466524823107622T_VEBT Lst)) K))))
% 9.16/7.11 (assert (forall ((K tptp.vEBT_VEBT) (Lst tptp.list_real)) (= (@ (@ tptp.map_real_VEBT_VEBT (lambda ((X2 tptp.real)) K)) Lst) (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_size_list_real Lst)) K))))
% 9.16/7.11 (assert (forall ((K tptp.vEBT_VEBT) (Lst tptp.list_o)) (= (@ (@ tptp.map_o_VEBT_VEBT (lambda ((X2 Bool)) K)) Lst) (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_size_list_o Lst)) K))))
% 9.16/7.11 (assert (forall ((K tptp.nat) (Lst tptp.list_nat)) (= (@ (@ tptp.map_nat_nat (lambda ((X2 tptp.nat)) K)) Lst) (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Lst)) K))))
% 9.16/7.11 (assert (forall ((K Bool) (Lst tptp.list_nat)) (= (@ (@ tptp.map_nat_o (lambda ((X2 tptp.nat)) K)) Lst) (@ (@ tptp.replicate_o (@ tptp.size_size_list_nat Lst)) K))))
% 9.16/7.11 (assert (forall ((K tptp.vEBT_VEBT) (Lst tptp.list_nat)) (= (@ (@ tptp.map_nat_VEBT_VEBT (lambda ((X2 tptp.nat)) K)) Lst) (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_size_list_nat Lst)) K))))
% 9.16/7.11 (assert (forall ((K tptp.vEBT_VEBT) (Lst tptp.list_int)) (= (@ (@ tptp.map_int_VEBT_VEBT (lambda ((X2 tptp.int)) K)) Lst) (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_size_list_int Lst)) K))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat)) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_nat F))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L)) (= (@ F (@ (@ tptp.nth_VEBT_VEBT L) I)) (@ F X))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) X)) (@ _let_1 L))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.map_VEBT_VEBT_real F))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT L)) (= (@ F (@ (@ tptp.nth_VEBT_VEBT L) I)) (@ F X))) (= (@ _let_1 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT L) I) X)) (@ _let_1 L))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_nat) (F (-> tptp.nat tptp.nat)) (X tptp.nat)) (let ((_let_1 (@ tptp.map_nat_nat F))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ F (@ (@ tptp.nth_nat L) I)) (@ F X))) (= (@ _let_1 (@ (@ (@ tptp.list_update_nat L) I) X)) (@ _let_1 L))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.list_nat) (F (-> tptp.nat Bool)) (X tptp.nat)) (let ((_let_1 (@ tptp.map_nat_o F))) (=> (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat L)) (= (@ F (@ (@ tptp.nth_nat L) I)) (@ F X))) (= (@ _let_1 (@ (@ (@ tptp.list_update_nat L) I) X)) (@ _let_1 L))))))
% 9.16/7.11 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_cnt2 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_cnt2 Summary))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_cnt2) TreeList)) tptp.zero_zero_nat)))))
% 9.16/7.11 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_cnt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.vEBT_VEBT_cnt Summary))) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) TreeList)) tptp.zero_zero_real)))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_cnt2 X) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (not (= Y tptp.one_one_nat))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_cnt2 Summary2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_cnt2) TreeList2)) tptp.zero_zero_nat)))))))))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.real)) (=> (= (@ tptp.vEBT_VEBT_cnt X) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (not (= Y tptp.one_one_real))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.vEBT_VEBT_cnt Summary2))) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) TreeList2)) tptp.zero_zero_real)))))))))))
% 9.16/7.11 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_space2 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_space2 Summary))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2) TreeList)) tptp.zero_zero_nat)))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space2 X) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (not (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_space2 Summary2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2) TreeList2)) tptp.zero_zero_nat)))))))))))
% 9.16/7.11 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_space (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 tptp.one)))) (@ tptp.vEBT_VEBT_space Summary))) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space) TreeList)) tptp.zero_zero_nat)))))
% 9.16/7.11 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space X) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (not (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 tptp.one)))) (@ tptp.vEBT_VEBT_space Summary2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space) TreeList2)) tptp.zero_zero_nat)))))))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 9.16/7.11 (assert (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 9.16/7.11 (assert (= (@ tptp.suminf_nat (lambda ((N3 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 9.16/7.11 (assert (= (@ tptp.suminf_int (lambda ((N3 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 9.16/7.11 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 9.16/7.11 (assert (forall ((H2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (X tptp.vEBT_VEBTi) (Xaa tptp.option_nat) (X13 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Tree_is) H2) X))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L))) (let ((_let_3 (@ tptp.pure_assn (= Xaa (@ tptp.vEBT_vebt_mint _let_2))))) (let ((_let_4 (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi X13) _let_1)) (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))))) (let ((_let_5 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (@ (@ tptp.ord_less_nat H2) _let_5) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw _let_2) X)) _let_3)) (@ _let_4 (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_5)) (@ (@ tptp.insert_nat H2) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) TreeList) Tree_is)))) (@ (@ tptp.times_times_assn (@ _let_4 _let_3)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) _let_2)) _let_1)))))))))))
% 9.16/7.11 (assert (forall ((I tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or66887138388493659n_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I) (@ (@ tptp.ord_less_real I) U)))))
% 9.16/7.11 (assert (forall ((I tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or3540276404033026485et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I) (@ (@ tptp.ord_less_set_nat I) U)))))
% 9.16/7.11 (assert (forall ((I tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I) (@ (@ tptp.set_or4029947393144176647an_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I) (@ (@ tptp.ord_less_rat I) U)))))
% 9.16/7.11 (assert (forall ((I tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I) (@ (@ tptp.set_or1222409239386451017an_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I) (@ (@ tptp.ord_less_num I) U)))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_nat I) U)))))
% 9.16/7.11 (assert (forall ((I tptp.code_integer) (L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.member_Code_integer I) (@ (@ tptp.set_or8404916559141939852nteger L) U)) (and (@ (@ tptp.ord_le3102999989581377725nteger L) I) (@ (@ tptp.ord_le6747313008572928689nteger I) U)))))
% 9.16/7.11 (assert (forall ((I tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or4662586982721622107an_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I) (@ (@ tptp.ord_less_int I) U)))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or66887138388493659n_real A) B)) (not (@ (@ tptp.ord_less_real A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or4029947393144176647an_rat A) B)) (not (@ (@ tptp.ord_less_rat A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or1222409239386451017an_num A) B)) (not (@ (@ tptp.ord_less_num A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (not (@ (@ tptp.ord_less_nat A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (@ (@ tptp.set_or8404916559141939852nteger A) B)) (not (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or4662586982721622107an_int A) B)) (not (@ (@ tptp.ord_less_int A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or66887138388493659n_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_real A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_rat A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or1222409239386451017an_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_num A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_nat A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.set_or8404916559141939852nteger A) B) tptp.bot_bo3990330152332043303nteger) (not (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or4662586982721622107an_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_int A) B)))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or66887138388493659n_real A) B))) (@ (@ tptp.ord_less_real A) B))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or4029947393144176647an_rat A) B))) (@ (@ tptp.ord_less_rat A) B))))
% 9.16/7.11 (assert (forall ((Y tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X13 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.nth_VEBT_VEBT TreeList) Y)) (@ (@ tptp.nth_VEBT_VEBTi Tree_is) Y)))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_2)) (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) TreeList) Tree_is))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))) (let ((_let_5 (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi X13) Tree_is)))) (=> (@ (@ tptp.ord_less_nat Y) _let_2) (@ (@ tptp.entails (@ _let_5 (@ (@ tptp.times_times_assn _let_4) (@ (@ tptp.times_times_assn _let_1) _let_3)))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_5 _let_4)) _let_3)) _let_1))))))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Tree_is tptp.list_VEBT_VEBTi) (X13 tptp.array_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.snga_assn_VEBT_VEBTi X13) Tree_is))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))) (let ((_let_3 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (@ (@ tptp.ord_less_nat I) _let_3) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.nth_VEBT_VEBT TreeList) I)) (@ (@ tptp.nth_VEBT_VEBTi Tree_is) I))) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_3)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) TreeList) Tree_is))) _let_1)) _let_2)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn _let_2) _let_1)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) TreeList) Tree_is)))))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Tree_is tptp.list_VEBT_VEBTi) (Rest tptp.assn) (X13 tptp.array_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.snga_assn_VEBT_VEBTi X13) Tree_is))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))) (let ((_let_3 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (@ (@ tptp.ord_less_nat I) _let_3) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.nth_VEBT_VEBT TreeList) I)) (@ (@ tptp.nth_VEBT_VEBTi Tree_is) I))) Rest)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn _let_1) _let_2)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_3)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) TreeList) Tree_is)))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn Rest) _let_2)) _let_1)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) TreeList) Tree_is)))))))))
% 9.16/7.11 (assert (forall ((Y tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Tree_is tptp.list_VEBT_VEBTi) (X13 tptp.array_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ tptp.snga_assn_VEBT_VEBTi X13) Tree_is))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))) (let ((_let_3 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (@ (@ tptp.ord_less_nat Y) _let_3) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.nth_VEBT_VEBT TreeList) Y)) (@ (@ tptp.nth_VEBT_VEBTi Tree_is) Y))) _let_1)) _let_2)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_3)) (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) TreeList) Tree_is))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn _let_2) _let_1)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) TreeList) Tree_is)))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (TreeList4 tptp.list_real) (Y tptp.vEBT_VEBT) (X tptp.vEBT_VEBTi) (X13 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Tree_is) I) X))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) I) Y))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))) (let ((_let_4 (@ (@ tptp.snga_assn_VEBT_VEBTi X13) _let_1))) (let ((_let_5 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (@ (@ tptp.ord_less_nat I) _let_5) (=> (= _let_5 (@ tptp.size_size_list_real TreeList4)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw Y) X)) _let_4)) _let_3)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_5)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) _let_2) _let_1))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn _let_4) _let_3)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) _let_2) _let_1))))))))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (TreeList4 tptp.list_o) (Y tptp.vEBT_VEBT) (X tptp.vEBT_VEBTi) (X13 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Tree_is) I) X))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) I) Y))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))) (let ((_let_4 (@ (@ tptp.snga_assn_VEBT_VEBTi X13) _let_1))) (let ((_let_5 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (@ (@ tptp.ord_less_nat I) _let_5) (=> (= _let_5 (@ tptp.size_size_list_o TreeList4)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw Y) X)) _let_4)) _let_3)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_5)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) _let_2) _let_1))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn _let_4) _let_3)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) _let_2) _let_1))))))))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (TreeList4 tptp.list_nat) (Y tptp.vEBT_VEBT) (X tptp.vEBT_VEBTi) (X13 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Tree_is) I) X))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) I) Y))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))) (let ((_let_4 (@ (@ tptp.snga_assn_VEBT_VEBTi X13) _let_1))) (let ((_let_5 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (@ (@ tptp.ord_less_nat I) _let_5) (=> (= _let_5 (@ tptp.size_size_list_nat TreeList4)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw Y) X)) _let_4)) _let_3)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_5)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) _let_2) _let_1))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn _let_4) _let_3)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) _let_2) _let_1))))))))))))
% 9.16/7.11 (assert (forall ((I tptp.nat) (TreeList tptp.list_VEBT_VEBT) (TreeList4 tptp.list_int) (Y tptp.vEBT_VEBT) (X tptp.vEBT_VEBTi) (X13 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Tree_is) I) X))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) I) Y))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))) (let ((_let_4 (@ (@ tptp.snga_assn_VEBT_VEBTi X13) _let_1))) (let ((_let_5 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (@ (@ tptp.ord_less_nat I) _let_5) (=> (= _let_5 (@ tptp.size_size_list_int TreeList4)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw Y) X)) _let_4)) _let_3)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_5)) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) _let_2) _let_1))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn _let_4) _let_3)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) _let_2) _let_1))))))))))))
% 9.16/7.11 (assert (forall ((H2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Xaa tptp.vEBT_VEBT) (L tptp.nat) (X tptp.vEBT_VEBTi) (Xb3 tptp.option_nat) (X13 tptp.array_VEBT_VEBTi) (Tree_is tptp.list_VEBT_VEBTi) (Summary tptp.vEBT_VEBT) (X14 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ tptp.list_u6098035379799741383_VEBTi Tree_is) H2) X))) (let ((_let_2 (@ tptp.pure_assn (= Xb3 (@ tptp.vEBT_vebt_mint Xaa))))) (let ((_let_3 (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi X13) _let_1)) (@ (@ tptp.vEBT_vebt_assn_raw Summary) X14))))) (let ((_let_4 (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (@ (@ tptp.ord_less_nat H2) _let_4) (=> (= Xaa (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList) H2)) L)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.vEBT_vebt_assn_raw Xaa) X)) _let_2)) (@ _let_3 (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) _let_4)) (@ (@ tptp.insert_nat H2) tptp.bot_bot_set_nat))) tptp.vEBT_vebt_assn_raw) TreeList) Tree_is)))) (@ (@ tptp.times_times_assn (@ _let_3 _let_2)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) H2) Xaa)) _let_1)))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_3 tptp.one_one_rat)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_3 tptp.one_one_assn)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_assn (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_3 tptp.one_one_real)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_3 tptp.one_one_Code_integer)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_3 tptp.one_one_complex)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_complex (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_3 tptp.one_one_nat)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_3 tptp.one_one_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_int (@ _let_2 (@ _let_1 N))) (@ G N)))))))))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (= (= (@ (@ tptp.set_or66887138388493659n_real A) B) (@ (@ tptp.set_or66887138388493659n_real C) D2)) (and (= A C) (= B D2)))))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (= (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) (@ (@ tptp.set_or4029947393144176647an_rat C) D2)) (and (= A C) (= B D2)))))))
% 9.16/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_num C) D2) (= (= (@ (@ tptp.set_or1222409239386451017an_num A) B) (@ (@ tptp.set_or1222409239386451017an_num C) D2)) (and (= A C) (= B D2)))))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (= (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) (@ (@ tptp.set_or4665077453230672383an_nat C) D2)) (and (= A C) (= B D2)))))))
% 9.16/7.11 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (= (= (@ (@ tptp.set_or8404916559141939852nteger A) B) (@ (@ tptp.set_or8404916559141939852nteger C) D2)) (and (= A C) (= B D2)))))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (= (= (@ (@ tptp.set_or4662586982721622107an_int A) B) (@ (@ tptp.set_or4662586982721622107an_int C) D2)) (and (= A C) (= B D2)))))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.set_or66887138388493659n_real A) B) (@ (@ tptp.set_or66887138388493659n_real C) D2)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (= A C))))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) (@ (@ tptp.set_or4029947393144176647an_rat C) D2)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (= A C))))))
% 9.16/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (= (@ (@ tptp.set_or1222409239386451017an_num A) B) (@ (@ tptp.set_or1222409239386451017an_num C) D2)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_num C) D2) (= A C))))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) (@ (@ tptp.set_or4665077453230672383an_nat C) D2)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (= A C))))))
% 9.16/7.11 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.set_or8404916559141939852nteger A) B) (@ (@ tptp.set_or8404916559141939852nteger C) D2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (= A C))))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.set_or4662586982721622107an_int A) B) (@ (@ tptp.set_or4662586982721622107an_int C) D2)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (= A C))))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (=> (= (@ (@ tptp.set_or66887138388493659n_real A) B) (@ (@ tptp.set_or66887138388493659n_real C) D2)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D2) (= B D2))))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) (@ (@ tptp.set_or4029947393144176647an_rat C) D2)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (= B D2))))))
% 9.16/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (= (@ (@ tptp.set_or1222409239386451017an_num A) B) (@ (@ tptp.set_or1222409239386451017an_num C) D2)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_num C) D2) (= B D2))))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) (@ (@ tptp.set_or4665077453230672383an_nat C) D2)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (= B D2))))))
% 9.16/7.11 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.set_or8404916559141939852nteger A) B) (@ (@ tptp.set_or8404916559141939852nteger C) D2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (= B D2))))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.set_or4662586982721622107an_int A) B) (@ (@ tptp.set_or4662586982721622107an_int C) D2)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (= B D2))))))
% 9.16/7.11 (assert (not (= tptp.pi tptp.zero_zero_real)))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (A2 (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (Xsi tptp.list_VEBT_VEBTi)) (=> (= N (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) A2) Xs2) Xsi) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi A2) Xs2) Xsi)))))
% 9.16/7.11 (assert (= tptp.vEBT_L6296928887356842470_VEBTi (lambda ((A6 (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (Xs tptp.list_VEBT_VEBT) (__flatten_var_0 tptp.list_VEBT_VEBTi)) (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs))) A6) Xs) __flatten_var_0))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or66887138388493659n_real A) B))))))
% 9.16/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or4029947393144176647an_rat A) B))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N) (@ P M4))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N) (@ P M4))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X2))))))
% 9.16/7.11 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 9.16/7.11 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 9.16/7.11 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 9.16/7.11 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 9.16/7.11 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (A2 (-> tptp.vEBT_VEBT tptp.vEBT_VEBTi tptp.assn)) (Xsi tptp.list_VEBT_VEBTi) (F2 tptp.assn)) (=> (= N (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.times_times_assn (@ (@ (@ (@ tptp.vEBT_L1528199826722428489_VEBTi (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) A2) Xs2) Xsi)) F2) (@ (@ tptp.times_times_assn (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi A2) Xs2) Xsi)) F2)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ G (@ tptp.suc I2)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I2) K)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 9.16/7.11 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I2) K)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N)))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (=> (@ (@ tptp.ord_less_nat X3) D2) (= (@ G X3) (@ H2 X3))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.groups708209901874060359at_nat H2) (@ (@ tptp.set_or4665077453230672383an_nat C) D2))))))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (=> (@ (@ tptp.ord_less_nat X3) D2) (= (@ G X3) (@ H2 X3))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.groups705719431365010083at_int H2) (@ (@ tptp.set_or4665077453230672383an_nat C) D2))))))))
% 9.16/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int) (G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int))) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) X3) (=> (@ (@ tptp.ord_less_int X3) D2) (= (@ G X3) (@ H2 X3))))) (= (@ (@ tptp.groups1705073143266064639nt_int G) (@ (@ tptp.set_or4662586982721622107an_int A) B)) (@ (@ tptp.groups1705073143266064639nt_int H2) (@ (@ tptp.set_or4662586982721622107an_int C) D2))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (P4 tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P4) (= (@ (@ tptp.times_times_assn (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P4))) (@ _let_2 (@ _let_1 P4)))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (P4 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P4) (= (@ (@ tptp.times_times_real (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P4))) (@ _let_2 (@ _let_1 P4)))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (P4 tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P4) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P4))) (@ _let_2 (@ _let_1 P4)))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (P4 tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P4) (= (@ (@ tptp.times_times_complex (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P4))) (@ _let_2 (@ _let_1 P4)))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (P4 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P4) (= (@ (@ tptp.times_times_nat (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P4))) (@ _let_2 (@ _let_1 P4)))))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (P4 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) P4) (= (@ (@ tptp.times_times_int (@ _let_2 (@ _let_1 N))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N) P4))) (@ _let_2 (@ _let_1 P4)))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat N) (@ _let_1 N))))))
% 9.16/7.11 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N4))))
% 9.16/7.11 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 9.16/7.11 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 9.16/7.11 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 9.16/7.11 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 9.16/7.11 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 9.16/7.11 (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))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 9.16/7.11 (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))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))))))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))))
% 9.16/7.11 (assert (= (@ tptp.sin_real tptp.pi) tptp.zero_zero_real))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 9.16/7.11 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 9.16/7.11 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 9.16/7.11 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 9.16/7.11 (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)))
% 9.16/7.11 (assert (forall ((U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) U))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 9.16/7.11 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 9.16/7.11 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or8404916559141939852nteger L) (@ (@ tptp.plus_p5714425477246183910nteger U) tptp.one_one_Code_integer)) (@ (@ tptp.set_or189985376899183464nteger L) U))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 9.16/7.11 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (= tptp.unique5052692396658037445od_int (lambda ((M4 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N3))) (let ((_let_2 (@ tptp.numeral_numeral_int M4))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I2 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M4 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N3))) (let ((_let_2 (@ tptp.numeral_numeral_nat M4))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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)))))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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)))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I2) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 9.16/7.11 (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))))))))))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 9.16/7.11 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I3)) tptp.one_one_real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ F I2)) (@ (@ tptp.power_power_real Z) I2))))))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (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)))))))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 9.16/7.11 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 9.16/7.11 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)))
% 9.16/7.11 (assert (forall ((N tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.one_one_real)))
% 9.16/7.11 (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))
% 9.16/7.11 (assert (forall ((N tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int) (Q7 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 Q7) R4)) (= R2 R4))))))
% 9.16/7.11 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int) (Q7 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 Q7) R4)) (= Q3 Q7))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (not (= (@ tptp.cos_real (@ tptp.arctan X)) tptp.zero_zero_real))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 9.16/7.11 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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)))))))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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 ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.pi) (= X (@ tptp.cos_real T6)) (= Y (@ tptp.sin_real T6)))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I2)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 9.16/7.11 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A12 K3) (= A23 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L2 tptp.int) (K3 tptp.int) (Q6 tptp.int)) (and (= A12 K3) (= A23 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q6) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q6) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K3 tptp.int) (Q6 tptp.int)) (and (= A12 K3) (= A23 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q6) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q6) L2)) R5))))))))
% 9.16/7.11 (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 ((Q5 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q5) A22)))))) (not (forall ((R3 tptp.int) (Q5 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q5) 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 Q5) A22)) R3)))))))))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 9.16/7.11 (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))))))))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (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 ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T6)) (= Y (@ tptp.sin_real T6)))))))))))
% 9.16/7.11 (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 ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T6)) (= Y (@ tptp.sin_real T6))))))))
% 9.16/7.11 (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 ((T6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (=> (@ (@ tptp.ord_less_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T6)) (not (= Y (@ tptp.sin_real T6))))))))))))
% 9.16/7.11 (assert (forall ((Xa3 tptp.array_VEBT_VEBTi) (X tptp.list_VEBT_VEBTi)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat tptp.na) _let_2))) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Xa3) X)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) (@ (@ tptp.replicate_VEBT_VEBT (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_nat _let_2) _let_3))) (@ tptp.vEBT_vebt_buildup (@ tptp.suc _let_3)))) X))) (@ tptp.vEBT_V739175172307565963ildupi (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc tptp.na))) _let_2)))) (lambda ((R5 tptp.vEBT_VEBTi)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat tptp.na) _let_2))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Xa3) X)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) (@ (@ tptp.replicate_VEBT_VEBT (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_nat _let_2) _let_3))) (@ tptp.vEBT_vebt_buildup (@ tptp.suc _let_3)))) X))) (@ (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc tptp.na))) _let_2)))) R5))))))))))))
% 9.16/7.11 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M4 tptp.int)) (exists ((N3 tptp.int)) (and (@ (@ tptp.ord_less_int M4) (@ tptp.abs_abs_int N3)) (@ (@ tptp.member_int N3) S3)))))))
% 9.16/7.11 (assert (= (@ tptp.tan_real tptp.pi) tptp.zero_zero_real))
% 9.16/7.11 (assert (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.suc (@ tptp.suc tptp.na)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_2) _let_3)) (=> (= X (@ (@ tptp.divide_divide_nat _let_3) _let_2)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi tptp.one_one_assn) (@ tptp.vEBT_V739175172307565963ildupi _let_1)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup _let_1))))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc tptp.na)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) _let_2)) (=> (= X (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi tptp.one_one_assn) (@ tptp.vEBT_V739175172307565963ildupi X)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup X)))))))))
% 9.16/7.11 (assert (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc tptp.na)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) _let_2) (=> (= X (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ (@ tptp.hoare_1429296392585015714_VEBTi tptp.one_one_assn) (@ tptp.vEBT_V739175172307565963ildupi X)) (@ tptp.vEBT_vebt_assn_raw (@ tptp.vEBT_vebt_buildup X)))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 9.16/7.11 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 9.16/7.11 (assert (= tptp.zero_zero_int tptp.zero_zero_int))
% 9.16/7.11 (assert (= tptp.one_one_int tptp.one_one_int))
% 9.16/7.11 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 9.16/7.11 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 9.16/7.11 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.11 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.11 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))))))
% 9.16/7.11 (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))))))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (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)))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M4 tptp.nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N3) (@ (@ tptp.member_nat N3) S3)))))))
% 9.16/7.11 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M2) (exists ((N9 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N9) (@ (@ tptp.member_nat N9) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K3)) K3))))
% 9.16/7.11 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 9.16/7.11 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 9.16/7.11 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L) L)))
% 9.16/7.11 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L) (@ tptp.uminus1351360451143612070nteger L))))
% 9.16/7.11 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 9.16/7.11 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z3) (@ (@ tptp.ord_less_real Z3) _let_1) (= (@ tptp.tan_real Z3) X)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (H2 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.time_time_VEBT_VEBTi (@ tptp.vEBT_V739175172307565963ildupi N)) H2)) (@ tptp.vEBT_V441764108873111860ildupi N))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat tptp.one_one_assn) (@ (@ tptp.vEBT_VEBT_highi X) N)) (lambda ((R5 tptp.nat)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_VEBT_high X) N)))))))
% 9.16/7.11 (assert (forall ((X tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.hoare_3067605981109127869le_nat tptp.one_one_assn) (@ (@ tptp.vEBT_VEBT_lowi X) N)) (lambda ((R5 tptp.nat)) (@ tptp.pure_assn (= R5 (@ (@ tptp.vEBT_VEBT_low X) N)))))))
% 9.16/7.11 (assert (= tptp.code_integer_of_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 9.16/7.11 (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)))))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.sqrt X) (@ tptp.sqrt Y)) (= X Y))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 9.16/7.11 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.11 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X) Y))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 9.16/7.11 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 9.16/7.11 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((X tptp.real) (Y tptp.real) (Xa3 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 Xa3) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((X tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X)) K))))
% 9.16/7.11 (assert (= tptp.unique3479559517661332726nteger (lambda ((M4 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M4))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))))
% 9.16/7.11 (assert (forall ((Xa3 tptp.nat) (X tptp.int)) (= (@ (@ tptp.bit_se2793503036327961859nteger Xa3) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.bit_se7879613467334960850it_int Xa3) X)))))
% 9.16/7.11 (assert (forall ((Xa3 tptp.int) (X tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa3)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa3) X)))))
% 9.16/7.11 (assert (forall ((Xa3 tptp.int) (X tptp.int)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.code_integer_of_int Xa3)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.modulo_modulo_int Xa3) X)))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (= tptp.zero_z3403309356797280102nteger (@ tptp.code_integer_of_int tptp.zero_zero_int)))
% 9.16/7.11 (assert (forall ((Xa3 tptp.int) (X tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa3)) (@ tptp.code_integer_of_int X)) (@ (@ tptp.ord_less_int Xa3) X))))
% 9.16/7.11 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B) D2)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D2) _let_1))))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N) (= (@ tptp.sqrt (@ _let_3 N)) (@ _let_3 (@ (@ tptp.divide_divide_nat N) _let_2)))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (Y tptp.real) (Xa3 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 Xa3) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (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)))))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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)))))))))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((X tptp.int) (Xa3 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa3)))) (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 Xa3)))))) (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 Xa3) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa3) 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 Xa3) _let_2))))))) (not _let_1)))))))))))))
% 9.16/7.11 (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))))))))))))))))
% 9.16/7.11 (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))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A1)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I3 tptp.int) (J3 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J3)) (=> (=> (@ (@ tptp.ord_less_eq_int I3) J3) (@ (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J3)) (@ (@ P I3) J3)))) (@ (@ P A0) A1)))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (assert (= (@ tptp.arcsin tptp.zero_zero_real) tptp.zero_zero_real))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q6 tptp.nat)) (@ (@ tptp.ord_less_nat Q6) N))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I2) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D2)))) _let_1)))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J3) (=> (@ (@ tptp.ord_less_nat J3) N) (@ (@ tptp.ord_less_eq_nat (@ A I3)) (@ A J3))))) (=> (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J3) (=> (@ (@ tptp.ord_less_nat J3) N) (@ (@ tptp.ord_less_eq_nat (@ B J3)) (@ B I3))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I2)) (@ B I2)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M4)) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real X) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M4)) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 9.16/7.11 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M4)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 9.16/7.11 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 9.16/7.11 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X2 tptp.complex)) X2)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) C)))) tptp.zero_zero_complex))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 9.16/7.11 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B9 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M4)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real H2) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B9) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 9.16/7.11 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)) (@ F I2)) (@ G I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)) tptp.one_one_nat)))) _let_1))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M4)) (@ tptp.semiri2265585572941072030t_real M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 9.16/7.11 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N) (@ (@ tptp.plus_plus_int N) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (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 ((M4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M4)) (@ tptp.semiri2265585572941072030t_real M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M4)) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M4)) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M4)) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M4)) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M4)) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T6) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 9.16/7.11 (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)))))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 9.16/7.11 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 9.16/7.11 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 9.16/7.11 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 9.16/7.11 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K3)) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N))) N))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J2)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J2)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R2) K3))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R2))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N)) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) tptp.zero_zero_nat))) (=> (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J3) (= (@ B J3) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I2)) (@ (@ tptp.power_power_nat X) I2)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J2 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J2)) (@ (@ tptp.power_power_nat X) J2)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat I2) (@ (@ tptp.binomial N) I2)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 9.16/7.11 (assert (forall ((Theta tptp.real)) (not (forall ((K2 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 9.16/7.11 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N3 tptp.nat)) N3)))
% 9.16/7.11 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M4)) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X)) N)))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))))
% 9.16/7.11 (assert (= tptp.divide_divide_real (lambda ((X2 tptp.real) (Y6 tptp.real)) (@ (@ tptp.times_times_real X2) (@ tptp.inverse_inverse_real Y6)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N2 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 9.16/7.11 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (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))))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 9.16/7.11 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (=> (@ (@ tptp.ord_less_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T6)) (@ tptp.sin_real T6)))))))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (= (@ tptp.sinh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (not (= (@ tptp.cosh_real X) tptp.zero_zero_real))))
% 9.16/7.11 (assert (= tptp.real_V4546457046886955230omplex (lambda ((R5 tptp.real)) (@ (@ tptp.complex2 R5) tptp.zero_zero_real))))
% 9.16/7.11 (assert (= tptp.real_V4546457046886955230omplex (lambda ((X2 tptp.real)) (@ (@ tptp.complex2 X2) tptp.zero_zero_real))))
% 9.16/7.11 (assert (forall ((X tptp.real) (Y tptp.real) (Xa3 tptp.real)) (= (= (@ (@ tptp.complex2 X) Y) (@ tptp.real_V4546457046886955230omplex Xa3)) (and (= X Xa3) (= Y tptp.zero_zero_real)))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.zero_zero_complex) (and (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 9.16/7.11 (assert (= tptp.zero_zero_complex (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.zero_zero_real)))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D2)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C)) (@ _let_1 D2))) (@ (@ tptp.plus_plus_real (@ _let_2 D2)) (@ _let_1 C))))))))
% 9.16/7.11 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (= (@ tptp.cot_real tptp.pi) tptp.zero_zero_real))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 9.16/7.11 (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))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))
% 9.16/7.11 (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))
% 9.16/7.11 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.array_VEBT_VEBTi) (X14 tptp.vEBT_VEBTi)) (= (@ tptp.size_size_VEBT_VEBTi (@ (@ (@ (@ tptp.vEBT_Nodei X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_a6397454172108246045_VEBTi tptp.size_size_VEBT_VEBTi) X13)) (@ tptp.size_size_VEBT_VEBTi X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))))
% 9.16/7.11 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 9.16/7.11 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 9.16/7.11 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 9.16/7.11 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 9.16/7.11 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 9.16/7.11 (assert (not (= tptp.imaginary_unit tptp.one_one_complex)))
% 9.16/7.11 (assert (not (= tptp.imaginary_unit tptp.zero_zero_complex)))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 9.16/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 9.16/7.11 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 9.16/7.11 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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)))
% 9.16/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 9.16/7.11 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.array_VEBT_VEBTi) (X14 tptp.vEBT_VEBTi)) (= (@ tptp.vEBT_size_VEBTi (@ (@ (@ (@ tptp.vEBT_Nodei X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_a6397454172108246045_VEBTi tptp.vEBT_size_VEBTi) X13)) (@ tptp.vEBT_size_VEBTi X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))))
% 9.16/7.11 (assert (= (@ tptp.csqrt tptp.zero_zero_complex) tptp.zero_zero_complex))
% 9.16/7.11 (assert (= (@ tptp.csqrt tptp.one_one_complex) tptp.one_one_complex))
% 9.16/7.11 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 9.16/7.11 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 9.16/7.11 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 9.16/7.11 (assert (= (@ tptp.arg tptp.zero_zero_complex) tptp.zero_zero_real))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))
% 9.16/7.11 (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)))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 9.16/7.11 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 9.16/7.11 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 9.16/7.11 (assert (= (@ tptp.cis tptp.pi) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 9.16/7.11 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 9.16/7.11 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 9.16/7.11 (assert (forall ((A tptp.real)) (not (= (@ tptp.cis A) tptp.zero_zero_complex))))
% 9.16/7.11 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 9.16/7.11 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 9.16/7.11 (assert (forall ((Z tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ tptp.cis (@ tptp.arg Z)) (@ tptp.sgn_sgn_complex Z)))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 9.16/7.11 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 9.16/7.11 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) tptp.one_one_complex)))))))
% 9.16/7.11 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q6 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q6))) (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))))
% 9.16/7.11 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q6 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q6))) (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))))
% 9.16/7.11 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q6 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q6))) (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))))
% 9.16/7.11 (assert (= tptp.divmod_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M4) N3))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M4)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q6 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q6)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M4) N3)) N3))))))
% 9.16/7.11 (assert (= tptp.arg (lambda ((Z6 tptp.complex)) (@ (@ (@ tptp.if_real (= Z6 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A3 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z6) (@ tptp.cis A3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A3) (@ (@ tptp.ord_less_eq_real A3) tptp.pi))))))))
% 9.16/7.11 (assert (= tptp.arctan (lambda ((Y6 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.tan_real X2) Y6))))))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (assert (= tptp.arccos (lambda ((Y6 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.cos_real X2) Y6)))))))
% 9.16/7.11 (assert (= tptp.divmod_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M4) N3)) (@ (@ tptp.modulo_modulo_nat M4) N3)))))
% 9.16/7.11 (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))))))
% 9.16/7.11 (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)))))))
% 9.16/7.11 (assert (= tptp.arcsin (lambda ((Y6 tptp.real)) (@ tptp.the_real (lambda ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.sin_real X2) Y6))))))))
% 9.16/7.11 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) C))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y))))))
% 9.16/7.11 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 9.16/7.11 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) tptp.one_one_real) tptp.one_one_real))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X)) (@ _let_2 (@ _let_1 X)))))))
% 9.16/7.11 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X) (@ (@ tptp.root M) (@ (@ tptp.root N) X)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ _let_1 Y))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ _let_1 X))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 Y))))))
% 9.16/7.11 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X)) (@ tptp.sgn_sgn_real X)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N4) X)) (@ (@ tptp.root N) X)))))))
% 9.16/7.11 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y) N))) (@ tptp.abs_abs_real Y)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N4) X))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N4) X)) (@ (@ tptp.root N) X)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y) N) X) (= (@ (@ tptp.root N) X) Y)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N) X) (= (@ (@ tptp.root N) X) Y))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N4) X))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N))) Y))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X)))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X)))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 9.16/7.11 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N) X)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y6 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)) X) (@ P Y6))))))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 9.16/7.11 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N3))))))))
% 9.16/7.11 (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))))
% 9.16/7.11 (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))))
% 9.16/7.11 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))))
% 9.16/7.12 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N))))
% 9.16/7.12 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N)))))
% 9.16/7.12 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N)))))
% 9.16/7.12 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (W tptp.num)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (W tptp.num)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 9.16/7.12 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 9.16/7.12 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))))
% 9.16/7.12 (assert (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L) N)))))
% 9.16/7.12 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 9.16/7.12 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 9.16/7.12 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)))
% 9.16/7.12 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 9.16/7.12 (assert (forall ((K tptp.int)) (not (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (= (@ _let_1 M3) (@ _let_1 N2))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (not (@ _let_1 N2)))))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 9.16/7.12 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N3))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 9.16/7.12 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K3))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K3) _let_1))))))))
% 9.16/7.12 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N3)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))))))
% 9.16/7.12 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N3))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 9.16/7.12 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 9.16/7.12 (assert (= tptp.bit_ri7632146776885996613nteger (lambda ((I2 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger I2)) tptp.one_one_Code_integer))))
% 9.16/7.12 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 9.16/7.12 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L2))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L2)))))
% 9.16/7.12 (assert (forall ((I tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int I) tptp.zero_zero_int) I)))
% 9.16/7.12 (assert (forall ((J tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.zero_zero_int) J) J)))
% 9.16/7.12 (assert (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L) N))))))
% 9.16/7.12 (assert (forall ((K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L) N)))))
% 9.16/7.12 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 9.16/7.12 (assert (forall ((J tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.zero_zero_int) J) J)))
% 9.16/7.12 (assert (forall ((I tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int I) tptp.zero_zero_int) I)))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L2))))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 9.16/7.12 (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)))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 9.16/7.12 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M4 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 M4) (@ (@ tptp.power_power_nat _let_1) N3))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 9.16/7.12 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y)) _let_1)))))))
% 9.16/7.12 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) _let_1)))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int) N))))
% 9.16/7.12 (assert (forall ((I tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int I) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.12 (assert (forall ((J tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) J) tptp.zero_zero_int)))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 9.16/7.12 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M4 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 M4)) (not (@ _let_2 N3))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M4) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 9.16/7.12 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K3)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 9.16/7.12 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 9.16/7.12 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M4 tptp.zero_zero_nat)) N3) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) M4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M4) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M4) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1))))))))))
% 9.16/7.12 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 9.16/7.12 (assert (forall ((Xa3 tptp.int) (X Bool)) (= (@ (@ tptp.bits_Bit_integer (@ tptp.code_integer_of_int Xa3)) X) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int X)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Xa3))))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 9.16/7.12 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 9.16/7.12 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 9.16/7.12 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 9.16/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 9.16/7.12 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 9.16/7.12 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 9.16/7.12 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 9.16/7.12 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 9.16/7.12 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 9.16/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 9.16/7.12 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 9.16/7.12 (assert (forall ((X tptp.num) (Xa3 tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa3 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa3) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M2 tptp.num)) (=> (= Xa3 (@ tptp.bit0 M2)) (not (= Y (@ tptp.bit1 M2)))))) (=> (=> _let_3 (forall ((M2 tptp.num)) (let ((_let_1 (@ tptp.bit1 M2))) (=> (= Xa3 _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N2 tptp.num)) (= X (@ tptp.bit0 N2))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit0 N2)) (forall ((M2 tptp.num)) (=> (= Xa3 (@ tptp.bit0 M2)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M2)))))))) (=> (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit0 N2)) (forall ((M2 tptp.num)) (=> (= Xa3 (@ tptp.bit1 M2)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M2)))))))) (=> (=> (exists ((N2 tptp.num)) (= X (@ tptp.bit1 N2))) _let_2) (=> (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit1 N2)) (forall ((M2 tptp.num)) (=> (= Xa3 (@ tptp.bit0 M2)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M2)))))))) (not (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit1 N2)) (forall ((M2 tptp.num)) (=> (= Xa3 (@ tptp.bit1 M2)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M2)))))))))))))))))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N))))))
% 9.16/7.12 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M4 tptp.zero_zero_nat)) N3) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) M4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M4) _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 M4) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1))))))))))
% 9.16/7.12 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M4 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 M4)) (not (@ _let_2 N3)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M4) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 9.16/7.12 (assert (not (@ tptp.least_4859182151741483524sb_int tptp.zero_zero_int)))
% 9.16/7.12 (assert (@ tptp.least_4859182151741483524sb_int tptp.one_one_int))
% 9.16/7.12 (assert (forall ((W tptp.num)) (not (@ tptp.least_4859182151741483524sb_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))))))
% 9.16/7.12 (assert (@ tptp.least_4859182151741483524sb_int (@ tptp.numeral_numeral_int tptp.one)))
% 9.16/7.12 (assert (forall ((W tptp.num)) (@ tptp.least_4859182151741483524sb_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))))
% 9.16/7.12 (assert (@ tptp.least_4859182151741483524sb_int (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 9.16/7.12 (assert (forall ((W tptp.num)) (not (@ tptp.least_4859182151741483524sb_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))))))
% 9.16/7.12 (assert (@ tptp.least_4859182151741483524sb_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))))
% 9.16/7.12 (assert (forall ((W tptp.num)) (@ tptp.least_4859182151741483524sb_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))))))
% 9.16/7.12 (assert (= tptp.least_7544222001954398261nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.bit_se9216721137139052372nteger X2) tptp.zero_zero_nat))))
% 9.16/7.12 (assert (= tptp.least_4859182151741483524sb_int (lambda ((I2 tptp.int)) (@ (@ tptp.bit_se1146084159140164899it_int I2) tptp.zero_zero_nat))))
% 9.16/7.12 (assert (= (lambda ((A3 tptp.int)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A3))) tptp.least_4859182151741483524sb_int))
% 9.16/7.12 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 9.16/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_V5144397997797733112_d_rel))) (let ((_let_3 (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (=> (= (@ tptp.vEBT_V8646137997579335489_i_l_d X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_2))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.vEBT_V8646137997579335489_i_l_d _let_4))) (let ((_let_6 (@ tptp.suc _let_4))) (let ((_let_7 (@ tptp.power_power_nat _let_3))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_3) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_2)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_7 _let_4)) _let_5))))) (=> (not _let_8) (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ tptp.vEBT_V8646137997579335489_i_l_d _let_6))) (@ (@ tptp.times_times_nat (@ _let_7 _let_6)) _let_5))))) (not (@ (@ tptp.accp_nat tptp.vEBT_V5144397997797733112_d_rel) _let_1)))))))))))))))))))))))
% 9.16/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_V1247956027447740395_p_rel))) (let ((_let_3 (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))) (=> (= (@ tptp.vEBT_V8346862874174094_d_u_p X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_2))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.vEBT_V8346862874174094_d_u_p _let_4))) (let ((_let_6 (@ (@ tptp.plus_plus_nat _let_5) tptp.one_one_nat))) (let ((_let_7 (@ tptp.suc _let_4))) (let ((_let_8 (@ tptp.power_power_nat _let_3))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_3) _let_1))) (=> (= X _let_1) (=> (and (=> _let_9 (= Y (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_2)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_8 _let_4)) _let_6))))) (=> (not _let_9) (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 _let_2)))) (@ tptp.vEBT_V8346862874174094_d_u_p _let_7))) (@ (@ tptp.times_times_nat (@ _let_8 _let_7)) _let_6))))) (not (@ (@ tptp.accp_nat tptp.vEBT_V1247956027447740395_p_rel) _let_1))))))))))))))))))))))))
% 9.16/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_V2957053500504383685pi_rel))) (let ((_let_3 (= Y _let_1))) (=> (= (@ tptp.vEBT_V441764108873111860ildupi 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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N2)))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_2))) (let ((_let_4 (@ (@ tptp.divide_divide_nat N2) _let_3))) (let ((_let_5 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (@ tptp.suc _let_4))) (let ((_let_7 (@ tptp.vEBT_V441764108873111860ildupi _let_6))) (let ((_let_8 (@ (@ tptp.times_times_nat _let_7) _let_5))) (let ((_let_9 (@ tptp.bit0 _let_2))) (let ((_let_10 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_9)))) (let ((_let_11 (@ (@ tptp.dvd_dvd_nat _let_3) N2))) (=> (= X _let_1) (=> (and (=> _let_11 (= Y (@ tptp.suc (@ tptp.suc (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_7) (@ (@ tptp.plus_plus_nat (@ _let_10 _let_5)) (@ (@ tptp.times_times_nat _let_3) _let_8)))))))) (=> (not _let_11) (= Y (@ tptp.suc (@ tptp.suc (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.vEBT_V441764108873111860ildupi (@ tptp.suc _let_6))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_9))) _let_5)) (@ _let_10 _let_8))))))))) (not (@ (@ tptp.accp_nat tptp.vEBT_V2957053500504383685pi_rel) _let_1))))))))))))))))))))))))))
% 9.16/7.12 (assert (= (@ tptp.code_dup tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 9.16/7.12 (assert (= (@ tptp.code_dup tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 9.16/7.12 (assert (forall ((Mmo tptp.option4927543243414619207at_nat) (Deg tptp.nat) (Tree_list tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Mmoi tptp.option4927543243414619207at_nat) (Degi tptp.nat) (Tree_array tptp.array_VEBT_VEBTi) (Summaryi tptp.vEBT_VEBTi)) (= (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ (@ tptp.vEBT_Node Mmo) Deg) Tree_list) Summary)) (@ (@ (@ (@ tptp.vEBT_Nodei Mmoi) Degi) Tree_array) Summaryi)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ tptp.pure_assn (and (= Mmoi Mmo) (= Degi Deg)))) (@ (@ tptp.vEBT_vebt_assn_raw Summary) Summaryi))) (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((Tree_is2 tptp.list_VEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Tree_array) Tree_is2)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) Tree_list) Tree_is2))))))))
% 9.16/7.12 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))))
% 9.16/7.12 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) X) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) _let_1)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 tptp.one)))) (@ tptp.vEBT_VEBT_space Summary2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space) TreeList2)) tptp.zero_zero_nat))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) _let_1))))))))))))
% 9.16/7.12 (assert (= (@ (@ tptp.times_times_assn tptp.top_top_assn) tptp.top_top_assn) tptp.top_top_assn))
% 9.16/7.12 (assert (not (= tptp.top_top_assn tptp.one_one_assn)))
% 9.16/7.12 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails P) tptp.top_top_assn)))
% 9.16/7.12 (assert (forall ((P tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn tptp.top_top_assn))) (let ((_let_2 (@ _let_1 P))) (= (@ _let_1 _let_2) _let_2)))))
% 9.16/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 Q) (@ _let_1 (@ (@ tptp.times_times_assn Q) tptp.top_top_assn))))))
% 9.16/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ (@ tptp.times_times_assn Q) tptp.top_top_assn))) (=> (@ (@ tptp.entails P) _let_1) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) R)) _let_1)))))
% 9.16/7.12 (assert (forall ((A2 tptp.assn)) (@ (@ tptp.entails A2) (@ (@ tptp.times_times_assn A2) tptp.top_top_assn))))
% 9.16/7.12 (assert (forall ((A2 tptp.assn) (A7 tptp.assn) (B3 tptp.assn) (B10 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A7))) (=> (@ (@ tptp.entails A2) (@ _let_1 tptp.top_top_assn)) (=> (@ (@ tptp.entails B3) (@ (@ tptp.times_times_assn B10) tptp.top_top_assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn A2) B3)) tptp.top_top_assn)) (@ (@ tptp.times_times_assn (@ _let_1 B10)) tptp.top_top_assn)))))))
% 9.16/7.12 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H2) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H2))))
% 9.16/7.12 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H2) (not (forall ((H5 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P) H5)))))))
% 9.16/7.12 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.top_top_assn) (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space2 X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) X) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Y (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) _let_1)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_space2 Summary2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2) TreeList2)) tptp.zero_zero_nat))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) _let_1))))))))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.real)) (=> (= (@ tptp.vEBT_VEBT_cnt X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel2) X) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Y tptp.one_one_real) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel2) _let_1)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.vEBT_VEBT_cnt Summary2))) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) TreeList2)) tptp.zero_zero_real))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel2) _let_1))))))))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_cnt2 X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) X) (=> (forall ((A5 Bool) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) _let_1)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_cnt2 Summary2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_cnt2) TreeList2)) tptp.zero_zero_nat))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) _let_1))))))))))))
% 9.16/7.12 (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) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (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 ((Mi 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 Mi) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 9.16/7.12 (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) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= X _let_1) (=> (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B2 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B2) (= 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 ((Mi 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 Mi) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Mi)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 9.16/7.12 (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) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (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 ((Mi 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 Mi) 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)))))))))))))
% 9.16/7.12 (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) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (let ((_let_2 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X _let_1) (=> (= Y (@ _let_2 (@ (@ (@ tptp.if_nat B2) tptp.one_one_nat) (@ _let_2 tptp.one_one_nat)))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T_m_a_x_t_rel) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= 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 ((Mi 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 Mi) 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)))))))))))))
% 9.16/7.12 (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) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc))) (=> (= X _let_1) (=> (= Y tptp.one_one_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_T5462971552011256508_l_rel) _let_1)))))))))))))))))
% 9.16/7.12 (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) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 9.16/7.12 (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)))))))))))))
% 9.16/7.12 (assert (= tptp.bits_b8758750999018896077nteger (lambda ((I2 tptp.code_integer)) (not (= (@ (@ tptp.modulo364778990260209775nteger I2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.12 (assert (forall ((X tptp.int)) (= (@ tptp.bits_b2549910563261871055nteger (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int X) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 9.16/7.12 (assert (forall ((I tptp.code_integer)) (= (@ tptp.zero_n356916108424825756nteger (@ tptp.bits_b8758750999018896077nteger I)) (@ (@ tptp.bit_se3949692690581998587nteger I) tptp.one_one_Code_integer))))
% 9.16/7.12 (assert (= tptp.bits_b8758750999018896077nteger (lambda ((I2 tptp.code_integer)) (not (= (@ (@ tptp.bit_se3949692690581998587nteger I2) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))))
% 9.16/7.12 (assert (= tptp.bit_se3949692690581998587nteger (lambda ((X2 tptp.code_integer) (Y6 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X2 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= X2 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) Y6) (@ (@ tptp.bits_Bit_integer (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.bits_b2549910563261871055nteger X2)) (@ tptp.bits_b2549910563261871055nteger Y6))) (and (@ tptp.bits_b8758750999018896077nteger X2) (@ tptp.bits_b8758750999018896077nteger Y6))))))))
% 9.16/7.12 (assert (= tptp.bit_se1080825931792720795nteger (lambda ((X2 tptp.code_integer) (Y6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (@ (@ (@ tptp.if_Code_integer (= X2 tptp.zero_z3403309356797280102nteger)) Y6) (@ (@ (@ tptp.if_Code_integer (= X2 _let_1)) _let_1) (@ (@ tptp.bits_Bit_integer (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.bits_b2549910563261871055nteger X2)) (@ tptp.bits_b2549910563261871055nteger Y6))) (or (@ tptp.bits_b8758750999018896077nteger X2) (@ tptp.bits_b8758750999018896077nteger Y6)))))))))
% 9.16/7.12 (assert (= tptp.bit_se3222712562003087583nteger (lambda ((X2 tptp.code_integer) (Y6 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X2 tptp.zero_z3403309356797280102nteger)) Y6) (@ (@ (@ tptp.if_Code_integer (= X2 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (@ tptp.bit_ri7632146776885996613nteger Y6)) (@ (@ tptp.bits_Bit_integer (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.bits_b2549910563261871055nteger X2)) (@ tptp.bits_b2549910563261871055nteger Y6))) (= (not (@ tptp.bits_b8758750999018896077nteger X2)) (@ tptp.bits_b8758750999018896077nteger Y6))))))))
% 9.16/7.12 (assert (= tptp.bits_b2549910563261871055nteger (lambda ((I2 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger I2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 9.16/7.12 (assert (forall ((X tptp.int)) (= (@ tptp.bits_b8758750999018896077nteger (@ tptp.code_integer_of_int X)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) X)))))
% 9.16/7.12 (assert (= tptp.upto_aux (lambda ((I2 tptp.int) (J2 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J2) I2)) Js) (@ (@ (@ tptp.upto_aux I2) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int)) (@ (@ tptp.cons_int J2) Js))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K) _let_1)) L)))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))))
% 9.16/7.12 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L)) (@ _let_1 L)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 9.16/7.12 (assert (forall ((I tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int tptp.zero_zero_nat) I) I)))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L)) R2)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) B)) (@ _let_1 B)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int) (R2 tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ tptp.bit_concat_bit N))) (= (= (@ (@ _let_2 K) L) (@ (@ _let_2 R2) S)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L S)))))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L)) N) (or (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N) M)))))))
% 9.16/7.12 (assert (= tptp.bit_se3928097537394005634nteger (lambda ((N3 tptp.nat) (X2 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger X2) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N3)))))
% 9.16/7.12 (assert (forall ((I tptp.int)) (= (@ (@ tptp.divide_divide_int I) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se8568078237143864401it_int tptp.one_one_nat) I))))
% 9.16/7.12 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 9.16/7.12 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N3) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N3)))))))
% 9.16/7.12 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N3 tptp.nat) (M4 tptp.nat)) (@ (@ tptp.divide_divide_nat M4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L) (@ (@ tptp.bit_se545348938243370406it_int N) L))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M)) K)))))
% 9.16/7.12 (assert (forall ((I tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int tptp.zero_zero_nat) I) I)))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 9.16/7.12 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M4) tptp.one_one_nat)))))
% 9.16/7.12 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M4) tptp.one_one_nat)))))
% 9.16/7.12 (assert (forall ((I tptp.code_integer)) (= (@ (@ tptp.bits_Bit_integer I) false) (@ (@ tptp.bit_se7788150548672797655nteger tptp.one_one_nat) I))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M))))))
% 9.16/7.12 (assert (= tptp.bit_concat_bit (lambda ((N3 tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N3) K3)) (@ (@ tptp.bit_se545348938243370406it_int N3) L2)))))
% 9.16/7.12 (assert (= tptp.bit_concat_bit (lambda ((N3 tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N3) K3)) (@ (@ tptp.bit_se545348938243370406it_int N3) L2)))))
% 9.16/7.12 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q3)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q3) (@ (@ tptp.minus_minus_nat N) M))))))
% 9.16/7.12 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 9.16/7.12 (assert (= tptp.bit_se7788150548672797655nteger (lambda ((N3 tptp.nat) (X2 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger X2) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N3)))))
% 9.16/7.12 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int))))))
% 9.16/7.12 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 9.16/7.12 (assert (forall ((I tptp.code_integer)) (= (@ (@ tptp.bits_Bit_integer I) true) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.bit_se7788150548672797655nteger tptp.one_one_nat) I)) tptp.one_one_Code_integer))))
% 9.16/7.12 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N3 tptp.nat) (M4 tptp.nat)) (@ (@ tptp.times_times_nat M4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 9.16/7.12 (assert (= tptp.generi2397576812484419408nteger (lambda ((X2 tptp.code_integer) (I2 tptp.nat) (B4 Bool)) (let ((_let_1 (@ (@ tptp.bit_se7788150548672797655nteger I2) tptp.one_one_Code_integer))) (@ (@ (@ tptp.if_Code_integer B4) (@ (@ tptp.bit_se1080825931792720795nteger X2) _let_1)) (@ (@ tptp.bit_se3949692690581998587nteger X2) (@ tptp.bit_ri7632146776885996613nteger _let_1)))))))
% 9.16/7.12 (assert (= tptp.uint322 (lambda ((I2 tptp.code_integer)) (let ((_let_1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))) (let ((_let_2 (@ (@ tptp.bit_se3949692690581998587nteger I2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_1))))))))))))))))))))))))))))))) (@ (@ (@ tptp.if_uint32 (@ (@ tptp.bit_se9216721137139052372nteger _let_2) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.uint32_signed (@ (@ tptp.minus_8373710615458151222nteger _let_2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))))))))))))))))))))))))))) (@ tptp.uint32_signed _let_2)))))))
% 9.16/7.12 (assert (= tptp.uint32_signed (lambda ((I2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))))))))))))))))))))))))) (@ (@ (@ tptp.if_uint32 (or (@ (@ tptp.ord_le6747313008572928689nteger I2) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) I2))) (@ (@ tptp.undefi2040150642751712519uint32 tptp.uint322) I2)) (@ tptp.uint322 I2))))))
% 9.16/7.12 (assert (= tptp.generi8991105624351003935it_int (lambda ((I2 tptp.int) (N3 tptp.nat) (B4 Bool)) (@ (@ (@ (@ (@ tptp.if_nat_int_int B4) tptp.bit_se7879613467334960850it_int) tptp.bit_se4203085406695923979it_int) N3) I2))))
% 9.16/7.12 (assert (forall ((I tptp.int) (N tptp.nat)) (= (@ (@ (@ tptp.generi8991105624351003935it_int I) N) true) (@ (@ tptp.bit_se1409905431419307370or_int I) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))))
% 9.16/7.12 (assert (forall ((I tptp.int) (N tptp.nat)) (= (@ (@ (@ tptp.generi8991105624351003935it_int I) N) false) (@ (@ tptp.bit_se725231765392027082nd_int I) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int))))))
% 9.16/7.12 (assert (= tptp.generi8991105624351003935it_int (lambda ((I2 tptp.int) (N3 tptp.nat) (B4 Bool)) (let ((_let_1 (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int))) (@ (@ (@ tptp.if_int B4) (@ (@ tptp.bit_se1409905431419307370or_int I2) _let_1)) (@ (@ tptp.bit_se725231765392027082nd_int I2) (@ tptp.bit_ri7919022796975470100ot_int _let_1)))))))
% 9.16/7.12 (assert (forall ((X tptp.assn) (Y tptp.assn) (A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.syntax7398250324933576852n_assn (@ (@ tptp.times_times_assn X) Y)) A) (= (@ (@ tptp.times_times_assn A) B) (@ (@ tptp.times_times_assn B) A)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X7 (-> tptp.nat tptp.real))) (forall ((J2 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M4) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N3) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X7 M4)) (@ X7 N3)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J2)))))))))))))
% 9.16/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.signed6714573509424544716de_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.12 (assert (forall ((X tptp.int)) (= (@ (@ tptp.signed6714573509424544716de_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 9.16/7.12 (assert (forall ((X tptp.int)) (= (@ (@ tptp.signed6714573509424544716de_int X) tptp.zero_zero_int) tptp.zero_zero_int)))
% 9.16/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.signed6714573509424544716de_int A) tptp.one_one_int) A)))
% 9.16/7.12 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (= (@ (@ tptp.signed6714573509424544716de_int A) B) A) (= B tptp.one_one_int)))))
% 9.16/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.signed6714573509424544716de_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.signed6714573509424544716de_int _let_2) _let_1) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))))
% 9.16/7.12 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (= (@ (@ tptp.signed6714573509424544716de_int A) B) (@ tptp.uminus_uminus_int A)) (= B (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I) J)) K) _let_1)))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat I) (@ (@ tptp.upt (@ tptp.suc I)) J))))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q3)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q3))))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N)))))
% 9.16/7.12 (assert (forall ((Ofs tptp.nat) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat I2) Ofs))) (@ (@ tptp.upt A) B)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat A) Ofs)) (@ (@ tptp.plus_plus_nat B) Ofs)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat I2) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 9.16/7.12 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I2 tptp.nat) (J2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I2) J2)))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat) (X tptp.nat) (Xs2 tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X) Xs2)) (and (@ (@ tptp.ord_less_nat I) J) (= I X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs2)))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat N3) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.upt M) N))))
% 9.16/7.12 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N3 tptp.nat) (M4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N3) (@ tptp.suc M4))))))
% 9.16/7.12 (assert (= tptp.set_ord_lessThan_nat (lambda ((N3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N3)))))
% 9.16/7.12 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.signed6714573509424544716de_int A) B))) (=> (not (= _let_1 tptp.zero_zero_int)) (= (@ tptp.sgn_sgn_int _let_1) (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)))))))
% 9.16/7.12 (assert (= tptp.set_ord_atMost_nat (lambda ((N3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N3))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.upt tptp.zero_zero_nat) N))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 K) (@ _let_2 L)) (= (@ (@ tptp.map_nat_o (@ tptp.bit_se1146084159140164899it_int K)) _let_1) (@ (@ tptp.map_nat_o (@ tptp.bit_se1146084159140164899it_int L)) _let_1)))))))
% 9.16/7.12 (assert (= tptp.signed6714573509424544716de_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K3)) (@ tptp.sgn_sgn_int L2))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K3)) (@ tptp.abs_abs_int L2))))))
% 9.16/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) tptp.top_top_assn) (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn Q) tptp.top_top_assn)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn) (F2 tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) F2) (@ (@ tptp.entails P) (@ (@ tptp.times_times_assn Q) F2)))))
% 9.16/7.12 (assert (= tptp.fI_QUERY (lambda ((P2 tptp.assn) (Q2 tptp.assn) (F5 tptp.assn)) (@ (@ tptp.entails P2) (@ (@ tptp.times_times_assn Q2) F5)))))
% 9.16/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (@ (@ (@ tptp.fI_QUERY P) Q) tptp.one_one_assn) (@ (@ tptp.entails P) Q))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (=> (not (= B tptp.zero_zero_int)) (@ (@ tptp.member_int (@ (@ tptp.signed6292675348222524329lo_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_1)) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int)))))))
% 9.16/7.12 (assert (forall ((X tptp.int)) (= (@ (@ tptp.signed6292675348222524329lo_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 9.16/7.12 (assert (forall ((X tptp.int)) (= (@ (@ tptp.signed6292675348222524329lo_int X) tptp.zero_zero_int) X)))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.signed6292675348222524329lo_int _let_2) _let_1) (@ (@ tptp.modulo_modulo_int _let_2) _let_1))))))
% 9.16/7.12 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.signed6292675348222524329lo_int A) B)) B)))))
% 9.16/7.12 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.signed6292675348222524329lo_int A) B)))))))
% 9.16/7.12 (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.signed6292675348222524329lo_int A) B)) tptp.zero_zero_int)))))
% 9.16/7.12 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.signed6292675348222524329lo_int A) B)))))))
% 9.16/7.12 (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_eq_int (@ (@ tptp.signed6292675348222524329lo_int A) B)) tptp.zero_zero_int)))))
% 9.16/7.12 (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_eq_int B) (@ (@ tptp.signed6292675348222524329lo_int A) B))))))
% 9.16/7.12 (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) (= (@ (@ tptp.signed6292675348222524329lo_int A) B) (@ (@ tptp.modulo_modulo_int A) B)))))))
% 9.16/7.12 (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_int (@ tptp.uminus_uminus_int B)) (@ (@ tptp.signed6292675348222524329lo_int A) B))))))
% 9.16/7.12 (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_int (@ (@ tptp.signed6292675348222524329lo_int A) B)) (@ tptp.uminus_uminus_int B))))))
% 9.16/7.12 (assert (= tptp.signed6292675348222524329lo_int (lambda ((A3 tptp.int) (B4 tptp.int)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A3)) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int A3)) (@ tptp.abs_abs_int B4))))))
% 9.16/7.12 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 9.16/7.12 (assert (forall ((T tptp.vEBT_VEBT) (D2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D2) (@ (@ tptp.vEBT_invar_vebt T) D2))))
% 9.16/7.12 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 9.16/7.12 (assert (forall ((T tptp.vEBT_VEBT) (D2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D2) (@ (@ tptp.vEBT_VEBT_valid T) D2))))
% 9.16/7.12 (assert (forall ((Uu Bool) (Uv Bool) (D2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D2) (= D2 tptp.one_one_nat))))
% 9.16/7.12 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (@ tptp.type_l796852477590012082l_num1 tptp.type_N8448461349408098053l_num1)))
% 9.16/7.12 (assert (= tptp.type_l4264026598287037464l_num0 (lambda ((Uu4 tptp.itself_Numeral_num0)) tptp.zero_zero_nat)))
% 9.16/7.12 (assert (= tptp.type_l4264026598287037465l_num1 (lambda ((Uu4 tptp.itself_Numeral_num1)) tptp.one_one_nat)))
% 9.16/7.12 (assert (= tptp.type_l31302759751748491nite_1 (lambda ((X2 tptp.itself_finite_1)) tptp.one_one_nat)))
% 9.16/7.12 (assert (= tptp.type_l31302759751748493nite_3 (lambda ((X2 tptp.itself_finite_3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 9.16/7.12 (assert (= tptp.type_l31302759751748492nite_2 (lambda ((X2 tptp.itself_finite_2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 9.16/7.12 (assert (forall ((M7 tptp.set_nat) (N4 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N4) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N4))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger X2) L))) (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger U) L))) (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 9.16/7.12 (assert (forall ((U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) U) (= (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U) (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ tptp.set_ord_lessThan_nat (@ tptp.nat2 U)))))))
% 9.16/7.12 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 9.16/7.12 (assert (forall ((S tptp.vEBT_VEBT) (M tptp.nat) (Listy tptp.list_VEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M))))) (=> (@ (@ tptp.vEBT_invar_vebt S) M) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Listy)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (= M (@ tptp.suc N)) (=> (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 N)))))) (=> (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height S)) _let_1) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT S) (@ tptp.set_VEBT_VEBT2 Listy))))) _let_1)))))))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (X13 tptp.list_VEBT_VEBT) (N tptp.nat) (X14 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT X13)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ tptp.vEBT_VEBT_height (@ (@ tptp.nth_VEBT_VEBT X13) I)))) (@ tptp.suc (@ tptp.suc (@ _let_1 (@ (@ tptp.ord_max_nat (@ tptp.vEBT_VEBT_height X14)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13))))))))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (X14 tptp.vEBT_VEBT) (M tptp.nat) (X13 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_VEBT_height X14))) (let ((_let_2 (@ tptp.times_times_nat N))) (@ (@ tptp.ord_less_eq_nat (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat M) (@ _let_2 (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat _let_1) (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13)))))))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D tptp.nat)) (@ (@ tptp.dvd_dvd_nat D) N)))) N))))
% 9.16/7.12 (assert (= tptp.divide_divide_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N3)) M4))))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X) Y) (=> (=> (exists ((A5 Bool) (B2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B2))) (not (= Y tptp.zero_zero_nat))) (not (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) 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 TreeList2))))))))))))))
% 9.16/7.12 (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) (B2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B2))) (=> (= 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) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg2) TreeList2) 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 TreeList2)))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1))))))))))))
% 9.16/7.12 (assert (forall ((N tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D tptp.int)) (@ (@ tptp.dvd_dvd_int D) N)))) (@ tptp.abs_abs_int N)))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N)))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 9.16/7.12 (assert (forall ((M tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) K))) (= (@ (@ tptp.ord_min_nat _let_1) M) _let_1))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) K))) (= (@ (@ tptp.ord_min_nat M) _let_1) _let_1))))
% 9.16/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc A))) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_min_nat _let_1) B) _let_1)))))
% 9.16/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc A))) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_min_nat B) _let_1) _let_1)))))
% 9.16/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_min_nat A) B)) (@ (@ tptp.minus_minus_nat A) B)) A)))
% 9.16/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.ord_min_nat A) B)) A)))
% 9.16/7.12 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_min_nat B) A)) (@ (@ tptp.minus_minus_nat A) B)) A)))
% 9.16/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.ord_min_nat B) A)) A)))
% 9.16/7.12 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) (@ tptp.pred_numeral K))))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int) (R2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N) K) L)) R2) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N)) L) R2)))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q3)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q3))))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N)) Q3) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q3)) (@ (@ tptp.times_times_nat N) Q3)))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I)) (@ (@ tptp.minus_minus_nat N) I)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N)) I))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N) K) L)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) L)))))
% 9.16/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.modulo_modulo_nat K))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.ord_min_nat M) N))))))))
% 9.16/7.12 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q3) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 9.16/7.12 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q3) tptp.zero_z5237406670263579293d_enat)))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M4) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 9.16/7.12 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 9.16/7.12 (assert (= (@ tptp.bit_bi6516823479961619367ts_int (lambda ((Uu3 tptp.nat)) false)) tptp.zero_zero_int))
% 9.16/7.12 (assert (= (@ tptp.bit_bi6516823479961619367ts_int (lambda ((Uu3 tptp.nat)) true)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 9.16/7.12 (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 ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N3)))) X2)))))
% 9.16/7.12 (assert (forall ((F (-> tptp.nat Bool))) (=> (@ tptp.bit_wf_set_bits_int F) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_bi6516823479961619367ts_int F))) (@ F tptp.zero_zero_nat)))))
% 9.16/7.12 (assert (forall ((F (-> tptp.nat Bool))) (= (@ tptp.bit_wf_set_bits_int (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) (@ tptp.bit_wf_set_bits_int F))))
% 9.16/7.12 (assert (forall ((F (-> tptp.nat Bool))) (=> (@ tptp.bit_wf_set_bits_int F) (= (@ tptp.bit_bi6516823479961619367ts_int F) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ F tptp.zero_zero_nat))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_bi6516823479961619367ts_int (@ (@ tptp.comp_nat_o_nat F) tptp.suc))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.nat Bool))) (=> (@ tptp.bit_wf_set_bits_int F) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_bi6516823479961619367ts_int F)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_bi6516823479961619367ts_int (@ (@ tptp.comp_nat_o_nat F) tptp.suc))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_Sh3965577149348748681tl_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 9.16/7.12 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 9.16/7.12 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_Sh2154871086232339855tr_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (X tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= 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)))))))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 9.16/7.12 (assert (forall ((N4 tptp.set_nat) (K tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.member_nat N2) N4) (@ (@ tptp.ord_less_eq_nat K) N2))) (@ (@ tptp.inj_on_nat_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat N3) K))) N4))))
% 9.16/7.12 (assert (@ (@ tptp.inj_on_set_nat_nat tptp.nat_set_encode) (@ tptp.collect_set_nat tptp.finite_finite_nat)))
% 9.16/7.12 (assert (forall ((N4 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N4)))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F6 Z3)))))))))
% 9.16/7.12 (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 ((H6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.ord_less_real H6) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.plus_plus_real X) H6))))))))))))
% 9.16/7.12 (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 ((H6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.ord_less_real H6) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X) H6))) (@ F X)))))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D2 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) D2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D2) (= (@ F X) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 9.16/7.12 (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 ((H6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.ord_less_real H6) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X) H6))) (@ F X)))))))))))
% 9.16/7.12 (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 ((H6 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.ord_less_real H6) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.minus_minus_real X) H6))))))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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 ((H6 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H6))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H6) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 9.16/7.12 (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 ((H6 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H6))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H6) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 9.16/7.12 (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 ((H6 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H6))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H6) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 9.16/7.12 (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 ((H6 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H6))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H6) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H6) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D2 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) D2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D2) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D2 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) D2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D2) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X)))) (= L tptp.zero_zero_real))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (X tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real X2) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S))))
% 9.16/7.12 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ G X2)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 9.16/7.12 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z6 tptp.real)) (@ (@ tptp.powr_real Z6) R2))) (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 9.16/7.12 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M2 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 9.16/7.12 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_real T6) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real H2) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 9.16/7.12 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real H2) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 9.16/7.12 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real H2) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T6) (@ (@ tptp.ord_less_real T6) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real H2) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 9.16/7.12 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M2 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))) (exists ((T6 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T6))) (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 ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))))
% 9.16/7.12 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real X) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real A) T6) (@ (@ tptp.ord_less_real T6) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) C)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real C) T6) (@ (@ tptp.ord_less_real T6) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) C)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) 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 ((T6 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T6))) (let ((_let_2 (@ tptp.ord_less_real X))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T6) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T6) (@ _let_1 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M4) C)) (@ tptp.semiri2265585572941072030t_real M4))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M4)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N))))))))))))))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)))) tptp.top_top_set_real))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B3 tptp.real)) (=> (forall ((M2 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M2)) (@ (@ Diff (@ tptp.suc M2)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M3 tptp.nat) (T7 tptp.real)) (let ((_let_1 (@ tptp.suc M3))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M3))) (@ (@ tptp.minus_minus_real (@ (@ Diff M3) 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 M3) 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) T7)) (@ (@ 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 M3)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T7) P5)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T7) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real))))))))))
% 9.16/7.12 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X10 tptp.real)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X10) _let_1)))))))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F6 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F6 X0))) (=> (forall ((N2 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ (@ F X2) N2))) (@ (@ F6 X0) N2)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X3)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N2 tptp.nat) (X3 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X3) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X3) N2)) (@ (@ F Y3) N2)))) (@ (@ tptp.times_times_real (@ L5 N2)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X2 tptp.real)) (@ tptp.suminf_real (@ F X2)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 9.16/7.12 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (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))))))))))
% 9.16/7.12 (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))))))))))
% 9.16/7.12 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.sqrt)))
% 9.16/7.12 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (@ tptp.root N))))
% 9.16/7.12 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 9.16/7.12 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N3 tptp.nat) (M4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N3)) M4)))))
% 9.16/7.12 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (= (@ G (@ F Z3)) Z3)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G)))))))
% 9.16/7.12 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.ln_ln_real))))
% 9.16/7.12 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or8404916559141939852nteger (@ (@ tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer)) U) (@ (@ tptp.set_or4266950643985792945nteger L) U))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))
% 9.16/7.12 (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))))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((D2 tptp.real) (X tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X))) D2) (= (@ G (@ F Z3)) Z3))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z3) X))) D2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G))))))
% 9.16/7.12 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) G)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F6 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F6 C3))))))))))))
% 9.16/7.12 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 9.16/7.12 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))
% 9.16/7.12 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N2))) (@ G N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ G N2))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((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))))))))))
% 9.16/7.12 (assert (forall ((X9 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N10 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N10) N2) (@ (@ tptp.ord_less_real R3) (@ X9 N2)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_real (@ X9 N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 9.16/7.12 (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))
% 9.16/7.12 (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))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))
% 9.16/7.12 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) L)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((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))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))
% 9.16/7.12 (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)))
% 9.16/7.12 (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)))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ A N3)))))))))
% 9.16/7.12 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J2 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J2)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K2 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J2)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J2))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 9.16/7.12 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J2 tptp.nat)) (@ tptp.cos_real (@ Theta J2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K2 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J2)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J2))) (@ (@ 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)))))
% 9.16/7.12 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat)))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))))))))
% 9.16/7.12 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat))))))
% 9.16/7.12 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) _let_1) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N9)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 9.16/7.12 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat)))))
% 9.16/7.12 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat))))))
% 9.16/7.12 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 9.16/7.12 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C4 tptp.real)) (= F3 (lambda ((X2 tptp.real)) (@ (@ tptp.times_times_real X2) C4)))))))
% 9.16/7.12 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 9.16/7.12 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y6))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y6)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 9.16/7.12 (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))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (@ (@ (@ tptp.filterlim_real_real tptp.exp_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_bot_real))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F2 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F2) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_bot_real) F2))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F2 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.power_power_real (@ F X2)) N))) tptp.at_top_real) F2))))))
% 9.16/7.12 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 9.16/7.12 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))
% 9.16/7.12 (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)))
% 9.16/7.12 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) Y6))) Y6))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_real)))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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))))))))))
% 9.16/7.12 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I2 tptp.nat)) (@ P (@ tptp.suc I2)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I2) K)))) tptp.at_top_nat))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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)))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (F2 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) (@ F6 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 (@ F6 X2)) (@ G2 X2)))) F2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F2) _let_1))))))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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)))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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)))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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)))))))))
% 9.16/7.12 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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))))))))))
% 9.16/7.12 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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)))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (F2 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) (@ F6 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 (@ F6 X2)) (@ G2 X2)))) F2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F2) _let_1))))))))))))
% 9.16/7.12 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (F2 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) (@ F6 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 (@ F6 X2)) (@ G2 X2)))) F2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X2)) (@ G0 X2)))) F2) _let_1))))))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F6 (-> tptp.real tptp.real)) (F2 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) (@ F6 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 (@ F6 X2)) (@ G2 X2)))) F2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X2 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X2)) (@ G X2)))) F2) _let_1))))))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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)))))))))
% 9.16/7.12 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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)))))))))
% 9.16/7.12 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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))))))))))
% 9.16/7.12 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 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 (@ F6 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))))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 9.16/7.12 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N3 tptp.nat) (M4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N3)) (@ tptp.suc M4))))))
% 9.16/7.12 (assert (forall ((P4 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B4 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)) B4)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P4)))))
% 9.16/7.12 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 9.16/7.12 (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)))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 9.16/7.12 (assert (forall ((R2 tptp.rat) (P4 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P4) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))))
% 9.16/7.12 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or189985376899183464nteger (@ (@ tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer)) U) (@ (@ tptp.set_or2715278749043346189nteger L) U))))
% 9.16/7.12 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 9.16/7.12 (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) (C3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C3) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 9.16/7.12 (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 ((T6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T6) (not (= R2 (@ (@ tptp.plus_plus_rat S2) T6)))))))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (= tptp.sgn_sgn_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (= A3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((Q3 tptp.int) (P4 tptp.int)) (=> (@ (@ tptp.ord_less_int Q3) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) Q3)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P4)) (@ tptp.uminus_uminus_int Q3)))))))
% 9.16/7.12 (assert (forall ((P4 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 9.16/7.12 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y6 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y6) (= X2 Y6)))))
% 9.16/7.12 (assert (forall ((R2 tptp.product_prod_int_int) (P4 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P4) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))))
% 9.16/7.12 (assert (forall ((Q3 tptp.int) (S tptp.int) (P4 tptp.int) (R2 tptp.int)) (=> (not (= Q3 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P4) Q3)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S))) (= (@ (@ tptp.times_times_int P4) S) (@ (@ tptp.times_times_int R2) Q3)))))))
% 9.16/7.12 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 9.16/7.12 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 9.16/7.12 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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) (Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 9.16/7.12 (assert (= tptp.bit_bi6516823479961619367ts_int (lambda ((F3 (-> tptp.nat Bool))) (@ (@ (@ tptp.if_int (exists ((N3 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) M4) (= (@ F3 M4) (@ F3 N3)))))) (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.ord_Least_nat (lambda ((N3 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) M4) (= (@ F3 M4) (@ F3 N3))))))) (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.map_nat_o F3) (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((N3 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) M4) (= (@ F3 M4) (@ F3 N3)))))))))))) tptp.zero_zero_int))))
% 9.16/7.12 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 9.16/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M4 tptp.nat)) (@ P (@ tptp.suc M4))))))))))
% 9.16/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (Q (-> tptp.nat Bool)) (M tptp.nat)) (=> (@ P N) (=> (@ Q M) (=> (not (@ P tptp.zero_zero_nat)) (=> (forall ((K2 tptp.nat)) (= (@ P (@ tptp.suc K2)) (@ Q K2))) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 9.16/7.12 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ F6 Z3) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 9.16/7.12 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F6 (-> 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) (@ F6 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real))))) (not (forall ((Xi2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi2) (=> (@ (@ tptp.ord_less_real Xi2) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F6 Xi2) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (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 ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa3) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa3 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (= Y (not (and (= Deg2 Xa3) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa3) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa3 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (not (and (= Deg2 Xa3) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))
% 9.16/7.12 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) X2) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima2)))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa3)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa3 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (and (= Deg2 Xa3) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa3) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Y (= Xa3 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= Y (and (= Deg2 Xa3) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X2) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa3)))))))))))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (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) Xa3)) (not (= Xa3 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa3)) (not (and (= Deg2 Xa3) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima)))))))))))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa3)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa3)) (=> (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) Xa3)) (= Xa3 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa3)) (and (= Deg2 Xa3) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X7))) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X7)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X7 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X7)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X2) (and (@ (@ tptp.ord_less_nat Mi2) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))) Mima))))))))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q6 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 Q6)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))))
% 9.16/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 9.16/7.12 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q6 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q6)))) (@ (@ tptp.bit_take_bit_num N) M)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))))
% 9.16/7.12 (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 ((Q6 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q6)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 9.16/7.12 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 9.16/7.12 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 9.16/7.12 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 9.16/7.12 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) (@ tptp.some_num Q3)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int Q3)))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N11 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N11)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N)))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M)))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N3 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N3) M))))) N))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q6 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q6)))) (@ (@ tptp.bit_take_bit_num N3) M)))) N))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N3 tptp.nat)) (@ tptp.some_num tptp.one))) N))))
% 9.16/7.12 (assert (= tptp.bit_take_bit_num (lambda ((N3 tptp.nat) (M4 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N3) (@ tptp.numeral_numeral_nat M4)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 9.16/7.12 (assert (forall ((Q3 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q3)) Q3)))
% 9.16/7.12 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 9.16/7.12 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 9.16/7.12 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M5)))) M)))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M5) N)))) M)))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M5)))) M))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M5 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M5) N)))) M))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 9.16/7.12 (assert (= tptp.bit_bi6516823479961619367ts_int (lambda ((F3 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.map_nat_o F3))) (let ((_let_3 (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (@ (@ (@ tptp.if_int (exists ((N3 tptp.nat)) (forall ((N11 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N11) (not (@ F3 N11)))))) (@ _let_3 (@ _let_2 (@ _let_1 (@ tptp.ord_Least_nat (lambda ((N3 tptp.nat)) (forall ((N11 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N11) (not (@ F3 N11)))))))))) (@ (@ (@ tptp.if_int (exists ((N3 tptp.nat)) (forall ((N11 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N11) (@ F3 N11))))) (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.ord_Least_nat (lambda ((N3 tptp.nat)) (forall ((N11 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N11) (@ F3 N11)))))) (@ _let_3 (@ (@ tptp.append_o (@ _let_2 (@ _let_1 (@ tptp.ord_Least_nat (lambda ((N3 tptp.nat)) (forall ((N11 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N3) N11) (@ F3 N11)))))))) (@ (@ tptp.cons_o true) tptp.nil_o))))) tptp.zero_zero_int))))))))
% 9.16/7.12 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.bot_bot_assn) P) tptp.bot_bot_assn)))
% 9.16/7.12 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn P) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 9.16/7.12 (assert (= (@ tptp.pure_assn false) tptp.bot_bot_assn))
% 9.16/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.bot_bot_assn) (not P))))
% 9.16/7.12 (assert (not (= tptp.bot_bot_assn tptp.one_one_assn)))
% 9.16/7.12 (assert (not (= tptp.top_top_assn tptp.bot_bot_assn)))
% 9.16/7.12 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.entails P) tptp.bot_bot_assn) (forall ((H tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P) H))))))
% 9.16/7.12 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 9.16/7.12 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 9.16/7.12 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails tptp.bot_bot_assn) P)))
% 9.16/7.12 (assert (forall ((H2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn tptp.bot_bot_assn) H2))))
% 9.16/7.12 (assert (forall ((Vd Bool) (Ve Bool) (V tptp.option4927543243414619207at_nat) (Va2 tptp.nat) (Vb tptp.array_VEBT_VEBTi) (Vc2 tptp.vEBT_VEBTi)) (= (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_Leaf Vd) Ve)) (@ (@ (@ (@ tptp.vEBT_Nodei V) Va2) Vb) Vc2)) tptp.bot_bot_assn)))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.vEBT_VEBTi) (Y tptp.assn)) (let ((_let_1 (not (= Y tptp.bot_bot_assn)))) (=> (= (@ (@ tptp.vEBT_vebt_assn_raw X) Xa3) Y) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (forall ((Ai Bool) (Bi Bool)) (=> (= Xa3 (@ (@ tptp.vEBT_Leafi Ai) Bi)) (not (= Y (@ tptp.pure_assn (and (= Ai A5) (= Bi B2))))))))) (=> (forall ((Mmo2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (Tree_list2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mmo2) Deg2) Tree_list2) Summary2)) (forall ((Mmoi2 tptp.option4927543243414619207at_nat) (Degi2 tptp.nat) (Tree_array2 tptp.array_VEBT_VEBTi) (Summaryi2 tptp.vEBT_VEBTi)) (=> (= Xa3 (@ (@ (@ (@ tptp.vEBT_Nodei Mmoi2) Degi2) Tree_array2) Summaryi2)) (not (= Y (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ tptp.pure_assn (and (= Mmoi2 Mmo2) (= Degi2 Deg2)))) (@ (@ tptp.vEBT_vebt_assn_raw Summary2) Summaryi2))) (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((Tree_is2 tptp.list_VEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Tree_array2) Tree_is2)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) Tree_list2) Tree_is2))))))))))) (=> (=> (exists ((V3 tptp.option4927543243414619207at_nat) (Va tptp.nat) (Vb3 tptp.list_VEBT_VEBT) (Vc3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node V3) Va) Vb3) Vc3))) (=> (exists ((Vd3 Bool) (Ve3 Bool)) (= Xa3 (@ (@ tptp.vEBT_Leafi Vd3) Ve3))) _let_1)) (not (=> (exists ((Vd3 Bool) (Ve3 Bool)) (= X (@ (@ tptp.vEBT_Leaf Vd3) Ve3))) (=> (exists ((V3 tptp.option4927543243414619207at_nat) (Va tptp.nat) (Vb3 tptp.array_VEBT_VEBTi) (Vc3 tptp.vEBT_VEBTi)) (= Xa3 (@ (@ (@ (@ tptp.vEBT_Nodei V3) Va) Vb3) Vc3))) _let_1))))))))))
% 9.16/7.12 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool) (C0 Bool) (C1 Bool) (C22 Bool) (C32 Bool) (C42 Bool) (C52 Bool) (C6 Bool) (C7 Bool)) (= (@ (@ tptp.ord_less_eq_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 C0) C1) C22) C32) C42) C52) C6) C7)) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.foldr_o_nat (lambda ((B4 Bool) (K3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B4)) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.cons_o B0) (@ (@ tptp.cons_o B1) (@ (@ tptp.cons_o B22) (@ (@ tptp.cons_o B32) (@ (@ tptp.cons_o B42) (@ (@ tptp.cons_o B52) (@ (@ tptp.cons_o B62) (@ (@ tptp.cons_o B72) tptp.nil_o))))))))) tptp.zero_zero_nat)) (@ (@ (@ tptp.foldr_o_nat (lambda ((B4 Bool) (K3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B4)) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.cons_o C0) (@ (@ tptp.cons_o C1) (@ (@ tptp.cons_o C22) (@ (@ tptp.cons_o C32) (@ (@ tptp.cons_o C42) (@ (@ tptp.cons_o C52) (@ (@ tptp.cons_o C6) (@ (@ tptp.cons_o C7) tptp.nil_o))))))))) tptp.zero_zero_nat)))))
% 9.16/7.12 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y222 Bool)) (= (= (@ (@ tptp.vEBT_Leafi X21) X222) (@ (@ tptp.vEBT_Leafi Y21) Y222)) (and (= X21 Y21) (= X222 Y222)))))
% 9.16/7.12 (assert (forall ((J tptp.nat)) (= (= (@ (@ tptp.upt tptp.zero_zero_nat) J) tptp.nil_nat) (= J tptp.zero_zero_nat))))
% 9.16/7.12 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I)))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 9.16/7.12 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool) (C0 Bool) (C1 Bool) (C22 Bool) (C32 Bool) (C42 Bool) (C52 Bool) (C6 Bool) (C7 Bool)) (= (@ (@ tptp.ord_less_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 C0) C1) C22) C32) C42) C52) C6) C7)) (@ (@ tptp.ord_less_nat (@ (@ (@ tptp.foldr_o_nat (lambda ((B4 Bool) (K3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B4)) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.cons_o B0) (@ (@ tptp.cons_o B1) (@ (@ tptp.cons_o B22) (@ (@ tptp.cons_o B32) (@ (@ tptp.cons_o B42) (@ (@ tptp.cons_o B52) (@ (@ tptp.cons_o B62) (@ (@ tptp.cons_o B72) tptp.nil_o))))))))) tptp.zero_zero_nat)) (@ (@ (@ tptp.foldr_o_nat (lambda ((B4 Bool) (K3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B4)) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.cons_o C0) (@ (@ tptp.cons_o C1) (@ (@ tptp.cons_o C22) (@ (@ tptp.cons_o C32) (@ (@ tptp.cons_o C42) (@ (@ tptp.cons_o C52) (@ (@ tptp.cons_o C6) (@ (@ tptp.cons_o C7) tptp.nil_o))))))))) tptp.zero_zero_nat)))))
% 9.16/7.12 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 9.16/7.12 (assert (forall ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (not (forall ((X3 tptp.nat) (Xs3 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X3) Xs3))))))))
% 9.16/7.12 (assert (forall ((V tptp.option4927543243414619207at_nat) (Va2 tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (Vd Bool) (Ve Bool)) (= (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ (@ (@ tptp.vEBT_Node V) Va2) Vb) Vc2)) (@ (@ tptp.vEBT_Leafi Vd) Ve)) tptp.bot_bot_assn)))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ (@ tptp.append_nat (@ _let_1 I)) (@ (@ tptp.upt I) J)) (@ _let_1 J))))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 9.16/7.12 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.array_VEBT_VEBTi) (X14 tptp.vEBT_VEBTi) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Nodei X11) X12) X13) X14) (@ (@ tptp.vEBT_Leafi X21) X222)))))
% 9.16/7.12 (assert (forall ((Y tptp.vEBT_VEBTi)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.array_VEBT_VEBTi) (X142 tptp.vEBT_VEBTi)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Nodei X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y (@ (@ tptp.vEBT_Leafi X212) X223))))))))
% 9.16/7.12 (assert (= (@ tptp.vEBT_V739175172307565963ildupi tptp.zero_zero_nat) (@ tptp.heap_T3630416162098727440_VEBTi (@ (@ tptp.vEBT_Leafi false) false))))
% 9.16/7.12 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBTi (@ (@ tptp.vEBT_Leafi X21) X222)) tptp.zero_zero_nat)))
% 9.16/7.12 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBTi (@ (@ tptp.vEBT_Leafi X21) X222)) tptp.zero_zero_nat)))
% 9.16/7.12 (assert (= (@ tptp.vEBT_V739175172307565963ildupi (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.heap_T3630416162098727440_VEBTi (@ (@ tptp.vEBT_Leafi false) false))))
% 9.16/7.12 (assert (forall ((X tptp.produc3625547720036274456_VEBTi)) (=> (forall ((A5 Bool) (B2 Bool) (Ai Bool) (Bi Bool)) (not (= X (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ tptp.vEBT_Leaf A5) B2)) (@ (@ tptp.vEBT_Leafi Ai) Bi))))) (=> (forall ((Mmo2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (Tree_list2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Mmoi2 tptp.option4927543243414619207at_nat) (Degi2 tptp.nat) (Tree_array2 tptp.array_VEBT_VEBTi) (Summaryi2 tptp.vEBT_VEBTi)) (not (= X (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ (@ (@ tptp.vEBT_Node Mmo2) Deg2) Tree_list2) Summary2)) (@ (@ (@ (@ tptp.vEBT_Nodei Mmoi2) Degi2) Tree_array2) Summaryi2))))) (=> (forall ((V3 tptp.option4927543243414619207at_nat) (Va tptp.nat) (Vb3 tptp.list_VEBT_VEBT) (Vc3 tptp.vEBT_VEBT) (Vd3 Bool) (Ve3 Bool)) (not (= X (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ (@ (@ tptp.vEBT_Node V3) Va) Vb3) Vc3)) (@ (@ tptp.vEBT_Leafi Vd3) Ve3))))) (not (forall ((Vd3 Bool) (Ve3 Bool) (V3 tptp.option4927543243414619207at_nat) (Va tptp.nat) (Vb3 tptp.array_VEBT_VEBTi) (Vc3 tptp.vEBT_VEBTi)) (not (= X (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ tptp.vEBT_Leaf Vd3) Ve3)) (@ (@ (@ (@ tptp.vEBT_Nodei V3) Va) Vb3) Vc3)))))))))))
% 9.16/7.12 (assert (forall ((A Bool) (B Bool) (Ai2 Bool) (Bi2 Bool)) (= (@ (@ tptp.vEBT_vebt_assn_raw (@ (@ tptp.vEBT_Leaf A) B)) (@ (@ tptp.vEBT_Leafi Ai2) Bi2)) (@ tptp.pure_assn (and (= Ai2 A) (= Bi2 B))))))
% 9.16/7.12 (assert (= tptp.upt (lambda ((I2 tptp.nat) (J2 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I2) J2)) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J2))) tptp.nil_nat))))
% 9.16/7.12 (assert (forall ((L tptp.nat) (H2 tptp.nat) (Is1 tptp.list_nat) (I tptp.nat) (Is2 tptp.list_nat)) (let ((_let_1 (@ tptp.upt L))) (= (= (@ _let_1 H2) (@ (@ tptp.append_nat Is1) (@ (@ tptp.cons_nat I) Is2))) (and (= Is1 (@ _let_1 I)) (= Is2 (@ (@ tptp.upt (@ tptp.suc I)) H2)) (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_nat I) H2))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (= tptp.ord_less_char (lambda ((C12 tptp.char) (C23 tptp.char)) (@ (@ tptp.ord_less_nat (@ tptp.comm_s629917340098488124ar_nat C12)) (@ tptp.comm_s629917340098488124ar_nat C23)))))
% 9.16/7.12 (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))))))))))))
% 9.16/7.12 (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))))))))))))
% 9.16/7.12 (assert (forall ((X15 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X15) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 9.16/7.12 (assert (forall ((X15 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X15) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 9.16/7.12 (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))))))))))))
% 9.16/7.12 (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)))))))))))))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Xa3 tptp.vEBT_VEBTi) (Y tptp.assn)) (=> (= (@ (@ tptp.vEBT_vebt_assn_raw X) Xa3) Y) (=> (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi X) Xa3)) (=> (forall ((A5 Bool) (B2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B2)) (forall ((Ai Bool) (Bi Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leafi Ai) Bi))) (=> (= Xa3 _let_1) (=> (= Y (@ tptp.pure_assn (and (= Ai A5) (= Bi B2)))) (not (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ tptp.vEBT_Leaf A5) B2)) _let_1))))))))) (=> (forall ((Mmo2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (Tree_list2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mmo2) Deg2) Tree_list2) Summary2)) (forall ((Mmoi2 tptp.option4927543243414619207at_nat) (Degi2 tptp.nat) (Tree_array2 tptp.array_VEBT_VEBTi) (Summaryi2 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei Mmoi2) Degi2) Tree_array2) Summaryi2))) (=> (= Xa3 _let_1) (=> (= Y (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ tptp.pure_assn (and (= Mmoi2 Mmo2) (= Degi2 Deg2)))) (@ (@ tptp.vEBT_vebt_assn_raw Summary2) Summaryi2))) (@ tptp.ex_ass463751140784270563_VEBTi (lambda ((Tree_is2 tptp.list_VEBT_VEBTi)) (@ (@ tptp.times_times_assn (@ (@ tptp.snga_assn_VEBT_VEBTi Tree_array2) Tree_is2)) (@ (@ (@ tptp.vEBT_L6296928887356842470_VEBTi tptp.vEBT_vebt_assn_raw) Tree_list2) Tree_is2)))))) (not (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ (@ (@ tptp.vEBT_Node Mmo2) Deg2) Tree_list2) Summary2)) _let_1))))))))) (=> (forall ((V3 tptp.option4927543243414619207at_nat) (Va tptp.nat) (Vb3 tptp.list_VEBT_VEBT) (Vc3 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node V3) Va) Vb3) Vc3)) (forall ((Vd3 Bool) (Ve3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leafi Vd3) Ve3))) (=> (= Xa3 _let_1) (=> (= Y tptp.bot_bot_assn) (not (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ (@ (@ tptp.vEBT_Node V3) Va) Vb3) Vc3)) _let_1))))))))) (not (forall ((Vd3 Bool) (Ve3 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Vd3) Ve3)) (forall ((V3 tptp.option4927543243414619207at_nat) (Va tptp.nat) (Vb3 tptp.array_VEBT_VEBTi) (Vc3 tptp.vEBT_VEBTi)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Nodei V3) Va) Vb3) Vc3))) (=> (= Xa3 _let_1) (=> (= Y tptp.bot_bot_assn) (not (@ (@ tptp.accp_P7675410724331315407_VEBTi tptp.vEBT_v8524038756793281170aw_rel) (@ (@ tptp.produc6084888613844515218_VEBTi (@ (@ tptp.vEBT_Leaf Vd3) Ve3)) _let_1)))))))))))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((X tptp.int) (Xa3 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa3)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa3))) (=> (= (@ (@ tptp.upto X) Xa3) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa3)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 9.16/7.12 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 9.16/7.12 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 9.16/7.12 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 9.16/7.12 (assert (forall ((I tptp.int)) (= (@ (@ tptp.upto I) I) (@ (@ tptp.cons_int I) tptp.nil_int))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 9.16/7.12 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 9.16/7.12 (assert (= tptp.upto_aux (lambda ((I2 tptp.int) (J2 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I2) J2)) __flatten_var_0))))
% 9.16/7.12 (assert (= tptp.upto (lambda ((I2 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.upto_aux I2) J2) tptp.nil_int))))
% 9.16/7.12 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I2 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I2) J2)))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I2 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I2) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))
% 9.16/7.12 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I2 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2)))))
% 9.16/7.12 (assert (= tptp.upto (lambda ((I2 tptp.int) (J2 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I2) J2)) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2))) tptp.nil_int))))
% 9.16/7.12 (assert (forall ((X tptp.int) (Xa3 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa3))) (=> (= (@ (@ tptp.upto X) Xa3) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa3)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I2 tptp.int) (J2 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J2) tptp.one_one_int))))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.upt M) N))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 9.16/7.12 (assert (forall ((U tptp.nat) (U3 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.filter_nat2 P))) (=> (@ (@ tptp.ord_less_eq_nat U) U3) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat U) I3) (@ (@ tptp.ord_less_nat I3) U3)) (not (@ P I3)))) (= (@ _let_2 (@ _let_1 U)) (@ _let_2 (@ _let_1 U3)))))))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X2 tptp.nat)) X2)) _let_1) _let_1))))
% 9.16/7.12 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X2 tptp.int)) X2)) _let_1) _let_1))))
% 9.16/7.12 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 9.16/7.12 (assert (forall ((Z tptp.complex) (N tptp.nat)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.semiri5074537144036343181t_real N)))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((Y tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (= (@ tptp.re Y) tptp.zero_zero_real) (= (@ tptp.cos_real (@ tptp.arg Y)) tptp.zero_zero_real)))))
% 9.16/7.12 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.re X)))))
% 9.16/7.12 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 9.16/7.12 (assert (= (@ tptp.re tptp.imaginary_unit) tptp.zero_zero_real))
% 9.16/7.12 (assert (= (@ tptp.re tptp.zero_zero_complex) tptp.zero_zero_real))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 9.16/7.12 (assert (= tptp.csqrt (lambda ((Z6 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z6))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z6))) (let ((_let_4 (@ tptp.im Z6))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ tptp.im (@ tptp.semiri5044797733671781792omplex N)) tptp.zero_zero_real)))
% 9.16/7.12 (assert (forall ((Z tptp.int)) (= (@ tptp.im (@ tptp.ring_17405671764205052669omplex Z)) tptp.zero_zero_real)))
% 9.16/7.12 (assert (forall ((Z tptp.real)) (= (@ tptp.im (@ tptp.real_V4546457046886955230omplex Z)) tptp.zero_zero_real)))
% 9.16/7.12 (assert (forall ((X tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.power_power_complex X) N)) tptp.zero_zero_real))))
% 9.16/7.12 (assert (forall ((V tptp.num)) (= (@ tptp.im (@ tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ tptp.im (@ tptp.semiri8010041392384452111omplex N)) tptp.zero_zero_real)))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 9.16/7.12 (assert (forall ((X tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_real (@ tptp.re X)) N)))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((Z tptp.complex) (N tptp.nat)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.semiri5074537144036343181t_real N)))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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))))))))))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.member_complex Z) tptp.ring_1_Ints_complex) (and (= (@ tptp.im Z) tptp.zero_zero_real) (exists ((I2 tptp.int)) (= (@ tptp.re Z) (@ tptp.ring_1_of_int_real I2)))))))
% 9.16/7.12 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 9.16/7.12 (assert (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real))
% 9.16/7.12 (assert (= (@ tptp.im tptp.zero_zero_complex) tptp.zero_zero_real))
% 9.16/7.12 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.im X)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.im Z) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex Z) (@ tptp.abs_abs_real (@ tptp.re Z))))))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.re Z) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex Z) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.abs_abs_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)) (= (@ tptp.im Z) tptp.zero_zero_real))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (= tptp.times_times_complex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.re Y6))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X2)))) (let ((_let_3 (@ tptp.im Y6))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X2)))) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_4 _let_1)) (@ _let_2 _let_3))) (@ (@ tptp.plus_plus_real (@ _let_4 _let_3)) (@ _let_2 _let_1))))))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z6 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z6)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z6)) _let_1)))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (assert (= tptp.divide1717551699836669952omplex (lambda ((X2 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y6))) (let ((_let_3 (@ tptp.re Y6))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X2)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X2)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.member_complex Z) tptp.real_V2521375963428798218omplex) (= (@ tptp.im Z) tptp.zero_zero_real))))
% 9.16/7.12 (assert (forall ((X tptp.real)) (@ (@ tptp.member_complex (@ (@ tptp.complex2 X) tptp.zero_zero_real)) tptp.real_V2521375963428798218omplex)))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.ord_less_nat I2) N)))) N)))
% 9.16/7.12 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 9.16/7.12 (assert (= (@ tptp.cnj tptp.zero_zero_complex) tptp.zero_zero_complex))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 9.16/7.12 (assert (= (@ tptp.cnj tptp.one_one_complex) tptp.one_one_complex))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I2) N)))) (@ tptp.suc N))))
% 9.16/7.12 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 9.16/7.12 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L)) tptp.one_one_int)))))
% 9.16/7.12 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L) tptp.one_one_int))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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 ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 9.16/7.12 (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 ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 9.16/7.12 (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 ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 9.16/7.12 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N4)) N))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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)))))))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) C)))) N)))))
% 9.16/7.12 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N) tptp.one_one_complex)))) N))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (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))))))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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)))))))))
% 9.16/7.12 (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)))))
% 9.16/7.12 (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))))))
% 9.16/7.12 (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))))
% 9.16/7.12 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A3) (@ tptp.cnj B4))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 9.16/7.12 (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)))))))
% 9.16/7.12 (assert (= (@ tptp.finite6454714172617411596l_num0 tptp.top_to3689904424835650196l_num0) tptp.zero_zero_nat))
% 9.16/7.12 (assert (= (@ tptp.finite6454714172617411597l_num1 tptp.top_to3689904429138878997l_num1) tptp.one_one_nat))
% 9.16/7.12 (assert (= (@ tptp.finite_card_nat tptp.top_top_set_nat) tptp.zero_zero_nat))
% 9.16/7.12 (assert (= (@ tptp.finite_card_literal tptp.top_top_set_literal) tptp.zero_zero_nat))
% 9.16/7.12 (assert (forall ((I tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I) J))))
% 9.16/7.12 (assert (forall ((I tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I) J))))
% 9.16/7.12 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.uint32) (Y tptp.uint32)) (= (@ (@ (@ tptp.if_uint32 false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.uint32) (Y tptp.uint32)) (= (@ (@ (@ tptp.if_uint32 true) X) Y) X)))
% 9.16/7.12 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X7 tptp.real)) (@ P X7)))))
% 9.16/7.12 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y) X)))
% 9.16/7.12 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 9.16/7.12 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.prcvc5 interrupted by timeout.
% 300.13/298.54 /export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 13188 CPU time limit exceeded (core dumped) ( read result; case "$result" in
% 300.13/298.54 unsat)
% 300.13/298.54 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 300.13/298.54 ;;
% 300.13/298.54 sat)
% 300.13/298.54 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 300.13/298.54 ;;
% 300.13/298.54 esac; exit 1 )
% 300.13/298.55 Cputime limit exceeded (core dumped) (core dumped)
% 300.13/298.55 % cvc5---1.0.5 exiting
% 300.13/298.55 Cputime limit exceeded (core dumped)
% 300.13/298.55 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------